agreg/Contraintes_temporelles.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#Texte-d'oral-de-modélisation---Agrégation-Option-Informatique\" data-toc-modified-id=\"Texte-d'oral-de-modélisation---Agrégation-Option-Informatique-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Texte d'oral de modélisation - Agrégation Option Informatique</a></div><div class=\"lev2 toc-item\"><a href=\"#Préparation-à-l'agrégation---ENS-de-Rennes,-2016-17\" data-toc-modified-id=\"Préparation-à-l'agrégation---ENS-de-Rennes,-2016-17-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Préparation à l'agrégation - ENS de Rennes, 2016-17</a></div><div class=\"lev2 toc-item\"><a href=\"#À-propos-de-ce-document\" data-toc-modified-id=\"À-propos-de-ce-document-12\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>À propos de ce document</a></div><div class=\"lev2 toc-item\"><a href=\"#Question-de-programmation\" data-toc-modified-id=\"Question-de-programmation-13\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Question de programmation</a></div><div class=\"lev2 toc-item\"><a href=\"#Réponse-à-l'exercice-requis\" data-toc-modified-id=\"Réponse-à-l'exercice-requis-14\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>Réponse à l'exercice requis</a></div><div class=\"lev3 toc-item\"><a href=\"#Structures-de-données\" data-toc-modified-id=\"Structures-de-données-141\"><span class=\"toc-item-num\">1.4.1&nbsp;&nbsp;</span>Structures de données</a></div><div class=\"lev3 toc-item\"><a href=\"#Arithmétiques-sur-nos-entiers-étendus\" data-toc-modified-id=\"Arithmétiques-sur-nos-entiers-étendus-142\"><span class=\"toc-item-num\">1.4.2&nbsp;&nbsp;</span>Arithmétiques sur nos entiers étendus</a></div><div class=\"lev4 toc-item\"><a href=\"#Max/min\" data-toc-modified-id=\"Max/min-1421\"><span class=\"toc-item-num\">1.4.2.1&nbsp;&nbsp;</span>Max/min</a></div><div class=\"lev4 toc-item\"><a href=\"#Somme/produit\" data-toc-modified-id=\"Somme/produit-1422\"><span class=\"toc-item-num\">1.4.2.2&nbsp;&nbsp;</span>Somme/produit</a></div><div class=\"lev3 toc-item\"><a href=\"#Opérations-de-base,-$\\oplus$-et-$\\otimes$\" data-toc-modified-id=\"Opérations-de-base,-$\\oplus$-et-$\\otimes$-143\"><span class=\"toc-item-num\">1.4.3&nbsp;&nbsp;</span>Opérations de base, <span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax\" id=\"MathJax-Element-391-Frame\" tabindex=\"0\" style=\"position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo>&amp;#x2295;</mo></math>\" role=\"presentation\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-2835\" style=\"width: 1.038em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 0.847em; height: 0px; font-size: 118%;\"><span style=\"position: absolute; clip: rect(1.872em, 1000.8em, 2.897em, -1000em); top: -2.637em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-2836\"><span class=\"mo\" id=\"MathJax-Span-2837\" style=\"font-family: STIXMathJax_Main;\">⊕</span></span><span style=\"display: inline-block; width: 0px; height: 2.637em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.196em; border-left: 0px solid; width: 0px; height: 0.987em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>⊕</mo></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-391\">\\oplus</script> et <span class=\"MathJax_Preview\" style=\"color: inherit;\"></span><span class=\"MathJax\" id=\"MathJax-Element-392-Frame\" tabindex=\"0\" style=\"position: relative;\" data-mathml=\"<math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;><mo>&amp;#x2297;</mo></math>\" role=\"presentation\"><nobr aria-hidden=\"true\"><span class=\"math\" id=\"MathJax-Span-2838\" style=\"width: 1.038em; display: inline-block;\"><span style=\"display: inline-block; position: relative; width: 0.847em; height: 0px; font-size: 118%;\"><span style=\"position: absolute; clip: rect(1.872em, 1000.8em, 2.897em, -1000em); top: -2.637em; left: 0em;\"><span class=\"mrow\" id=\"MathJax-Span-2839\"><span class=\"mo\" id=\"MathJax-Span-2840\" style=\"font-family: STIXMathJax_Main;\">⊗</span></span><span style=\"display: inline-block; width: 0px; height: 2.637em;\"></span></span></span><span style=\"display: inline-block; overflow: hidden; vertical-align: -0.196em; border-left: 0px solid; width: 0px; height: 0.987em;\"></span></span></nobr><span class=\"MJX_Assistive_MathML\" role=\"presentation\"><math xmlns=\"http://www.w3.org/1998/Math/MathML\"><mo>⊗</mo></math></span></span><script type=\"math/tex\" id=\"MathJax-Element-392\">\\otimes</script></a></div><div class=\"lev4 toc-item\"><a href=\"#Intersection\" data-toc-modified-id=\"Intersection-1431\"><span class=\"toc-item-num\">1.4.3.1&nbsp;&nbsp;</span>Intersection</a></div><div class=\"lev4 toc-item\"><a href=\"#Composition\" data-toc-modified-id=\"Composition-1432\"><span class=\"toc-item-num\">1.4.3.2&nbsp;&nbsp;</span>Composition</a></div><div class=\"lev4 toc-item\"><a href=\"#Union\" data-toc-modified-id=\"Union-1433\"><span class=\"toc-item-num\">1.4.3.3&nbsp;&nbsp;</span>Union</a></div><div class=\"lev4 toc-item\"><a href=\"#Exemples\" data-toc-modified-id=\"Exemples-1434\"><span class=\"toc-item-num\">1.4.3.4&nbsp;&nbsp;</span>Exemples</a></div><div class=\"lev4 toc-item\"><a href=\"#Une-étape-de-plus-:-ne-pas-inclure-des-intervalles-inclus-dans-ceux-déjà-présents\" data-toc-modified-id=\"Une-étape-de-plus-:-ne-pas-inclure-des-intervalles-inclus-dans-ceux-déjà-présents-1435\"><span class=\"toc-item-num\">1.4.3.5&nbsp;&nbsp;</span>Une étape de plus : ne pas inclure des intervalles inclus dans ceux déjà présents</a></div><div class=\"lev3 toc-item\"><a href=\"#L'algorithme-PC\" data-toc-modified-id=\"L'algorithme-PC-144\"><span class=\"toc-item-num\">1.4.4&nbsp;&nbsp;</span>L'algorithme PC</a></div><div class=\"lev4 toc-item\"><a href=\"#Structure-de-données-pour-les-réseaux-STP\" data-toc-modified-id=\"Structure-de-données-pour-les-réseaux-STP-1441\"><span class=\"toc-item-num\">1.4.4.1&nbsp;&nbsp;</span>Structure de données pour les réseaux STP</a></div><div class=\"lev4 toc-item\"><a href=\"#L'algorithme-PC\" data-toc-modified-id=\"L'algorithme-PC-1442\"><span class=\"toc-item-num\">1.4.4.2&nbsp;&nbsp;</span>L'algorithme PC</a></div><div class=\"lev3 toc-item\"><a href=\"#Exemple-de-réseau-non-distributif\" data-toc-modified-id=\"Exemple-de-réseau-non-distributif-145\"><span class=\"toc-item-num\">1.4.5&nbsp;&nbsp;</span>Exemple de réseau non distributif</a></div><div class=\"lev3 toc-item\"><a href=\"#D'autres-exemples\" data-toc-modified-id=\"D'autres-exemples-146\"><span class=\"toc-item-num\">1.4.6&nbsp;&nbsp;</span>D'autres exemples</a></div><div class=\"lev2 toc-item\"><a href=\"#Conclusion\" data-toc-modified-id=\"Conclusion-15\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Conclusion</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Texte d'oral de modélisation - Agrégation Option Informatique\n",
    "## Préparation à l'agrégation - ENS de Rennes, 2016-17\n",
    "- *Date* : 7 avril 2017\n",
    "- *Auteur* : [Lilian Besson](https://GitHub.com/Naereen/notebooks/)\n",
    "- *Texte*: Annale 2009, \"Contraintes temporelles\""
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## À propos de ce document\n",
    "- Ceci est une *proposition* de correction, partielle et probablement non-optimale, pour la partie implémentation d'un [texte d'annale de l'agrégation de mathématiques, option informatique](http://Agreg.org/Textes/).\n",
    "- Ce document est un [notebook Jupyter](https://www.Jupyter.org/), et [est open-source sous Licence MIT sur GitHub](https://github.com/Naereen/notebooks/tree/master/agreg/), comme les autres solutions de textes de modélisation que [j](https://GitHub.com/Naereen)'ai écrite cette année.\n",
    "- L'implémentation sera faite en OCaml, version 4+ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The OCaml toplevel, version 4.04.2\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : int = 0\n"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Sys.command \"ocaml -version\";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Notez que certaines fonctions des modules usuels [`List`](http://caml.inria.fr/pub/docs/manual-ocaml/libref/List.html) et [`Array`](http://caml.inria.fr/pub/docs/manual-ocaml/libref/List.html) ne sont pas disponibles en OCaml 3.12.\n",
    "> J'essaie autant que possible de ne pas les utiliser, ou alors de les redéfinir si je m'en sers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Question de programmation\n",
    "La question de programmation pour ce texte était donnée en question 1 en page 9 :\n",
    "\n",
    "> \"Programmer l'algorithme PC. Faites le tourner sur l'exemple de réseau non distributif.\"\n",
    "\n",
    "La consigne était très courte, mais avec aucune indication.\n",
    "Notez qu'il est rare que le texte exige un exemple particulier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Réponse à l'exercice requis\n",
    "Ça va être assez long, en fait...\n",
    "\n",
    "1. D'abord, il faut définir les types de données avec lesquels on va travailler,\n",
    "2. Ensuite, implémenter les deux opérations $\\oplus$ et $\\otimes$ sur les ensembles d'intervalles,\n",
    "3. Puis implémenter l'algorithme PC (similaire à Floyd-Warshall),\n",
    "4. Et enfin, l'exécuter sur l'exemple de réseau non distributif donné en page 8.\n",
    "\n",
    "Si possible, on va essayer de faire des *tests* pour chaque fonction intermédiaire, et un exemple de plus à la fin.\n",
    "\n",
    "Un des problèmes que l'on va rencontrer est le fait que l'on doit manipuler $-\\infty$ et $+\\infty$, pour pouvoir gérer une contrainte qui n'est pas une contrainte, à savoir l'interavalle $(-\\infty, +\\infty)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "### Structures de données\n",
    "\n",
    "On va travailler avec des valeurs entières ou $\\pm\\infty$. En écrivant nous même les opérations arithmétiques ($+,max$) sur les entiers \"étendus\" on obtiendra ce qu'on veut."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "type entier_etendu = MInf | PInf | E of int\n"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type entier_etendu = MInf | PInf | E of int;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On se restreint aux intervalles à coordonnées *entières*, et on considère des listes d'intervalles.\n",
    "Tous les intervalles sont fermés à gauche et à droite."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "type intervalle = entier_etendu * entier_etendu\n"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type intervalle = (entier_etendu * entier_etendu);;  (* (a, b) représente l'intervalle [a, b] *)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "type intervalles = intervalle list\n"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type intervalles = intervalle list;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On définit tout de suite deux exemples, $T_a$ et $S_a$ tirés de la Figure 2.a) et $T_b,S_b$ de la Figure 2.b).\n",
    "Cela permettra de vérifier les opérations $\\oplus$ et $\\otimes$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $T_a = \\{ [1, 4], [6, 8] \\}$ et $S_a = \\{ [0, 1], [3, 5], [6, 7] \\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val t_a : intervalles = [(E 1, E 4); (E 6, E 8)]\n"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val s_a : intervalles = [(E 0, E 1); (E 3, E 5); (E 6, E 7)]\n"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let t_a : intervalles = [\n",
    "    (E(1), E(4));\n",
    "    (E(6), E(8))\n",
    "];;\n",
    "\n",
    "let s_a : intervalles = [\n",
    "    (E(0), E(1));\n",
    "    (E(3), E(5));\n",
    "    (E(6), E(7))\n",
    "];;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $T_b = \\{ [-1, 0], [2, 4] \\}$ et $S_b = \\{ [0, 1], [4, 4] \\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val t_b : intervalles = [(E (-1), E 0); (E 2, E 4)]\n"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val s_b : intervalles = [(E 0, E 1); (E 4, E 4)]\n"
      ]
     },
     "execution_count": 80,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let t_b : intervalles = [\n",
    "    (E(-1), E(0));\n",
    "    (E(2), E(4))\n",
    "];;\n",
    "\n",
    "let s_b : intervalles = [\n",
    "    (E(0), E(1));\n",
    "    (E(4), E(4))  (* Intervalle de longueur nulle *)\n",
    "];;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Et la contrainte vide, $T = \\{[-\\infty, +\\infty\\}$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val t_vide : intervalles = [(MInf, PInf)]\n"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let t_vide : intervalles = [\n",
    "    (MInf, PInf)\n",
    "];;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "### Arithmétiques sur nos entiers étendus"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Max/min"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val max_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>\n"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let max_ee x y =\n",
    "    match x, y with\n",
    "    | MInf, _ -> y\n",
    "    | PInf, _ -> PInf\n",
    "    | _, MInf -> x\n",
    "    | _, PInf -> PInf\n",
    "    | E(vx), E(vy) -> E(max vx vy)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 10\n"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = PInf\n"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 10\n"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = PInf\n"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 10\n"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 10\n"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "max_ee MInf (E(10));;\n",
    "max_ee PInf (E(10));;\n",
    "max_ee (E(10)) MInf;;\n",
    "max_ee (E(10)) PInf;;\n",
    "max_ee (E(-10)) (E(10));;\n",
    "max_ee (E(10)) (E(-10));;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val min_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>\n"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let min_ee x y =\n",
    "    match x, y with\n",
    "    | PInf, _ -> y\n",
    "    | MInf, _ -> MInf\n",
    "    | _, PInf -> x\n",
    "    | _, MInf -> MInf\n",
    "    | E(vx), E(vy) -> E(min vx vy)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = MInf\n"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 10\n"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = MInf\n"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 10\n"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E (-10)\n"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E (-10)\n"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "min_ee MInf (E(10));;\n",
    "min_ee PInf (E(10));;\n",
    "min_ee (E(10)) MInf;;\n",
    "min_ee (E(10)) PInf;;\n",
    "min_ee (E(-10)) (E(10));;\n",
    "min_ee (E(10)) (E(-10));;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut utiliser la fonction minimum pour trier deux entiers étendus :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val pluspetiteq_ee : entier_etendu -> entier_etendu -> bool = <fun>\n"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let pluspetiteq_ee x y =\n",
    "    let m = min_ee x y in\n",
    "    m = x || x = y\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val pluspetit_ee : entier_etendu -> entier_etendu -> bool = <fun>\n"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let pluspetit_ee x y =\n",
    "    let m = min_ee x y in\n",
    "    m = x && x != y\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Somme/produit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val plus_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>\n"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let plus_ee x y =\n",
    "    match x, y with\n",
    "    | MInf, PInf -> failwith \"-inf + +inf = ?\"\n",
    "    | PInf, MInf -> failwith \"-inf + +inf = ?\"\n",
    "    | PInf, _ -> PInf\n",
    "    | MInf, _ -> MInf\n",
    "    | _, MInf -> MInf\n",
    "    | _, PInf -> PInf\n",
    "    | E(vx), E(vy) -> E(vx + vy)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = MInf\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = PInf\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = MInf\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = PInf\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 0\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 0\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 20\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E (-20)\n"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plus_ee MInf (E(10));;\n",
    "plus_ee PInf (E(10));;\n",
    "plus_ee (E(10)) MInf;;\n",
    "plus_ee (E(10)) PInf;;\n",
    "plus_ee (E(-10)) (E(10));;\n",
    "plus_ee (E(10)) (E(-10));;\n",
    "plus_ee (E(10)) (E(10));;\n",
    "plus_ee (E(-10)) (E(-10));;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val produit_ee : entier_etendu -> entier_etendu -> entier_etendu = <fun>\n"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let produit_ee x y =\n",
    "    match x, y with\n",
    "    | MInf, PInf -> MInf\n",
    "    | PInf, MInf -> PInf\n",
    "    | PInf, E(vy) when vy < 0 -> MInf\n",
    "    | PInf, _ -> PInf\n",
    "    | MInf, E(vy) when vy < 0 -> PInf\n",
    "    | MInf, _ -> MInf\n",
    "    | E(vx), PInf when vx < 0 -> MInf\n",
    "    | _, PInf -> PInf\n",
    "    | E(vx), MInf when vx < 0 -> PInf\n",
    "    | _, MInf -> MInf\n",
    "    | E(vx), E(vy) -> E(vx * vy)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = MInf\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = PInf\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = MInf\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = PInf\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E (-100)\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E (-100)\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 100\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : entier_etendu = E 100\n"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "produit_ee MInf (E(10));;\n",
    "produit_ee PInf (E(10));;\n",
    "produit_ee (E(10)) MInf;;\n",
    "produit_ee (E(10)) PInf;;\n",
    "produit_ee (E(-10)) (E(10));;\n",
    "produit_ee (E(10)) (E(-10));;\n",
    "produit_ee (E(10)) (E(10));;\n",
    "produit_ee (E(-10)) (E(-10));;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "### Opérations de base, $\\oplus$ et $\\otimes$\n",
    "On peut écrire des opérations d'intersection et de composition sur deux intervalles, ensuite il suffira de les généraliser à un ensemble d'intervalle.\n",
    "\n",
    "On suit les définitions de l'énoncé.\n",
    "\n",
    "#### Intersection\n",
    "$$\n",
    "\\forall T = (I_1,\\dots,I_l),\n",
    "\\forall S = (J_1,\\dots,J_m),\\\\\n",
    "T \\oplus S := \\{ K_1, \\dots, K_n\\}\n",
    "\\;\\;\\text{Où}\\;\\; K_k = I_i \\cap J_j.\n",
    "$$\n",
    "Notez que $n \\leq l + m$ ici."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour l'intersection de deux intervalles, l'intervalle vide $\\emptyset$ peut être obtenu, donc la fonction suivante renvoie un type `intervalle option` : soit `None` si $I \\cap J = \\emptyset$, soit `Some (x, y)` si $I \\cap J = [x, y]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val intersection : intervalle -> intervalle -> intervalle option = <fun>\n"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let intersection (i : intervalle) (j : intervalle) : intervalle option =\n",
    "    let a = fst i and b = snd i in\n",
    "    let c = fst j and d = snd j in\n",
    "    if pluspetit_ee b c || pluspetit_ee d a then\n",
    "        None\n",
    "    else\n",
    "        Some (max_ee a c, min_ee b d)\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ensuite, il suffit d'explorer tous les couples $(I, J)$ possible, et de ne garder que ceux qui donnent un intervalle.\n",
    "On supprimera les doublons en vérifiant au fur et à mesure (ça a la même complexité que si on le fait à la fin).\n",
    "\n",
    "En manipulant une liste d'intervalle `option`, on doit ruser un peu pour n'ajouter que ceux qui ne sont pas dans `acc` et qui sont des vrais intervalles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ajoute_nouveaux_option :\n",
       "  intervalles -> intervalle option list -> intervalle list = <fun>\n"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let ajoute_nouveaux_option (acc : intervalles) (liste_option : intervalle option list) =\n",
    "    List.map\n",
    "    (fun i -> match i with Some i2 -> i2 | None -> (MInf, PInf))\n",
    "    (List.filter (fun i ->\n",
    "        match i with\n",
    "        | None -> false\n",
    "        | Some i2 -> not (List.mem i2 acc)\n",
    "    ) liste_option)\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec tout ça, on a une belle fonction récursive, avec un accumulateur `acc` qui contient la liste des intervalles dans $T \\oplus S$, construite en considérant les intervalles de $S$ les un après les autres.\n",
    "\n",
    "On s'assure de n'avoir ni intervalles vide, ni doublon, grâce à `ajoute_nouveaux_option`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val intersections : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let intersections (t : intervalles) (s : intervalles) : intervalles =\n",
    "    let rec inter_aux acc tx sx =\n",
    "        match sx with\n",
    "        | [] -> acc    (* Plus rien à ajouter *)\n",
    "        | j :: s2 ->   (* On traite j, puis récursivement la suite de s *)\n",
    "            let t_inter_j = List.map (intersection j) tx in\n",
    "            inter_aux ((ajoute_nouveaux_option acc t_inter_j) @ acc) tx s2\n",
    "    in\n",
    "    List.sort compare (inter_aux [] t s)\n",
    "    (* On trie pour les avoir en ordre croissant, c'est tout *)\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci :\n",
    "$$ T \\oplus S = \\texttt{t ++ s}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let ( ++ ) = intersections;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Composition\n",
    "Ce sera plus facile.\n",
    "$$\n",
    "\\forall T = (I_1,\\dots,I_l),\n",
    "\\forall S = (J_1,\\dots,J_m),\\\\\n",
    "T \\otimes S := \\{ K_1, \\dots, K_n\\}\n",
    "\\;\\;\\text{Où}\\;\\; K_k = [a + c, b + d], \\;\\text{si}\\; I_i = [a, b], J_j = [c, d].\n",
    "$$\n",
    "Notez que $n \\leq l \\times m$ ici."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour la composition de deux intervalles, il n'y pas de difficulté particulière :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val composition : intervalle -> intervalle -> intervalle = <fun>\n"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let composition (i : intervalle) (j : intervalle) : intervalle =\n",
    "    let a = fst i and b = snd i in\n",
    "    let c = fst j and d = snd j in\n",
    "    (* (a + c, b + d) *)\n",
    "    ((plus_ee a c), (plus_ee d b))\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Et on les combine facilement, en gardant la même architecture que pour `intersections`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ajoute_nouveaux : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 104,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let ajoute_nouveaux (acc : intervalles) (liste : intervalles) : intervalles =\n",
    "    List.filter (fun i -> not (List.mem i acc)) liste\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val compositions : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let compositions (t : intervalles) (s : intervalles) : intervalles =\n",
    "    let rec compo_aux acc tx sx =\n",
    "        match sx with\n",
    "        | [] -> acc    (* Plus rien à ajouter *)\n",
    "        | j :: s2 ->   (* On traite j, puis récursivement la suite de s *)\n",
    "            let t_compo_j = List.map (composition j) tx in\n",
    "            compo_aux ((ajoute_nouveaux acc t_compo_j) @ acc) tx s2\n",
    "    in\n",
    "    List.sort compare (compo_aux [] t s)\n",
    "    (* On trie pour les avoir en ordre croissant, c'est tout *)\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour frimer un peu et simplifier l'écriture de l'algorithme PC, on peut définir une opération infixe en raccourci :\n",
    "$$ T \\otimes S = \\texttt{t ** s}.$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ( ** ) : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let ( ** ) = compositions;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Union\n",
    "On peut aussi rapidement définier $T \\cup S$, pour l'union. C'est très facile."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val union : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let union (t : intervalles) (s : intervalles) : intervalles =\n",
    "    List.append t s\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Exemples\n",
    "On aimerait reproduire les exemples de la Figure 2 du texte.\n",
    "![images/intersection_composition_contraintes.png](images/intersection_composition_contraintes.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pour les deux intervalles de la Figure 2.a) : $T_a = \\{ [1, 4], [6, 8] \\}$ et $S_a = \\{ [0, 1], [3, 5], [6, 7] \\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 3, E 4); (E 6, E 7)]\n"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_a ++ s_a;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On retrouve bien le résultat de la Figure 2.a)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : intervalles =\n",
       "[(E 1, E 5); (E 4, E 9); (E 6, E 9); (E 7, E 11); (E 9, E 13); (E 12, E 15)]\n"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles =\n",
       "[(E 1, E 4); (E 6, E 8); (E 0, E 1); (E 3, E 5); (E 6, E 7)]\n"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_a ** s_a;;\n",
    "union t_a s_a;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pour les deux intervalles de la Figure 2.b) : $T_b = \\{ [-1, 0], [2, 4] \\}$ et $S_b = \\{ [0, 1], [4, 4] \\}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 3, E 4); (E 6, E 8)]\n"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_b ** s_b;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On retrouve bien le résultat de la Figure 2.b).\n",
    "\n",
    "L'intervalle $[3, 4]$ est inclus dans $[2, 5]$, donc on devrait ajouter une étape de nettoyage pour donner une forme canonique aux intervalles produit par `composition`. On le fait plus bas."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E (-1), E 0); (E 2, E 4)]\n"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 0, E 1); (E 4, E 4)]\n"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_b;;\n",
    "s_b;;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : intervalles = []\n"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E (-1), E 0); (E 2, E 4); (E 0, E 1); (E 4, E 4)]\n"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t_b ++ s_b;;\n",
    "union t_b s_b;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque que les intervalles sont bien donnés dans l'ordre croissant, puisqu'on a pensé à trier la sortie des deux fonctions, mais ça ne change rien."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Une étape de plus : ne pas inclure des intervalles inclus dans ceux déjà présents\n",
    "\n",
    "On va raffiner les fonctions définis ci-dessus en ajoutant un test, sur leur résultat final.\n",
    "\n",
    "- `est_inclus i j` teste si $I \\subseteq J$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val est_inclus : intervalle -> intervalle -> bool = <fun>\n"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let est_inclus (i : intervalle) (j : intervalle) : bool =\n",
    "    let a = fst i and b = snd i in\n",
    "    let c = fst j and d = snd j in\n",
    "    (* on peut aussi écrire directement\n",
    "    let a, b = i and c, d = j in\n",
    "    pour extraire les valeurs d'un coupe i=(a,b) et j=(c,d)\n",
    "    *)\n",
    "    (* c <= a && b <= d *)\n",
    "    (pluspetiteq_ee c a) && (pluspetiteq_ee b d)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = false\n"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "est_inclus (E(3), E(4)) (E(2), E(5));; (* true *)\n",
    "est_inclus (E(2), E(5)) (E(3), E(4));; (* false *)\n",
    "est_inclus (E(1), E(1)) (E(1), E(1));; (* true *)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `est_inclus_dans_un i acc` teste si $I \\subseteq J$ pour **un** $J \\neq I \\in \\mathrm{Acc}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val est_inclus_dans_un : intervalle -> intervalles -> bool = <fun>\n"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let est_inclus_dans_un (i : intervalle) (acc : intervalles) : bool =\n",
    "    List.exists (fun j -> (i != j) && (est_inclus i j)) acc\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On peut écrire une fonction `filtre` qui retire les intervalles inclus dans d'autres, puis retire les doublons."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val retire_les_inclus : intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val retire_les_doublons : intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val filtre : intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let retire_les_inclus (liste : intervalles) : intervalles =\n",
    "    List.filter (fun i -> not (est_inclus_dans_un i liste)) liste\n",
    ";;\n",
    "\n",
    "let retire_les_doublons (liste : intervalles) : intervalles =\n",
    "    let reponse = ref [] in\n",
    "    List.iter (fun i ->\n",
    "        if not (List.mem i !reponse) then\n",
    "        reponse := i :: !reponse\n",
    "    ) liste;\n",
    "    !reponse\n",
    ";;\n",
    "\n",
    "let filtre liste =\n",
    "    retire_les_doublons (retire_les_inclus liste)\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- L'intersection ne devrait pas être impactée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val intersections2 : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let intersections2 (t : intervalles) (s : intervalles) : intervalles =\n",
    "    List.sort compare (filtre (intersections t s))\n",
    "    (* On trie pour les avoir en ordre croissant, c'est tout *)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ( ++ ) : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 3, E 4); (E 6, E 7)]\n"
      ]
     },
     "execution_count": 125,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let ( ++ ) = intersections2;;\n",
    "\n",
    "t_a ++ s_a;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Mais la composition va donner la bonne réponse désormais pour l'exemple de la figure 2.b)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val compositions2 : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let compositions2 (t : intervalles) (s : intervalles) : intervalles =\n",
    "    List.sort compare (filtre (compositions t s))\n",
    "    (* On trie pour les avoir en ordre croissant, c'est tout *)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val ( ** ) : intervalles -> intervalles -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E (-1), E 1); (E 2, E 5); (E 6, E 8)]\n"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let ( ** ) = compositions2;;\n",
    "\n",
    "t_b ** s_b;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> C'était un peu long, mais c'est propre au moins."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notez que pour obtenir une vraie forme canonique, il faudrait aussi rassembler les intervalles consécutifs ($\\{ [0, 1], [1, 2] \\} \\rightarrow \\{ [0, 1] \\}$) et se recoupant ($\\{ [0, 3], [2, 4] \\} \\rightarrow \\{ [0, 4] \\}$).\n",
    "\n",
    "> Ça prendrait trop de temps. Et ce n'était pas exigé."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "### L'algorithme PC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Structure de données pour les réseaux STP\n",
    "On a besoin désormais de considérer des réseaux STP, qui sont des graphes dont les sommets sont des entiers, et dont les arêtes sont étiquetées par des *listes* (non vides) d'intervalles.\n",
    "\n",
    "L'algorithme PC demande de pouvoir accéder rapidement et facilement à l'arête entre deux sommets $x,y$, $T_{x,y}$.\n",
    "Ainsi, la structure de matrice d'adjacence semble appropriée.\n",
    "Les arêtes inexistantes dans le réseau auront simplement $T_{x,y} = \\emptyset$, c'est-à-dire `[]` (liste vide).\n",
    "\n",
    "> On supposera que toutes les matrices données aux différentes fonctions définies plus bas sont carrées, on ne le vérifie pas (mais ce serait facile)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "type sommet = int\n"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "type arete = intervalles\n"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "type reseauSTP = intervalles array array\n"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type sommet = int;;\n",
    "type arete = intervalles;; (* c'est l'idée *)\n",
    "\n",
    "type reseauSTP = intervalles array array;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On essaie tout de suite notre structure de données avec l'exemple du réseau STP de la figure 4 :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 235,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val t_01 : intervalles = [(E 0, E 1); (E 10, E 20)]\n"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_12 : intervalles = [(E 0, E 10)]\n"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_13 : intervalles = [(E 25, E 50)]\n"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_23 : intervalles = [(E 0, E 20); (E 40, E 40)]\n"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_vide : (entier_etendu * entier_etendu) list = [(MInf, PInf)]\n"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val stp_4 : reseauSTP =\n",
       "  [|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];\n",
       "      [(MInf, PInf)]|];\n",
       "    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];\n",
       "    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "      [(E 0, E 20); (E 40, E 40)]|];\n",
       "    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]\n"
      ]
     },
     "execution_count": 235,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let t_01 : intervalles = [(E(0), E(1)); (E(10), E(20))];;\n",
    "let t_12 : intervalles = [(E(0), E(10))];;\n",
    "let t_13 : intervalles = [(E(25), E(50))];;\n",
    "let t_23 : intervalles = [(E(0), E(20)); (E(40), E(40))];;\n",
    "\n",
    "let t_vide = [(MInf, PInf)];;\n",
    "\n",
    "let stp_4 : reseauSTP = [|\n",
    "    [| t_vide; t_01;   t_vide; t_vide |];\n",
    "    [| t_vide; t_vide; t_12;   t_13 |];\n",
    "    [| t_vide; t_vide; t_vide; t_23 |];\n",
    "    [| t_vide; t_vide; t_vide; t_vide |];\n",
    "|];;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut vérifier qu'il n'est pas distributif, en prenant l'exemple du texte (fin page 8) :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 236,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val s_13 : intervalles = [(E 0, E 30); (E 40, E 50)]\n"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 25, E 30); (E 40, E 50)]\n"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 25, E 31); (E 35, E 50); (E 40, E 51); (E 50, E 70)]\n"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 25, E 51); (E 35, E 70)]\n"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 0, E 31); (E 10, E 50); (E 40, E 51); (E 50, E 70)]\n"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 25, E 50); (E 50, E 70)]\n"
      ]
     },
     "execution_count": 236,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let s_13 = t_12 ** t_23;;\n",
    "\n",
    "t_13 ++ s_13;;\n",
    "t_01 ** (t_13 ++ s_13);;  (* 1er cas *)\n",
    "\n",
    "t_01 ** t_13;;\n",
    "t_01 ** s_13;;\n",
    "(t_01 ** t_13) ++ (t_01 ** s_13);; (* 2nd cas *)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En simplifiant, on obtient :\n",
    "\n",
    "- $T_{01} \\otimes (T_{13} \\oplus S_{13} = \\{ [25, 31], [35, 70] \\}$,\n",
    "- $(T_{01} \\otimes T_{13}) \\oplus (T_{01} \\otimes S_{13}) = \\{ [25, 70] \\}$,\n",
    "\n",
    "qui sont bien différents."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Enfin, on peut rapidement vérifier si la matrice d'un graphe est bien carrée :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 237,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val est_carree : 'a array array -> bool = <fun>\n"
      ]
     },
     "execution_count": 237,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let est_carree matrice =\n",
    "    let n = Array.length matrice in\n",
    "    Array.fold_left (fun b x -> b && (n = (Array.length x))) true matrice\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 238,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : bool = true\n"
      ]
     },
     "execution_count": 238,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "est_carree stp_4;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### L'algorithme PC\n",
    "Ça semble être un bon choix.\n",
    "Maintenant, passons à l'algorithme PC.\n",
    "\n",
    "![images/algorithme_PC.png](images/algorithme_PC.png)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Il n'y a pas de boucle `until` en Caml, mais avec une boucle `while` on arrivera presque à la même chose."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 239,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "exception Fini\n"
      ]
     },
     "execution_count": 239,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "exception Fini;; (* Pour faire le [exit]. *)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut l'écrire avant pour la rendre plus claire, mais l'étape clé de l'algorithme PC (et Floyd-Warshall) est une opération dite de *relaxation* :\n",
    "$$ T_{i,j} \\oplus (T_{i,k} \\otimes T_{k,j}).$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 240,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val relaxe : reseauSTP -> int -> int -> int -> intervalles = <fun>\n"
      ]
     },
     "execution_count": 240,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let relaxe (reseau : reseauSTP) i j k =\n",
    "    let t_ij = reseau.(i).(j)\n",
    "    and t_ik = reseau.(i).(k)\n",
    "    and t_kj = reseau.(k).(j)\n",
    "    in t_ij ++ (t_ik ** t_kj)\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a tout ce qu'il faut pour écrire l'algorithme.\n",
    "Mais comme il ne marche pas encore, on va le débogguer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 241,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val string_of_entieretendu : entier_etendu -> string = <fun>\n"
      ]
     },
     "execution_count": 241,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let string_of_entieretendu = function\n",
    "    | MInf -> \"-oo\"\n",
    "    | PInf -> \"+oo\"\n",
    "    | E(x) -> string_of_int x\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 242,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val print_intervalle : intervalle -> unit = <fun>\n"
      ]
     },
     "execution_count": 242,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let print_intervalle (une_contrainte : intervalle) =\n",
    "    let a, b = une_contrainte in\n",
    "    Printf.printf \"(%s, %s) \" (string_of_entieretendu a) (string_of_entieretendu b)\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val print_intervalles : intervalles -> unit = <fun>\n"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let print_intervalles (contraintes : intervalles) =\n",
    "    List.iter print_intervalle contraintes\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val flush_force : unit -> unit = <fun>\n"
      ]
     },
     "execution_count": 244,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let flush_force () =\n",
    "    Printf.printf \"\\n\";\n",
    "    flush_all();\n",
    "    Printf.printf \"\\n\";\n",
    "    flush_all();\n",
    "    Printf.printf \"\\n\";\n",
    "    flush_all();\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 245,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val print_reseau : reseauSTP -> unit = <fun>\n"
      ]
     },
     "execution_count": 245,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let print_reseau (reseau : reseauSTP) : unit =\n",
    "    flush_force ();\n",
    "    Printf.printf \"\\nReseau =\\n\";\n",
    "    Array.iteri (fun i ligne ->\n",
    "        Array.iteri (fun j case ->\n",
    "            if case != [(MInf, PInf)] then begin\n",
    "            Printf.printf \"\\n    T[i=%i, j=%i] = [\" i j;\n",
    "            print_intervalles case;\n",
    "            Printf.printf \"]\";\n",
    "        end) ligne\n",
    "    ) reseau;\n",
    "    flush_all ();\n",
    ";;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 246,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : reseauSTP =\n",
       "[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];\n",
       "    [(MInf, PInf)]|];\n",
       "  [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];\n",
       "  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "    [(E 0, E 20); (E 40, E 40)]|];\n",
       "  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]\n"
      ]
     },
     "execution_count": 246,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stp_4;;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 247,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "flush_force();;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 248,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 248,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print_reseau stp_4;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On est prêt à écrire l'algorithme :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 249,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val algorithmePC :\n",
       "  ?max_etape:int -> reseauSTP -> reseauSTP * intervalles list = <fun>\n"
      ]
     },
     "execution_count": 249,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let algorithmePC ?(max_etape=10) (reseau : reseauSTP) : (reseauSTP * intervalles list) =\n",
    "    let resT = Array.map Array.copy reseau in (* on ne modifie pas l'entrée *)\n",
    "    let resS = ref [||] in\n",
    "    let n = Array.length resT in\n",
    "    let allseen = ref [] in (* Pour débogguer, je veux la liste des Tij vus *)\n",
    "    let etape = ref 0 in\n",
    "    begin\n",
    "        try begin\n",
    "        while !etape < max_etape && !resS != resT do\n",
    "            incr etape;\n",
    "            resS := Array.map Array.copy resT; (* S := T *)\n",
    "            for k = 0 to n - 1 do\n",
    "                for i = 0 to n - 1 do\n",
    "                    for j = 0 to n - 1 do\n",
    "                        Printf.printf \"\\n\\nEtape %i, k = %i, i = %i, j = %i.\\n\" !etape k i j;\n",
    "                        print_string \"Contraintes :\";\n",
    "                        print_reseau resT;\n",
    "                        resT.(i).(j) <- relaxe resT i j k;\n",
    "                        allseen := (resT.(i).(j)) :: !allseen; (* on l'ajoute *)\n",
    "                        if resT.(i).(j) = [] then\n",
    "                            raise Fini\n",
    "                    done\n",
    "                done\n",
    "            done\n",
    "        done;\n",
    "        end\n",
    "        with Fini -> () (* On ignore l'exception, on a juste terminé. *)\n",
    "    end;\n",
    "    resT, !allseen\n",
    ";;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "### Exemple de réseau non distributif\n",
    "On va traiter l'exemple de la Figure 4 du texte, comme défini plus haut :\n",
    "\n",
    "![images/reseau_distributif.png](images/reseau_distributif.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : reseauSTP =\n",
       "[|[|[(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)];\n",
       "    [(MInf, PInf)]|];\n",
       "  [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];\n",
       "  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "    [(E 0, E 20); (E 40, E 40)]|];\n",
       "  [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|]\n"
      ]
     },
     "execution_count": 250,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stp_4;;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 0, E 10)]\n"
      ]
     },
     "execution_count": 251,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "relaxe stp_4 1 2 3;;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : intervalles = [(E 25, E 50)]\n"
      ]
     },
     "execution_count": 252,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stp_4.(1).(3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 253,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 0, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(0, 1) (10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(0, 10) ]\n",
      "    T[i=1, j=3] = [(25, 50) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(0, 20) (40, 40) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : reseauSTP * intervalles list =\n",
       "([|[|[]; [(E 0, E 1); (E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)]|];\n",
       "   [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 10)]; [(E 25, E 50)]|];\n",
       "   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "     [(E 0, E 20); (E 40, E 40)]|];\n",
       "   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]|]|],\n",
       " [[]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "  [(E 0, E 20); (E 40, E 40)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "  [(MInf, PInf)]; [(E 25, E 50)]; [(E 0, E 10)]; [(MInf, PInf)];\n",
       "  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 0, E 1); (E 10, E 20)];\n",
       "  [(MInf, PInf)]])\n"
      ]
     },
     "execution_count": 253,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "algorithmePC stp_4;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Je ne suis pas sûr de comment interprêter ce résultat...\n",
    "> \n",
    "> - soit j'ai fait une erreur dans l'implémentation,\n",
    "> - soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "### D'autres exemples\n",
    "\n",
    "On peut étudier le STP de la Figure 1., en enlevant la contrainte $[60, \\infty)$, qui ne rentre pas dans notre implémentation.\n",
    "\n",
    "![images/stp_figure1.png](images/stp_figure1.png)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "val t_01 : intervalles = [(E 10, E 20)]\n"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_12 : intervalles = [(E 30, E 40)]\n"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_32 : intervalles = [(E 10, E 20)]\n"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_34 : intervalles = [(E 20, E 30); (E 40, E 50)]\n"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val t_40 : intervalles = [(E 60, E 70)]\n"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "val stp_1 : reseauSTP =\n",
       "  [|[|[(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "      [(MInf, PInf)]|];\n",
       "    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];\n",
       "      [(MInf, PInf)]|];\n",
       "    [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "      [(MInf, PInf)]|];\n",
       "    [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 10, E 20)]; [(MInf, PInf)];\n",
       "      [(E 20, E 30); (E 40, E 50)]|];\n",
       "    [|[(E 60, E 70)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "      [(MInf, PInf)]|]|]\n"
      ]
     },
     "execution_count": 254,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "let t_01 : intervalles = [(E(10), E(20))];;\n",
    "let t_12 : intervalles = [(E(30), E(40))];;\n",
    "let t_32 : intervalles = [(E(10), E(20))];;\n",
    "let t_34 : intervalles = [(E(20), E(30)); (E(40), E(50))];;\n",
    "let t_40 : intervalles = [(E(60), E(70))];;\n",
    "\n",
    "let stp_1 : reseauSTP = [|\n",
    "    [| t_vide; t_01; t_vide; t_vide; t_vide |];\n",
    "    [| t_vide; t_vide; t_12; t_vide; t_vide |];\n",
    "    [| t_vide; t_vide; t_vide; t_vide; t_vide   |];\n",
    "    [| t_vide; t_vide; t_32; t_vide; t_34 |];\n",
    "    [| t_40; t_vide; t_vide; t_vide; t_vide |];\n",
    "|];;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 255,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "- : unit = ()\n"
      ]
     },
     "execution_count": 255,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n"
     ]
    }
   ],
   "source": [
    "print_reseau stp_1;;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 256,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 0, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 1, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 2, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 3, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 4, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 4, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(-oo, +oo) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 4, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 4, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 0, i = 4, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 0, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 0, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 0, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(-oo, +oo) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 0, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 0, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 1, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 1, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 1, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 1, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 1, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 2, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 2, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 2, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 2, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 2, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 3, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 3, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 3, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 3, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 3, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 4, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 4, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 4, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(-oo, +oo) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Etape 1, k = 1, i = 4, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 1, i = 4, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 0, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 0, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 0, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 0, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 0, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 1, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 1, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 1, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 1, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 1, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 2, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 2, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 2, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 2, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 2, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 3, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 3, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 3, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 3, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 3, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 4, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 4, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 4, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 4, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 2, i = 4, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 0, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 0, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 0, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 0, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 0, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 1, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 1, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 1, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 1, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 1, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 2, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 2, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 2, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 2, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 2, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 3, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 3, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 3, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 3, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 3, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 4, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 4, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 4, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 4, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 3, i = 4, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 0, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 0, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 0, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 0, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 0, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 1, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 1, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 1, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 1, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 1, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 2, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 2, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 2, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 2, j = 3.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 2, j = 4.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 3, j = 0.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(-oo, +oo) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 3, j = 1.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(80, 100) (100, 120) ]\n",
      "    T[i=3, j=1] = [(-oo, +oo) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n",
      "    T[i=4, j=4] = [(-oo, +oo) ]\n",
      "\n",
      "Etape 1, k = 4, i = 3, j = 2.\n",
      "Contraintes :\n",
      "\n",
      "\n",
      "\n",
      "Reseau =\n",
      "\n",
      "    T[i=0, j=0] = [(-oo, +oo) ]\n",
      "    T[i=0, j=1] = [(10, 20) ]\n",
      "    T[i=0, j=2] = [(40, 60) ]\n",
      "    T[i=0, j=3] = [(-oo, +oo) ]\n",
      "    T[i=0, j=4] = [(-oo, +oo) ]\n",
      "    T[i=1, j=0] = [(-oo, +oo) ]\n",
      "    T[i=1, j=1] = [(-oo, +oo) ]\n",
      "    T[i=1, j=2] = [(30, 40) ]\n",
      "    T[i=1, j=3] = [(-oo, +oo) ]\n",
      "    T[i=1, j=4] = [(-oo, +oo) ]\n",
      "    T[i=2, j=0] = [(-oo, +oo) ]\n",
      "    T[i=2, j=1] = [(-oo, +oo) ]\n",
      "    T[i=2, j=2] = [(-oo, +oo) ]\n",
      "    T[i=2, j=3] = [(-oo, +oo) ]\n",
      "    T[i=2, j=4] = [(-oo, +oo) ]\n",
      "    T[i=3, j=0] = [(80, 100) (100, 120) ]\n",
      "    T[i=3, j=1] = [(90, 120) (110, 140) ]\n",
      "    T[i=3, j=2] = [(10, 20) ]\n",
      "    T[i=3, j=3] = [(-oo, +oo) ]\n",
      "    T[i=3, j=4] = [(20, 30) (40, 50) ]\n",
      "    T[i=4, j=0] = [(60, 70) ]\n",
      "    T[i=4, j=1] = [(70, 90) ]\n",
      "    T[i=4, j=2] = [(100, 130) ]\n",
      "    T[i=4, j=3] = [(-oo, +oo) ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "- : reseauSTP * intervalles list =\n",
       "([|[|[(MInf, PInf)]; [(E 10, E 20)]; [(E 40, E 60)]; [(MInf, PInf)];\n",
       "     [(MInf, PInf)]|];\n",
       "   [|[(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)]; [(MInf, PInf)];\n",
       "     [(MInf, PInf)]|];\n",
       "   [|[(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "     [(MInf, PInf)]|];\n",
       "   [|[(E 80, E 100); (E 100, E 120)]; [(E 90, E 120); (E 110, E 140)]; \n",
       "     []; [(MInf, PInf)]; [(E 20, E 30); (E 40, E 50)]|];\n",
       "   [|[(E 60, E 70)]; [(E 70, E 90)]; [(E 100, E 130)]; [(MInf, PInf)];\n",
       "     [(MInf, PInf)]|]|],\n",
       " [[]; [(E 90, E 120); (E 110, E 140)]; [(E 80, E 100); (E 100, E 120)];\n",
       "  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(E 30, E 40)];\n",
       "  [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)]; [(MInf, PInf)];\n",
       "  [(E ...); ...]; ...])\n"
      ]
     },
     "execution_count": 256,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "algorithmePC stp_1;;"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "> Je ne suis pas sûr de comment interprêter ce résultat...\n",
    "> \n",
    "> - soit j'ai fait une erreur dans l'implémentation,\n",
    "> - soit l'algorithme PC devait ne rien modifier à $T$ sur cet exemple..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Conclusion\n",
    "\n",
    "Voilà pour la question obligatoire de programmation :\n",
    "\n",
    "- on a décomposé le problème en sous-fonctions,\n",
    "- on a essayé d'être fainéant, en réutilisant les sous-fonctions,\n",
    "- on a fait des exemples et *on les garde* dans ce qu'on présente au jury,\n",
    "- on a testé la fonction exigée sur de petits exemples et sur un exemple de taille réelle (venant du texte)\n",
    "\n",
    "Et on a essayé de faire *un peu plus*, en implémentant la vérification d'une contrainte de plus.\n",
    "\n",
    "> Bien-sûr, ce petit notebook ne se prétend pas être une solution optimale, ni exhaustive."
   ]
  }
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