Python/dynamic_programming/minimum_partition.py

"""
Partition a set into two subsets such that the difference of subset sums is minimum
"""


def find_min(numbers: list[int]) -> int:
    """
    >>> find_min([1, 2, 3, 4, 5])
    1
    >>> find_min([5, 5, 5, 5, 5])
    5
    >>> find_min([5, 5, 5, 5])
    0
    >>> find_min([3])
    3
    >>> find_min([])
    0
    >>> find_min([1, 2, 3, 4])
    0
    >>> find_min([0, 0, 0, 0])
    0
    >>> find_min([-1, -5, 5, 1])
    0
    >>> find_min([-1, -5, 5, 1])
    0
    >>> find_min([9, 9, 9, 9, 9])
    9
    >>> find_min([1, 5, 10, 3])
    1
    >>> find_min([-1, 0, 1])
    0
    >>> find_min(range(10, 0, -1))
    1
    >>> find_min([-1])
    Traceback (most recent call last):
        --
    IndexError: list assignment index out of range
    >>> find_min([0, 0, 0, 1, 2, -4])
    Traceback (most recent call last):
        ...
    IndexError: list assignment index out of range
    >>> find_min([-1, -5, -10, -3])
    Traceback (most recent call last):
        ...
    IndexError: list assignment index out of range
    """
    n = len(numbers)
    s = sum(numbers)

    dp = [[False for x in range(s + 1)] for y in range(n + 1)]

    for i in range(n + 1):
        dp[i][0] = True

    for i in range(1, s + 1):
        dp[0][i] = False

    for i in range(1, n + 1):
        for j in range(1, s + 1):
            dp[i][j] = dp[i - 1][j]

            if numbers[i - 1] <= j:
                dp[i][j] = dp[i][j] or dp[i - 1][j - numbers[i - 1]]

    for j in range(int(s / 2), -1, -1):
        if dp[n][j] is True:
            diff = s - 2 * j
            break

    return diff


if __name__ == "__main__":
    from doctest import testmod

    testmod()