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added doctests for dynamicprogramming/minimum_partition (#10033)

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* added doctests

* added doctests

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* Add doctests to integer_partition.py

* Update minimum_partition.py

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This commit is contained in:
SalmanSi
2023-10-13 22:48:31 +05:00
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parent 1117a50665
commit d96029e13d
2 changed files with 57 additions and 5 deletions
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dynamic_programming/integer_partition.py
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@ -3,10 +3,34 @@ The number of partitions of a number n into at least k parts equals the number o
partitions into exactly k parts plus the number of partitions into at least k-1 parts.
Subtracting 1 from each part of a partition of n into k parts gives a partition of n-k
into k parts. These two facts together are used for this algorithm.
* https://en.wikipedia.org/wiki/Partition_(number_theory)
* https://en.wikipedia.org/wiki/Partition_function_(number_theory)
"""
def partition(m: int) -> int:
"""
>>> partition(5)
7
>>> partition(7)
15
>>> partition(100)
190569292
>>> partition(1_000)
24061467864032622473692149727991
>>> partition(-7)
Traceback (most recent call last):
...
IndexError: list index out of range
>>> partition(0)
Traceback (most recent call last):
...
IndexError: list assignment index out of range
>>> partition(7.8)
Traceback (most recent call last):
...
TypeError: 'float' object cannot be interpreted as an integer
"""
memo: list[list[int]] = [[0 for _ in range(m)] for _ in range(m + 1)]
for i in range(m + 1):
memo[i][0] = 1