2035. Partition Array Into Two Arrays to Minimize Sum Difference

Description

You are given an integer array nums of 2 * n integers. You need to partition nums into two arrays of length n to minimize the absolute difference of the sums of the arrays. To partition nums, put each element of nums into one of the two arrays.

Return the minimum possible absolute difference.

 

Example 1:

Input: nums = [3,9,7,3]
Output: 2
Explanation: One optimal partition is: [3,9] and [7,3].
The absolute difference between the sums of the arrays is abs((3 + 9) - (7 + 3)) = 2.

Example 2:

Input: nums = [-36,36]
Output: 72
Explanation: One optimal partition is: [-36] and [36].
The absolute difference between the sums of the arrays is abs((-36) - (36)) = 72.

Example 3:

Input: nums = [2,-1,0,4,-2,-9]
Output: 0
Explanation: One optimal partition is: [2,4,-9] and [-1,0,-2].
The absolute difference between the sums of the arrays is abs((2 + 4 + -9) - (-1 + 0 + -2)) = 0.

 

Constraints:

• 1 <= n <= 15
• nums.length == 2 * n
• -107 <= nums[i] <= 107

Solution

partition-array-into-two-arrays-to-minimize-sum-difference.py

class Solution:
    def minimumDifference(self, nums: List[int]) -> int:

        def construct(A):
            n = len(A)
            mp = {}

            for k in range(1, n + 1):
                sums = []
                for comb in combinations(A, k):
                    sums.append(sum(comb))
                mp[k] = sums

            return mp

        n = len(nums) // 2
        left, right = nums[:n], nums[n:]
        left_part, right_part = construct(left), construct(right)
        res = abs(sum(left) - sum(right))
        total = sum(nums)
        half = total // 2

        for k in range(1, n - 1):
            l, r = left_part[k], right_part[n - k]
            r.sort()

            for x in l:
                target = half - x
                index = bisect.bisect_left(r, target)

                for p in (index - 1, index):
                    if 0 <= p < len(r):
                        leftSum = x + r[p]
                        rightSum = total - leftSum
                        res = min(res, abs(leftSum - rightSum))

        return res