Partition Array Into Two Arrays to Minimize Sum Difference

Partition Array Into Two Arrays to Minimize Sum Difference - Problem

Array Two Pointers Binary Search Dynamic Programming Bit Manipulation Ordered Set Bitmask Hard

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.

Input & Output

Example 1 — Basic Case

$ Input: nums = [3,9,7,3]

› Output: 2

💡 Note: Split into [3,9] and [7,3]. Sum difference is |12-10| = 2, which is minimal.

Example 2 — Perfect Split

$ Input: nums = [-36,36]

› Output: 72

💡 Note: Only two elements, must split as [-36] and [36]. Difference is |-36-36| = 72.

Example 3 — Multiple Options

$ Input: nums = [2,-1,0,4,-2,-9]

› Output: 0

💡 Note: Can split as [2,-1,-2] and [0,4,-9] both summing to -1. Difference is |-1-(-1)| = 0.

Constraints

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

Visualization

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Asked in

G Google 45 f Facebook 38 M Microsoft 32 a Amazon 28

This problem requires partitioning an array of 2n elements into two equal-sized subsets to minimize sum difference. The key insight is using meet-in-the-middle technique: split the array in half, generate all subset sums for each half, then use binary search to find optimal pairings. Best approach achieves O(3^n) time complexity. Time: O(3^n), Space: O(2^n)

Common Approaches

✓ Brute Force - Try All Combinations

⏱️ Time: O(2^(2n)) Space: O(n)

Generate all possible combinations of choosing n elements from 2n elements. For each combination, calculate the sum difference and keep track of the minimum.

Meet in the Middle with Binary Search

⏱️ Time: O(3^n) Space: O(2^n)

Split the 2n elements into two halves of n elements each. Generate all possible subset sums for each half, then use binary search to find the optimal way to combine subsets from both halves.

Brute Force - Try All Combinations — Algorithm Steps

Generate all C(2n, n) combinations of choosing n elements
For each combination, calculate sum of chosen vs remaining elements
Track the minimum absolute difference

Visualization

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Step-by-Step Walkthrough

Generate Combinations

Create all ways to choose n elements

Calculate Difference

For each split, find |sum1 - sum2|

Find Minimum

Keep track of smallest difference

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <limits.h>

int findMinDiff(int* nums, int size, int index, int sum1, int count1, int target, int totalSum) {
    if (count1 == target) {
        int diff = sum1 - (totalSum - sum1);
        return diff < 0 ? -diff : diff;
    }
    
    if (index >= size) {
        return INT_MAX;
    }
    
    // Include current element
    int include = findMinDiff(nums, size, index + 1, sum1 + nums[index], count1 + 1, target, totalSum);
    
    // Exclude current element
    int exclude = INT_MAX;
    if (size - index - 1 >= target - count1 - 1) {
        exclude = findMinDiff(nums, size, index + 1, sum1, count1, target, totalSum);
    }
    
    return include < exclude ? include : exclude;
}

int solution(int* nums, int size) {
    int n = size / 2;
    int totalSum = 0;
    for (int i = 0; i < size; i++) {
        totalSum += nums[i];
    }
    return findMinDiff(nums, size, 0, 0, 0, n, totalSum);
}

int main() {
    char line[1000];
    fgets(line, sizeof(line), stdin);
    
    // Parse JSON array
    int nums[100];
    int size = 0;
    char* token = strtok(line + 1, ",]");
    while (token != NULL) {
        nums[size++] = atoi(token);
        token = strtok(NULL, ",]");
    }
    
    int result = solution(nums, size);
    printf("%d\n", result);
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(2^(2n))

Need to check all C(2n,n) combinations which is exponential

✓ Linear Growth

Space Complexity

O(n)

Space for storing current combination and recursion stack

⚡ Linearithmic Space

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Medium Frequency

~45 min Avg. Time

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Input & Output

Constraints

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Related Problems

Common Approaches

Brute Force - Try All Combinations — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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