mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-24 13:31:07 +00:00
56 lines
1.2 KiB
Python
56 lines
1.2 KiB
Python
"""
|
|
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 math import ceil
|
|
|
|
|
|
def diagonal_sum(n):
|
|
"""Returns the sum of the numbers on the diagonals in a n by n spiral
|
|
formed in the same way.
|
|
|
|
>>> diagonal_sum(1001)
|
|
669171001
|
|
>>> diagonal_sum(500)
|
|
82959497
|
|
>>> diagonal_sum(100)
|
|
651897
|
|
>>> diagonal_sum(50)
|
|
79697
|
|
>>> diagonal_sum(10)
|
|
537
|
|
"""
|
|
total = 1
|
|
|
|
for i in range(1, int(ceil(n / 2.0))):
|
|
odd = 2 * i + 1
|
|
even = 2 * i
|
|
total = total + 4 * odd ** 2 - 6 * even
|
|
|
|
return total
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import sys
|
|
|
|
if len(sys.argv) == 1:
|
|
print(diagonal_sum(1001))
|
|
else:
|
|
try:
|
|
n = int(sys.argv[1])
|
|
print(diagonal_sum(n))
|
|
except ValueError:
|
|
print("Invalid entry - please enter a number")
|