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* added doctests * added doctests * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Add doctests to integer_partition.py * Update minimum_partition.py --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com>
62 lines
1.7 KiB
Python
62 lines
1.7 KiB
Python
"""
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The number of partitions of a number n into at least k parts equals the number of
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partitions into exactly k parts plus the number of partitions into at least k-1 parts.
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Subtracting 1 from each part of a partition of n into k parts gives a partition of n-k
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into k parts. These two facts together are used for this algorithm.
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* https://en.wikipedia.org/wiki/Partition_(number_theory)
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* https://en.wikipedia.org/wiki/Partition_function_(number_theory)
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"""
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def partition(m: int) -> int:
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"""
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>>> partition(5)
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7
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>>> partition(7)
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15
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>>> partition(100)
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190569292
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>>> partition(1_000)
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24061467864032622473692149727991
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>>> partition(-7)
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Traceback (most recent call last):
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...
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IndexError: list index out of range
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>>> partition(0)
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Traceback (most recent call last):
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...
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IndexError: list assignment index out of range
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>>> partition(7.8)
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Traceback (most recent call last):
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...
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TypeError: 'float' object cannot be interpreted as an integer
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"""
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memo: list[list[int]] = [[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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