Solution to problem 57

src/Python/Problem057.py

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+#!/usr/bin/env python3
+"""
+Created on 09 Oct 2021
+
+@author: David Doblas Jiménez
+@email: daviddoji@pm.me
+
+Solution for problem 57 of Project Euler
+https://projecteuler.net/problem=57
+"""
+
+from fractions import Fraction
+from utils import timeit
+
+
+@timeit("Problem 57")
+def compute():
+    """
+    It is possible to show that the square root of two can be expressed 
+    as an infinite continued fraction.
+
+    By expanding this for the first four iterations, we get:
+
+        1 +  1/2 = 3/2 = 1.5
+        1 + 1/2+1/2 = 7/5 = 1.4
+        1 + 1/2+1/2+1/2 = 17/12 = 1.41666...
+        1 + 1/2+1/2+1/2+1/2 = 41/29 = 1.41379...
+
+    The next three expansions are 99/70, 239/169, and 577/408, but the eighth 
+    expansion, 1393/985, is the first example where the number of digits in 
+    the numerator exceeds the number of digits in the denominator.
+
+    In the first one-thousand expansions, how many fractions contain a numerator 
+    with more digits than the denominator?
+    """
+
+    ans = 0
+    f = Fraction(1, 2)
+    for i in range(1000):
+        f = 1 / (2 + f)
+        result = 1 + f
+        if len(str(result.numerator)) > len(str(result.denominator)):
+            ans += 1
+    
+    return ans
+
+
+if __name__ == "__main__":
+
+    print(f"Result for Problem 57: {compute()}")