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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
56 lines
1.1 KiB
Python
56 lines
1.1 KiB
Python
"""
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Counting Summations
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Problem 76: https://projecteuler.net/problem=76
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It is possible to write five as a sum in exactly six different ways:
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4 + 1
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3 + 2
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3 + 1 + 1
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2 + 2 + 1
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2 + 1 + 1 + 1
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1 + 1 + 1 + 1 + 1
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How many different ways can one hundred be written as a sum of at least two
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positive integers?
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"""
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def solution(m: int = 100) -> int:
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"""
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Returns the number of different ways the number m can be written as a
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sum of at least two positive integers.
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>>> solution(100)
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190569291
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>>> solution(50)
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204225
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>>> solution(30)
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5603
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>>> solution(10)
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41
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>>> solution(5)
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6
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>>> solution(3)
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2
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>>> solution(2)
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1
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>>> solution(1)
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0
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"""
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memo = [[0 for _ in range(m)] for _ in range(m + 1)]
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for i in range(m + 1):
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memo[i][0] = 1
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for n in range(m + 1):
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for k in range(1, m):
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memo[n][k] += memo[n][k - 1]
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if n > k:
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memo[n][k] += memo[n - k - 1][k]
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return memo[m][m - 1] - 1
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if __name__ == "__main__":
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print(solution(int(input("Enter a number: ").strip())))
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