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37 lines
1.0 KiB
Python
37 lines
1.0 KiB
Python
"""
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The number of partitions of a number n into at least k parts equals the number of partitions into exactly k parts
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plus the number of partitions into at least k-1 parts. Subtracting 1 from each part of a partition of n into k parts
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gives a partition of n-k into k parts. These two facts together are used for this algorithm.
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"""
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def partition(m):
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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 > 0:
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memo[n][k] += memo[n - k - 1][k]
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return memo[m][m - 1]
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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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try:
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n = int(input("Enter a number: ").strip())
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print(partition(n))
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except ValueError:
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print("Please enter a number.")
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else:
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try:
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n = int(sys.argv[1])
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print(partition(n))
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except ValueError:
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print("Please pass a number.")
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