minimum_partition.py

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


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

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

 for i in range(1, 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][j - 1]

 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