minimum_partition.py

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


deffind_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= [[Falseforxinrange(s+1)] foryinrange(n+1)]

foriinrange(n+1):
dp[i][0] =True

foriinrange(1, s+1):
dp[0][i] =False

foriinrange(1, n+1):
forjinrange(1, s+1):
dp[i][j] =dp[i-1][j]

ifnumbers[i-1] <=j:
dp[i][j] =dp[i][j] ordp[i-1][j-numbers[i-1]]

forjinrange(int(s/2), -1, -1):
ifdp[n][j] isTrue:
diff=s-2*j
break

returndiff


if__name__=="__main__":
fromdoctestimporttestmod

testmod()