pb14

Author: EISAWESOME

README.md

@@ -206,4 +206,15 @@ Given an integer k and a string s, find the length of the longest substring that
 For example, given s = "abcba" and k = 2, the longest substring with k distinct characters is "bcb".
 
 ### Solution
-[JS](pb13/answer.js) (10:47)
+[JS](pb13/answer.js) (10:47)
+
+---
+
+## 14
+> This problem was asked by Google.
+
+The area of a circle is defined as `πr²`. Estimate `π` to 3 decimal places using a Monte Carlo method.
+Hint: The basic equation of a circle is `x² + y² = r²`.
+
+### Solution
+[Python](pb14/answer.py) (19:37)

pb14/Problem.md

@@ -0,0 +1,4 @@
+> This problem was asked by Google.
+
+The area of a circle is defined as `πr²`. Estimate `π` to 3 decimal places using a Monte Carlo method.
+Hint: The basic equation of a circle is `x² + y² = r²`.

pb14/answer.py

@@ -0,0 +1,32 @@
+#!/usr/bin/env python3
+# Time : 19:37
+
+import math
+from random import random
+from PIL import Image
+from PIL import ImageDraw
+
+# Square area = (2r)²
+# Circle area = π * r²
+# Cirle-Square area ratio = π / 4
+# So if you pick K random points in the square,  K * π / 4 should be inside the circle
+# With L being the number of points inside the circle, whe have
+# π = 4M / K
+def approx_pi(nb_trials):
+    inside_circle = 0
+    img = Image.new('RGB', (500, 500), "white")
+    draw = ImageDraw.Draw(img)        
+    for _ in range(nb_trials):
+
+      # Picks point at random in a 1 x 1 square
+        x = random()
+        y = random()
+        # If the picked point lands in a r=1 circle
+        if math.hypot(x, y) < 1:          
+            inside_circle +=1
+            draw.point((int(x * 500), int(y * 500)), fill="blue")
+    img.save('pi.png')
+    print('π is approx.: ', round((4.0 * inside_circle / nb_trials), 3))
+
+
+approx_pi(10**6)