From b0ed9372341558460be73707dc88c3a350ad25ff Mon Sep 17 00:00:00 2001
From: AVerzier <46388943+AVerzier@users.noreply.github.com>
Date: Thu, 12 Sep 2019 20:20:59 +0200
Subject: [PATCH 1/3] Use randint, for loops and python 3 "print" function

---
 frog-2.py | 38 --------------------------------------
 frog.py   | 27 +++++++++++++++++++++++++++
 2 files changed, 27 insertions(+), 38 deletions(-)
 delete mode 100644 frog-2.py
 create mode 100644 frog.py

diff --git a/frog-2.py b/frog-2.py
deleted file mode 100644
index c0b0eec..0000000
--- a/frog-2.py
+++ /dev/null
@@ -1,38 +0,0 @@
-def frog(final_dist=100,max=6):
-    
-    # I wrote this quickly in a pub
-    # Don't judge me
-    
-    total_dist = 1
-    
-    while total_dist <= final_dist:
-        
-        import random
-        
-        cap = 10**max
-        
-        trials = 0
-        total_leaps = 0
-        
-        while trials <= cap:
-            
-            dist = total_dist
-            leaps = 0
-            
-            while dist > 0:
-                this_jump = int(random.random()*(dist)+1)
-                dist -= this_jump
-                leaps += 1
-                
-            total_leaps += leaps
-            
-            trials += 1
-            
-        print "{0}\t{1}".format(total_dist,(total_leaps*1.0)/trials)
-    
-        total_dist += 1
-    
-    return "DONE"
-            
-    
-    
\ No newline at end of file
diff --git a/frog.py b/frog.py
new file mode 100644
index 0000000..c991afc
--- /dev/null
+++ b/frog.py
@@ -0,0 +1,27 @@
+from random import randint
+
+
+def frog(final_dist=100, cap=10**3):
+
+    # I wrote this quickly in a pub
+    # Don't judge me
+
+    for total_dist in range(final_dist+1):
+
+        total_leaps = 0
+
+        for _ in range(cap):
+
+            dist = total_dist
+            leaps = 0
+
+            while dist > 0:
+                this_jump = randint(1, dist)
+                dist -= this_jump
+                leaps += 1
+
+            total_leaps += leaps
+
+        print(f"Total distance : {total_dist} -> Average number of leaps : {total_leaps/cap}")
+
+    return "DONE"

From 3531b523aaa564d3dd75f5c1e71d702cbb91b791 Mon Sep 17 00:00:00 2001
From: AVerzier <46388943+AVerzier@users.noreply.github.com>
Date: Thu, 12 Sep 2019 22:01:32 +0200
Subject: [PATCH 2/3] Use numpy arrays, plot the results

---
 frog.py | 69 ++++++++++++++++++++++++++++++++++++++++++++-------------
 1 file changed, 53 insertions(+), 16 deletions(-)

diff --git a/frog.py b/frog.py
index c991afc..4f80c12 100644
--- a/frog.py
+++ b/frog.py
@@ -1,27 +1,64 @@
-from random import randint
 
+import numpy as np
+import matplotlib.pyplot as plt
 
-def frog(final_dist=100, cap=10**3):
 
-    # I wrote this quickly in a pub
-    # Don't judge me
+randomGenerator = np.random.default_rng()  # Require numpy v1.17+
 
-    for total_dist in range(final_dist+1):
 
-        total_leaps = 0
+ite = 1000  # Number of loops for the average
+maxDistance = 1000
 
-        for _ in range(cap):
 
-            dist = total_dist
-            leaps = 0
+totalDist = np.arange(1, maxDistance)
 
-            while dist > 0:
-                this_jump = randint(1, dist)
-                dist -= this_jump
-                leaps += 1
+randomLeap = np.empty_like(totalDist)
+totalLeaps = np.zeros_like(totalDist)
 
-            total_leaps += leaps
+for i in range(ite):
 
-        print(f"Total distance : {total_dist} -> Average number of leaps : {total_leaps/cap}")
+    print(f" - Iteration {i+1}/{ite}", end="\r")
 
-    return "DONE"
+    distLeft = totalDist.copy()
+
+    leaps = np.zeros_like(totalDist)
+
+    stillLeaping = np.ones_like(totalDist, dtype=bool)
+
+    while np.any(stillLeaping):
+
+        randomLeap[stillLeaping] = randomGenerator.integers(
+            1, distLeft[stillLeaping], endpoint=True)
+
+        np.subtract(distLeft, randomLeap, where=stillLeaping, out=distLeft)
+
+        leaps[stillLeaping] += 1
+
+        stillLeaping[distLeft == 0] = False  # Arrived at the end
+
+    np.add(totalLeaps, leaps, out=totalLeaps)
+
+print()
+
+averageLeaps = totalLeaps/ite
+
+A, B = np.polyfit(np.log(totalDist), averageLeaps, 1)
+
+print(f"Average number of leaps ≈ {A:.5}*ln(Total distance)+{B:.5}")
+
+plt.plot(totalDist, A*np.log(totalDist)+B, linewidth=2, label=f"y≈{A:.5}*ln(x)+{B:.5}")
+
+plt.scatter(totalDist, averageLeaps, s=2, marker="*", color="green")
+
+plt.grid(True)
+
+# plt.xscale("symlog")
+
+plt.xlabel("Total distance")
+plt.ylabel("Leaps")
+
+plt.legend()
+
+plt.title("Average number of leaps")
+
+plt.show()

From 54049579434990788585e084935551837174c7bb Mon Sep 17 00:00:00 2001
From: AVerzier <46388943+AVerzier@users.noreply.github.com>
Date: Thu, 12 Sep 2019 22:06:28 +0200
Subject: [PATCH 3/3] Update README.md

---
 README.md | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/README.md b/README.md
index fda46c1..a746b50 100644
--- a/README.md
+++ b/README.md
@@ -1,6 +1,6 @@
 # frog_problem
-Here is the frog problem code I wrote in an Edinburgh pub.
 
-Feel free to make better version. This one has not changed since I wrote it. V1 was the same code but saved before I changed it to work for different distances so I have not bothered upload it as well (it was still very unifinished).
+It uses numpy arrays to simulate multiple frogs.
+The answer to how many jumps the frog needs to do to reach the end is quite clear :)
 
-Video is here: https://youtu.be/ZLTyX4zL2Fc
+Original Video is here: https://youtu.be/ZLTyX4zL2Fc