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56 lines
1.2 KiB
Python
56 lines
1.2 KiB
Python
"""
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Starting with the number 1 and moving to the right in a clockwise direction a 5
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by 5 spiral is formed as follows:
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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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It can be verified that the sum of the numbers on the diagonals is 101.
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What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed
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in the same way?
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"""
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from math import ceil
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def diagonal_sum(n):
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"""Returns the sum of the numbers on the diagonals in a n by n spiral
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formed in the same way.
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>>> diagonal_sum(1001)
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669171001
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>>> diagonal_sum(500)
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82959497
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>>> diagonal_sum(100)
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651897
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>>> diagonal_sum(50)
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79697
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>>> diagonal_sum(10)
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537
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"""
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total = 1
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for i in range(1, int(ceil(n / 2.0))):
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odd = 2 * i + 1
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even = 2 * i
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total = total + 4 * odd ** 2 - 6 * even
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return total
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if __name__ == "__main__":
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import sys
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if len(sys.argv) == 1:
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print(diagonal_sum(1001))
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else:
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try:
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n = int(sys.argv[1])
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print(diagonal_sum(n))
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except ValueError:
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print("Invalid entry - please enter a number")
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