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* Rename all Project Euler directories: Reason: The change was done to maintain consistency throughout the directory and to keep all directories in sorted order. Due to the above change, some config files had to be modified: 'problem_22` -> `problem_022` * Update scripts to pad zeroes in PE directories
45 lines
1.1 KiB
Python
45 lines
1.1 KiB
Python
"""
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Problem 15: https://projecteuler.net/problem=15
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Starting in the top left corner of a 2×2 grid, and only being able to move to
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the right and down, there are exactly 6 routes to the bottom right corner.
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How many such routes are there through a 20×20 grid?
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"""
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from math import factorial
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def solution(n: int = 20) -> int:
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"""
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Returns the number of paths possible in a n x n grid starting at top left
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corner going to bottom right corner and being able to move right and down
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only.
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>>> solution(25)
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126410606437752
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>>> solution(23)
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8233430727600
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>>> solution(20)
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137846528820
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>>> solution(15)
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155117520
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>>> solution(1)
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2
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"""
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n = 2 * n # middle entry of odd rows starting at row 3 is the solution for n = 1,
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# 2, 3,...
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k = n / 2
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return int(factorial(n) / (factorial(k) * factorial(n - k)))
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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(solution(20))
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else:
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try:
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n = int(sys.argv[1])
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print(solution(n))
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except ValueError:
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print("Invalid entry - please enter a number.")
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