Python/project_euler/problem_015/sol1.py

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"""
Problem 15: https://projecteuler.net/problem=15
Starting in the top left corner of a 2×2 grid, and only being able to move to
the right and down, there are exactly 6 routes to the bottom right corner.
How many such routes are there through a 20×20 grid?
"""
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from math import factorial
def solution(n: int = 20) -> int:
"""
Returns the number of paths possible in a n x n grid starting at top left
corner going to bottom right corner and being able to move right and down
only.
>>> solution(25)
126410606437752
>>> solution(23)
8233430727600
>>> solution(20)
137846528820
>>> solution(15)
155117520
>>> solution(1)
2
"""
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n = 2 * n # middle entry of odd rows starting at row 3 is the solution for n = 1,
# 2, 3,...
k = n // 2
return int(factorial(n) / (factorial(k) * factorial(n - k)))
if __name__ == "__main__":
import sys
if len(sys.argv) == 1:
print(solution(20))
else:
try:
n = int(sys.argv[1])
print(solution(n))
except ValueError:
print("Invalid entry - please enter a number.")