#!/usr/bin/env python3

# Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
#
# 21 22 23 24 25
# 20  7  8  9 10
# 19  6  1  2 11
# 18  5  4  3 12
# 17 16 15 14 13
#
# It can be verified that the sum of the numbers on the diagonals is 101.
#
# What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?

from projecteuler import timing


@timing
def p028() -> None:
    N = 1001

    limit = N * N

    i = 0
    j = 1
    step = 0
    _sum = 1

    # Starting with the central 1, it's easy to see that the next four numbers in the diagonal
    # are 1+2, 1+2+2, 1+2+2+2 and 1+2+2+2+2, then for the next four number the step is increased
    # by two, so from 9 to 9+4, 9+4+4 etc, for the next four number the step is again increased
    # by two, and so on. We go on until the value is equal to N*N, with N=1001 for this problem.
    while j < limit:
        if i == 0:
            step = step + 2
        j = j + step
        _sum = _sum + j
        i = (i + 1) % 4

    print('Project Euler, Problem 28')
    print(f'Answer: {_sum}')


if __name__ == '__main__':
    p028()