Python/dynamic_programming/minimum_partition.py

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


def find_min(arr: 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
    """
    n = len(arr)
    s = sum(arr)

    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 arr[i - 1] <= j:
                dp[i][j] = dp[i][j] or dp[i - 1][j - arr[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()