Python/project_euler/problem_02/sol4.py

"""
Problem:
Each new term in the Fibonacci sequence is generated by adding the previous two
terms. By starting with 1 and 2, the first 10 terms will be:

    1,2,3,5,8,13,21,34,55,89,..

By considering the terms in the Fibonacci sequence whose values do not exceed
n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
10.
"""
from __future__ import print_function
import math
from decimal import *

try:
    raw_input  # Python 2
except NameError:
    raw_input = input  # Python 3


def solution(n):
    """Returns the sum of all fibonacci sequence even elements that are lower
    or equals to n.
    
    >>> solution(10)
    10
    >>> solution(15)
    10
    >>> solution(2)
    2
    >>> solution(1)
    0
    >>> solution(34)
    44
    """
    getcontext().prec = 100
    phi = (Decimal(5) ** Decimal(0.5) + 1) / Decimal(2)

    index = (math.floor(math.log(n * (phi + 2), phi) - 1) // 3) * 3 + 2
    num = Decimal(round(phi ** Decimal(index + 1))) / (phi + 2)
    sum = num // 2
    return int(sum)


if __name__ == "__main__":
    print(solution(int(raw_input().strip())))