Function partition

dynamic_programming/integer_partition.py:11–44

>>> 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) Traceba

(m: int)

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

    for n in range(m + 1):
        for k in range(1, m):
            memo[n][k] += memo[n][k - 1]
            if n - k > 0:
                memo[n][k] += memo[n - k - 1][k]

    return memo[m][m - 1]


if __name__ == "__main__":