"""
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()