partition a set into two subsets such that the difference of subset sums is minimum findmin1 2 3 4 5 1 findmin5 5 5 5 5 5 findmin5 5 5 5 0 findmin3 3 findmin 0 findmin1 2 3 4 0 findmin0 0 0 0 0 findmin1 5 5 1 0 findmin1 5 5 1 0 findmin9 9 9 9 9 9 findmin1 5 10 3 1 findmin1 0 1 0 findminrange10 0 1 1 findmin1 traceback most recent call last indexerror list assignment index out of range findmin0 0 0 1 2 4 traceback most recent call last indexerror list assignment index out of range findmin1 5 10 3 traceback most recent call last indexerror list assignment index out of range 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
def find_min(numbers: list[int]) -> int:
    
    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()