0501_alldiff_nqueens.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyMqKPM+Q4W9QznY4Zjv7xO5",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/lmcanavals/cs_topics/blob/main/0501_alldiff_nqueens.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# N Queens"
      ],
      "metadata": {
        "id": "Fwz5i28f1-hm"
      }
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "ddoXGsoI0z19"
      },
      "outputs": [],
      "source": [
        "!python -m pip install ortools &> /dev/null"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from ortools.sat.python import cp_model\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "wcj7kktn07JO"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "def showBoard(board: list):\n",
        "    n = len(board)\n",
        "    b = np.zeros((n, n, 3), dtype=int)\n",
        "    b[:, :] = [230, 150, 130]\n",
        "    b[::2, ::2] = [250, 210, 180]\n",
        "    b[1::2, 1::2] = [250, 210, 180]\n",
        "    plt.imshow(b)\n",
        "    for row, col in enumerate(board):\n",
        "        if col != -1:\n",
        "            plt.text(col, row, u\"\\u265B\", size=200/n, ha='center', va='center')\n",
        "    plt.axis(\"off\")\n",
        "    plt.show()"
      ],
      "metadata": {
        "id": "dpA0ZdJ57NOu"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model = cp_model.CpModel()\n",
        "\n",
        "n = 8\n",
        "queens = [model.NewIntVar(0, n-1, f\"x_{i}\") for i in range(n)]\n",
        "model.AddAllDifferent(queens)\n",
        "model.AddAllDifferent(queens[i] + i for i in range(n))\n",
        "model.AddAllDifferent(queens[i] - i for i in range(n))\n",
        "\n",
        "solver = cp_model.CpSolver()\n",
        "if solver.Solve(model) == cp_model.OPTIMAL:\n",
        "    board = [solver.Value(queens[i]) for i in range(n)]\n",
        "    showBoard(board)\n",
        "else:\n",
        "    print(\":(\")"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "_QxAaaSY1Tiv",
        "outputId": "1a808764-bb6b-4530-9357-84de40944e40"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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mAPDT8gp657Q9Mb25uqbt+Ojc+TBPAKj56BSV7x0mJzubL3p0JH0qhoI6lSsL8ykbWsDpaIzXd+4N6xXvHLzg5bVzYZ6QlZXFzyt2ADC1bARDBvTPeM1Sd2IoqNNJdQhbkzMDgFP1MXYdPgYkjo9S84R4PB7eY+iTm5vhSqXuxzea1SlNLCniM8VXtHv/yfooLa3xNFYk9QyGgjqlL02byCNfuKXd+ysOHGThq2vTV5DUQxgK6pSeWrmGp1auuajv3DB+dJqqkXoOZwqSpMBQkCQFHh+pUyobWkBJweB2769raExfMVIPYiioU/rqzKkOmqUOYCioU3r6lbUsfLX8or5z3diytNQi9SSGgjqdtY8/3NElSD2Wg2ZJUmAoSJICQ0GSFBgKkqTAUJAkBYaCJCkwFCRJgaEgSQoMBUlSYChIkgJDQZIUtPtvH53YsC2ddaRN4Q2f7egSLklXvd/gPc8073fmddV73h52CpKkwFCQJAWGgiQpMBQkSYGhIEkKDAVJUmAoSJKCDg+Ft48eZ+Gra1n11r6OLkWSerx2v7z2acXjcbZU19DU3MItE68C4GRdlC8/vZj6xiYAFj94D/OmXQ3A3vc/5MipM1w/bhT9evfKVJmS1KNlLBSefHkVz63eCMDDf3gjj905h7rGJmJN58KeY2fqACjfU82fL/pPmltbmTpyBCu/8yCR7A5vaiSp28vYb9r1+94JP//PrrcBKBtawAsP3QvAfTddy/03zQBg9e79NLe2ArDj4PucrItmqkxJ6tEyFgrf/uKtDMsbCMBf3jYrrE8cUQTA5NJiciIRAL5y7RRykp3BPddN44rk9yRJ6ZW2UPj3tVsY/+0FzP3hcxw9fZYvTJ3AikcfAKCssCDsS80TYufOh7XJpcX0ys3h0Xm38uz8uzjf0sI3l7zEpO/+kG+9+DLNLS3pKluSerS0hMLZWAN///PXqWts4q1DR1m8ZjMAg/v1BWBzdU3YW9+UDIXkv5A4Moo1nWNs0VAAyvcc4L8rdnCqPsbPNm9nTVV1OsqWpB4vLaEwoE/vcFQEcFXyl/ugvn2IZGez5UBN+Cx0Ck1tncLm/YnPRxbmAzAiPy8cJ+VGIowZVpiOsiWpx0vL00eR7GxWPPoA//abzWyvOcKfXT8dgKysLPL69aHyvSM0t7SQE4kQbUw8fRS94CmkTdXvAVA6JBEKE0uKGDOskCkjh/Pg7FmGgiSlSdpmCqVD8nnszjnsO3acfUc/DOv5/fsRazrHzkNHAahLdgqpUGhuaeHNdw8zsE9vCgb0A+DXb+1j/wcf8d0vf56rS4rSVbIk9Xhpffqob69cbhw/mkWrNoS11FxhS3Ku0DZoToRCap5Qmjw6Anj2tXJmjC5leH5eOsuVpB4v7Y+kzp0ygRVbd3Hk1BkA8vsnQqHiwEEAomHQnAiFME9IHh2t3vU2bx06yu3TJ6e7VEnq8dIeCnMmjycOPL96E5A4PgJ4451DtLa2huOjVCik5glXJjuFZ18vJzsriy9Nm5juUiWpx0t7KBQM6MeM0aUs21TJqfpY6BRqGxqpev9D6i8YNKfmCZAIhbVV1WyveZ/rxpb5ApskZUBG3mieO2UCDefO88JvKxicDAWAiuoaohcMmlPzBIArh+TzzGvlANw+fVImypSkHi9joQDw0/IKeue0PQW7ubqm7fjo3PkwTwCo+egUle8dJic7my96dCRJGZGRULiyMJ+yoQWcjsZ4fefesF7xzsELXl47F+YJWVlZ/LxiBwBTy0YwZED/TJQpST1exv4gXqpD2JqcGQCcqo+x6/AxIHF8lJonxOPx8B5Dn9zcTJUoST1exv7/FCDxZvJniq9o9/6T9VFaWuNprEiSdKGMhsKXpk3kkS/c0u79FQcOsvDVtekrSJL0MRkNhadWruGplWsu6js3jB+dpmokSf+b/x+XkqTAUJAkBRk9PiobWkBJweB2769raExfMZKk/09GQ+GrM6c6aJakTiyjofD0K2tZ+Gr5RX3nurFlaalFkvT/y1gorH384Uz9R0mSLpGDZklSYChIkgJDQZIUGAqSpMBQkCQFhoIkKTAUJEmBoSBJCgwFSVJgKEiSAkNBkhS0+28fFd7w2XTWkTYnNmzr6BIuSVe93+A9zzTvd+Z11XtePHne791jpyBJCgwFSVJgKEiSAkNBkhQYCpKkwFCQJAWGgiQpMBQkdTtVBw7y5E+W8Up5RUeX0uW0++U1Seps4vE46yt303TuPHNmJV6G++jUWW6a/zfURRsA+K+F3+PuOdcDsGt/DYeOHeeWGdfQv1+fDqu7MzMUJHVZ33vmBZ5Z8hIA33ngj1nwzfupjcaINjSFPUePnwRg1cZK7vyrJ2hubuFzk8ay/sWniUQiHVJ3Z+bxkaQu6zcVO8LPr5a/AcCY0mJ+8U/fB+Che+bx0D2JP+3w+vqtNDe3ALB1dzUfna7NbLFdhKEgqcv6/kN/SvHQAgC+dd9dYf2a8aMAmDZhDDk5iW7g3nm3hJ/vu/M2igrzM1xt12AoSOoy/nXZSgpnfZWZX3uEIx+c4I7Z17F2yVMAjC4pDvtq62MARBsaw9q0CVfROzeXx79xL4ufeITz55v5+t8+w/Cb7+XBv/tR6CJ6OkNBUpdwpraeR59aTG19jG17DvAvS38JQMGgAQCsq9wV9tYnh8z1sbZQ2Fq1n2hDI58ZXQrAqk3bWLpyDSdO17JkxWp+tWFrpi6lUzMUJHUJA/v3ZXjyqAhg/KgSAPIG9icSyWZDZVX4rC6WCIULO4XfvpkIjdElRQCUFg8Nx0m5OTmMKytJ7wV0ET59JKlLiEQirPmPf+SfX1zBG7v28/Wv/BEAWVlZ5A8awJad+2hubiEnJxIeR40mwwFg3dZEKJSNGAbANeNGMW7kCKZfPZa/nn8H48pGZPiKOic7BUldRtmIYSx45H6qDhxkd3VNWC/IG0S0oZHKqmoA6qKJmUJ9slNobm5h0/a9DBrQjyGDBwGwcm0Fe989zD88PJ8p40dn9kI6MUNBUpfSt09vZs+cysIXfhHWCvISc4X1lbsB2jqFZCik5gmpLgFgwfPLmTV1AiVFhZkqvUswFCR1OXfMnsnPfrWOQ8eOA1CQNxCADdsSc4W246NEKKTmCaOS84TX1r3Jtj0H+JO5N2a07q7AUJDU5cy7+Vri8Tg/WvIy0BYKG7fvobW1ldroxx9JTc0TRiU7hQXPLSc7O5u759yQ6dI7PUNBUpczZPAgZk2dyE9fWsXJM7UMGZwIhbN1UXa+/d7HHklNzRMg0Sn8ekMlb+7ez03TJ/kC2ycwFCR1SbfPnkmssYlFy18hP9kpAGyo3N02aI41hHkCJAfVzy8H8OjodzAUJHVJt986E4BFy1+hT69eYX1d5W5qk51CrKEpzBMA3j38AVt27iMnJ8Jdt83KbMFdhKEgqUsaVVLEmNJiTp6p5ZdrNof1jduqqKtv6xRS84SsrCyWrlwDwIxJ4yjMz8t80V2AoSCpy+rdKxeAzTv2hrUTp2vZvu8dIDFTSM0T4vF4eI+hb+9e6JP5RrOkLu2a8aO4+qqR7d5/4vRZWlpa01hR12YoSOrS7p5zPY/9xdfavX/jtiqe/MmyNFbUtRkKkrq0H/x4KT/48dKL+s7sP5iSpmq6PmcKkqTAUJAkBR4fSerSxpQWM3L4Fe3efzb5uKo+maEgqUubf8fnHTRfRoaCpC7tiUXLLvqX/M2fm5ymaro+Q0FSl7Xj5UUdXUK346BZkhQYCpKkwFCQJAWGgiQpMBQkSYGhIEkKDAVJUmAoSJICQ0GSFBgKkqTAUJAkBe3+20cnNmxLZx1pU3jDZzu6hEvSVe83eM8zzfudeV31nreHnYIkKTAUJEmBoSBJCgwFSVJgKEiSAkNBkhQYCpKkwFCQ0uzto8dZ+OpaVr21r6NLkX6vdr+8Jun/Fo/H2VJdQ1NzC7dMvAqAk3VRvvz0YuobmwBY/OA9zJt2NQB73/+QI6fOcP24UfTr3avD6pYuZChIl8mTL6/iudUbAXj4D2/ksTvnUNfYRKzpXNhz7EwdAOV7qvnzRf9Jc2srU0eOYOV3HiSSbeOujud/C6XLZP2+d8LP/7PrbQDKhhbwwkP3AnDfTddy/00zAFi9ez/Nra0A7Dj4PifrohmuVvpkhoJ0mXz7i7cyLG8gAH9526ywPnFEEQCTS4vJiUQA+Mq1U8hJdgb3XDeNK5LfkzqaoSBdon9fu4Xx317A3B8+x9HTZ/nC1AmsePQBAMoKC8K+1Dwhdu58WJtcWkyv3BwenXcrz86/i/MtLXxzyUtM+u4P+daLL9Pc0pLZi5GSDAXpEpyNNfD3P3+dusYm3jp0lMVrNgMwuF9fADZX14S99U3JUEj+C4kjo1jTOcYWDQWgfM8B/rtiB6fqY/xs83bWVFVn6EqkjzMUpEswoE/vcFQEcFXyl/ugvn2IZGez5UBN+Cx0Ck1tncLm/YnPRxbmAzAiPy8cJ+VGIowZVpjO8qXfyaePpEsQyc5mxaMP8G+/2cz2miP82fXTAcjKyiKvXx8q3ztCc0sLOZEI0cbE00fRC55C2lT9HgClQxKhMLGkiDHDCpkycjgPzp5lKKjD2ClIl6h0SD6P3TmHfceOs+/oh2E9v38/Yk3n2HnoKAB1yU4hFQrNLS28+e5hBvbpTcGAfgD8+q197P/gI7775c9zdUlRhq9EamMoSJ9C31653Dh+NItWbQhrqbnCluRcoW3QnAiF1DyhNHl0BPDsa+XMGF3K8Py8DFUufTJDQfqU5k6ZwIqtuzhy6gwA+f0ToVBx4CAA0TBoToRCmCckj45W73qbtw4d5fbpkzNYtfTJDAXpU5ozeTxx4PnVm4DE8RHAG+8corW1NRwfpUIhNU+4MtkpPPt6OdlZWXxp2sQMVy79/wwF6VMqGNCPGaNLWbapklP1sdAp1DY0UvX+h9RfMGhOzRMgEQprq6rZXvM+140t8wU2dQqGgnQZzJ0ygYZz53nhtxUMToYCQEV1DdELBs2peQLAlUPyeea1cgBunz4p4zVLn8RQkC6DuVMmAPDT8gp657Q96b25uqbt+Ojc+TBPAKj56BSV7x0mJzubL3p0pE7CUJAugysL8ykbWsDpaIzXd+4N6xXvHLzg5bVzYZ6QlZXFzyt2ADC1bARDBvTPeM3SJzEUpMsk1SFsTc4MAE7Vx9h1+BiQOD5KzRPi8Xh4j6FPbm6GK5V+N99oli6jiSVFfKb4inbvP1kfpaU1nsaKpItjKEiX0ZemTeSRL9zS7v0VBw6y8NW16StIukiGgnQZPbVyDU+tXHNR37lh/Og0VSNdPGcKkqTAUJAkBR4fSZdR2dACSgoGt3t/XUNj+oqRLoGhIF1GX5051UGzujRDQbqMnn5lLQtfLb+o71w3tiwttUiXwlCQLpO1jz/c0SVIn5qDZklSYChIkgJDQZIUGAqSpMBQkCQFhoIkKTAUJEmBoSBJCgwFSVJgKEiSAkNBkhS0+28fFd7w2XTWkTYnNmzr6BIuSVe93+A9zzTvd+Z11XtePHne791jpyBJCgwFSVJgKEiSAkNBkhQYCpKkwFCQJAWGgiQpMBR6oKoDB3nyJ8t4pbyio0uR1Mm0++U1dT3xeJz1lbtpOneeObMSLwp9dOosN83/G+qiDQD818Lvcfec6wHYtb+GQ8eOc8uMa+jfr0+H1S2p4xgK3dj3nnmBZ5a8BMB3HvhjFnzzfmqjMaINTWHP0eMnAVi1sZI7/+oJmptb+Nyksax/8WkikUiH1C2p43h81I39pmJH+PnV8jcAGFNazC/+6fsAPHTPPB66J/Ha++vrt9Lc3ALA1t3VfHS6NrPFSuoUDIVu7PsP/SnFQwsA+NZ9d4X1a8aPAmDahDHk5CS6gXvn3RJ+vu/O2ygqzM9wtZI6A0OhG/nXZSspnPVVZn7tEY58cII7Zl/H2iVPATC6pDjsq62PARBtaAxr0yZcRe/cXB7/xr0sfuIRzp9v5ut/+wzDb76XB//uR6GLkNS9GQrdxJnaeh59ajG19TG27TnAvyz9JQAFgwYAsK5yV9hbnxwy18faQmFr1X6iDY18ZnQpAKs2bWPpyjWcOF3LkhWr+dWGrZm6FEkdyFDoJgb278vw5FERwPhRJQDkDexPJJLNhsqq8FldLBEKF3YKv30zERqjS4oAKC0eGo6TcnNyGFdWkt4LkNQp+PRRNxGJRFjzH//IP7+4gjd27efrX/kjALKyssgfNIAtO/fR3NxCTk4kPI4aTYYDwLqtiVAoGzEMgGvGjWLcyBFMv3osfz3/DsaVjcjwFUnqCHYK3UjZiGEseOR+qg4cZHd1TVgvyBtEtKGRyqpqAOqiiZlCfbJTaG5uYdP2vQwa0I8hgwcBsHJtBXvfPcw/PDyfKeNHZ/ZCJHUYQ6Gb6dunN7NnTmXhC78IawV5ibnC+srdAG2dQjIUUvOEVJcAsOD55cyaOoGSosJMlS6pEzAUuqE7Zs/kZ79ax6FjxwEoyBsIwIZtiblC2/FRIhRS84RRyXnCa+veZNueA/zJ3BszWrekjmcodEPzbr6WeDzOj5a8DLSFwsbte2htbaU2+vFHUlPzhFHJTmHBc8vJzs7m7jk3ZLp0SR3MUOiGhgwexKypE/npS6s4eaaWIYMToXC2LsrOt9/72COpqXkCJDqFX2+o5M3d+7lp+iRfYJN6IEOhm7p99kxijU0sWv4K+clOAWBD5e62QXOsIcwTIDmofn45gEdHUg9lKHRTt986E4BFy1+hT69eYX1d5W5qk51CrKEpzBMA3j38AVt27iMnJ8Jdt83KbMGSOgVDoZsaVVLEmNJiTp6p5ZdrNof1jduqqKtv6xRS84SsrCyWrlwDwIxJ4yjMz8t80ZI6nKHQjfXulQvA5h17w9qJ07Vs3/cOkJgppOYJ8Xg8vMfQt3cvJPVMvtHczV0zfhRXXzWy3ftPnD5LS0trGiuS1JkZCt3c3XOu57G/+Fq792/cVsWTP1mWxookdWaGQjf3gx8v5Qc/XnpR35n9B1PSVI2kzs6ZgiQpMBQkSYHHR93cmNJiRg6/ot37zyYfV5XUMxkK3dz8Oz7voFlSuxkK3dwTi5Zd9C/5mz83OU3VSOrsDIVubMfLizq6BEldjINmSVJgKEiSAkNBkhQYCpKkwFCQJAWGgiQpMBQkSYGhIEkKDAVJUmAoSJICQ0GSFBgKkqSg3X8Q78SGbemsI20Kb/hsR5dwSbrq/QbveaZ5vzOvq97z9rBTkCQFhoIkKTAUJEmBoSBJCgwFSVJgKEiSAkNB0ieqOnCQJ3+yjFfKKzq6FGVQu99TkNQ9xeNx1lfupunceebMSjx//9Gps9w0/2+oizYA8F8Lv8fdc64HYNf+Gg4dO84tM66hf78+HVa30sNQkHq47z3zAs8seQmA7zzwxyz45v3URmNEG5rCnqPHTwKwamMld/7VEzQ3t/C5SWNZ/+LTRCKRDqlb6eHxkdTD/aZiR/j51fI3ABhTWswv/un7ADx0zzweumceAK+v30pzcwsAW3dX89Hp2swWq7QzFKQe7vsP/SnFQwsA+NZ9d4X1a8aPAmDahDHk5CS6gXvn3RJ+vu/O2ygqzM9wtUo3Q0HqYf512UoKZ32VmV97hCMfnOCO2dexdslTAIwuKQ77autjAEQbGsPatAlX0Ts3l8e/cS+Ln3iE8+eb+frfPsPwm+/lwb/7Uegi1HUZClIPcqa2nkefWkxtfYxtew7wL0t/CUDBoAEArKvcFfbWJ4fM9bG2UNhatZ9oQyOfGV0KwKpN21i6cg0nTteyZMVqfrVha6YuRWliKEg9yMD+fRmePCoCGD+qBIC8gf2JRLLZUFkVPquLJULhwk7ht28mQmN0SREApcVDw3FSbk4O48pK0nsBSjufPpJ6kEgkwpr/+Ef++cUVvLFrP1//yh8BkJWVRf6gAWzZuY/m5hZyciLhcdRoMhwA1m1NhELZiGEAXDNuFONGjmD61WP56/l3MK5sRIavSJebnYLUw5SNGMaCR+6n6sBBdlfXhPWCvEFEGxqprKoGoC6amCnUJzuF5uYWNm3fy6AB/RgyeBAAK9dWsPfdw/zDw/OZMn50Zi9EaWEoSD1Q3z69mT1zKgtf+EVYK8hLzBXWV+4GaOsUkqGQmiekugSABc8vZ9bUCZQUFWaqdKWZoSD1UHfMnsnPfrWOQ8eOA1CQNxCADdsSc4W246NEKKTmCaOS84TX1r3Jtj0H+JO5N2a0bqWXoSD1UPNuvpZ4PM6PlrwMtIXCxu17aG1tpTb68UdSU/OEUclOYcFzy8nOzubuOTdkunSlkaEg9VBDBg9i1tSJ/PSlVZw8U8uQwYlQOFsXZefb733skdTUPAESncKvN1Ty5u793DR9ki+wdTOGgtSD3T57JrHGJhYtf4X8ZKcAsKFyd9ugOdYQ5gmQHFQ/vxzAo6NuyFCQerDbb50JwKLlr9CnV6+wvq5yN7XJTiHW0BTmCQDvHv6ALTv3kZMT4a7bZmW2YKWdoSD1YKNKihhTWszJM7X8cs3msL5xWxV19W2dQmqekJWVxdKVawCYMWkchfl5mS9aaWUoSD1c7165AGzesTesnThdy/Z97wCJmUJqnhCPx8N7DH1790Ldj280S+Ka8aO4+qqR7d5/4vRZWlpa01iROoqhIIm751zPY3/xtXbv37itiid/siyNFamjGAqS+MGPl/KDHy+9qO/M/oMpaapGHcmZgiQpMBQkSYHHR5IYU1rMyOFXtHv/2eTjqup+DAVJzL/j8w6aBRgKkoAnFi276F/yN39ucpqqUUcyFKQebsfLizq6BHUiDpolSYGhIEkKDAVJUmAoSJICQ0GSFBgKkqTAUJAkBYaCJCkwFCRJgaEgSQoMBUlSYChIkoKseDwe7+giJEmdg52CJCkwFCRJgaEgSQoMBUlSYChIkgJDQZIUGAqSpMBQkCQFhoIkKfh/oYV30/tuXo4AAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "mySeN4lA43S6"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}