#!/usr/bin/env python
"""
Created on 01 Jan 2018

@author: David Doblas Jiménez
@email: daviddoji@pm.me

Solution for problem 12 of Project Euler
https://projecteuler.net/problem=12
"""

from itertools import count
from math import floor, sqrt

from utils import timeit


# Returns the number of integers in the range [1, n] that divide n.
def num_divisors(n):
    end = floor(sqrt(n))
    divs = []
    for i in range(1, end + 1):
        if n % i == 0:
            divs.append(i)
    if end**2 == n:
        divs.pop()
    return 2 * len(divs)


@timeit("Problem 12")
def compute():
    """
    The sequence of triangle numbers is generated by adding the natural
    numbers. So the 7th triangle number would be:
    1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.

    The first ten terms would be:
    1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

    Let us list the factors of the first seven triangle numbers:

     1: 1
     3: 1,3
     6: 1,2,3,6
    10: 1,2,5,10
    15: 1,3,5,15
    21: 1,3,7,21
    28: 1,2,4,7,14,28

    We can see that 28 is the first triangle number to have over five divisors.

    What is the value of the first triangle number to have over five hundred
    divisors?
    """

    triangle = 0
    for i in count(1):
        # This is the ith triangle number, i.e. num = 1 + 2 + ... + i =
        # = i*(i+1)/2
        triangle += i
        if num_divisors(triangle) > 500:
            return str(triangle)


if __name__ == "__main__":
    print(f"Result for Problem 12 is {compute()}")