#!/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()}")