51 lines
1.2 KiB
Python
51 lines
1.2 KiB
Python
#!/usr/bin/env python3
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# Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
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#
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# 21 22 23 24 25
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# 20 7 8 9 10
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# 19 6 1 2 11
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# 18 5 4 3 12
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# 17 16 15 14 13
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#
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# It can be verified that the sum of the numbers on the diagonals is 101.
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#
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# What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
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from timeit import default_timer
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def main():
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start = default_timer()
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N = 1001
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limit = N * N
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i = 0
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j = 1
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step = 0
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sum_ = 1
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# Starting with the central 1, it's easy to see that the next four numbers in the diagonal
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# 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
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# by two, so from 9 to 9+4, 9+4+4 etc, for the next four number the step is again increased
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# by two, and so on. We go on until the value is equal to N*N, with N=1001 for this problem.
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while j < limit:
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if i == 0:
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step = step + 2
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j = j + step
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sum_ = sum_ + j
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i = (i + 1) % 4
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end = default_timer()
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print('Project Euler, Problem 28')
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print(f'Answer: {sum_}')
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print(f'Elapsed time: {end - start:.9f} seconds')
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if __name__ == '__main__':
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main()
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