Pair Sum Closest to 0 Problem in Java

10 May 2025 | 4 min read

The Pair Sum Closest to 0 problem requires the identification of numbers within an array that provide the minimum sum approaching zero. Total absolute difference minimization emerges as critical in domains like finance alongside physics and optimization while dealing with optimization tasks.

Running the brute force technique evaluates every possible pair, which results in an O(n²) complexity. Sorting an array will enable an optimal solution to run efficiently through the two-pointer technique thanks to its O(n log n) complexity. This approach efficiently finds the closest pair while ensuring minimal computational overhead.

Brute Force Approach

The process of finding the pair of numbers with the closest zero sum value requires checking every pair (arr[i],arr[j]) with i<j. Compute the pair sums then verify if their absolute value remains smaller than the current closest sum value. If so, update the closest sum and store the corresponding pair.

This brute-force approach ensures every possible combination is examined. However, due to the nested loops iterating through all pairs, the time complexity is O(n²), making it inefficient for large datasets. Optimized approaches, such as sorting with two pointers, can reduce complexity to O(n log n).

Optimized Approach

Step 1: Sorting

Sort the given array in ascending order to facilitate the two-pointer approach.

Step 2: Initialize Two Pointers

Use two pointers:
1. Left pointer at the beginning (index 0).
2. Right pointer at the end (index n - 1).

Step 3: Find the Closest Sum

While left < right, compute the sum of the two numbers at arr[left] and arr[right].
Keep track of the minimum absolute sum and update the closest pair.

Step 4: Move Pointers Based on Sum

If the sum is negative, move the left pointer rightward to increase the sum.
If the sum is positive, move the right pointer leftward to decrease the sum.

Step 5: Repeat Until Pointers Meet

Continue the process until left crosses right.
The final pair gives the closest sum to zero.

Let’s implement the above algorithm in a Java program.

Output:

 
Pair closest to zero: -80, 85

Explanation

The program first sorts the array, enabling an efficient two-pointer approach. It initializes left and right pointers and iterates through the array, updating the closest sum when a better pair is found.

Depending on the sum's sign, the left or right pointer is adjusted accordingly. This greedy strategy ensures an optimal O(n log n) solution, efficiently finding the pair closest to zero.

Key Observations

Sorting Helps in Optimization
- Sorting enables the two-pointer approach, reducing complexity.
Two-Pointer Strategy Ensures Efficiency
- Instead of checking all pairs (O(n²)), we efficiently navigate the sorted array (O(n log n)).
Handling Positive and Negative Sums
- If the sum is negative, move right to increase it.
- If the sum is positive, move left to decrease it.
Time Complexity Consideration
- Sorting: O(n log n)
- Two-pointer traversal: O(n)
- Total Complexity: O(n log n)

Conclusion

The Pair Sum Closest to Zero problem is efficiently solved using a sorting and two-pointer approach. While the brute force approach (O(n²)) is straightforward, it is inefficient for large arrays. The greedy two-pointer approach (O(n log n)) provides an optimal and scalable solution.

This problem is essential in real-world scenarios like stock trading analysis, temperature analysis, and optimization problems. By leveraging sorting and greedy techniques, we efficiently minimize absolute sum differences, making this algorithm both practical and computationally efficient

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