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minimum_partition.py

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"""

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

"""

def findMin(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