## Introduction:

Pair sum problems are a common and important aspect of coding interviews, challenging candidates to find pairs of elements in an array that add up to a specific target value. Mastering these problems requires a solid understanding of algorithms, data structures, and problem-solving techniques. In this article, we will delve into the world of pair sum problems, exploring various algorithms, efficient solutions, and essential tips to excel in coding interviews.

**Understanding Pair Sum Problems:** Pair sum problems challenge candidates to identify two elements in an array whose sum matches a specific target value. Whether the array is sorted or unsorted, understanding the problem’s requirements is crucial for devising effective solutions.

**Example:**

Input: arr[] = {0, -1, 2, -3, 1}, x= -2 Output: Pair found: (-3,1) Explanation: If we calculate the sum of the output,1 + (-3) = -2

Input: arr[] = {1, -2, 1, 0, 5}, x = 0 Output: Pair does not exist

### Naive Solution (Brute-Force Approach) using Java:

The naive solution involves checking all possible pairs in the array to find those with the desired sum. Here’s a Java implementation of the brute-force approach:

**Time Complexity:** The nested loops in the naive solution result in a time complexity of O(n^2), where n is the size of the array.**Auxiliary Space:*** *O(1)

### Optimal Solution using Java:

The optimal solution for pair sum problems utilizes a HashSet to achieve linear time complexity. Here’s a Java implementation of the optimal approach:

import java.util.HashSet;

public class PairSumOptimalSolution {

public static void findPairSum(int[] arr, int targetSum) {

HashSet set = new HashSet<>();

for (int num : arr) {

int complement = targetSum – num;

if (set.contains(complement)) {

System.out.println(“Pair found: (” + num + “, ” + complement + “)”);

}

set.add(num);

}

}

```
public static void main(String[] args) {
int[] array = { 2, 4, 8, 5, 3, 9, 7 };
int target = 12;
findPairSum(array, target);
}
```

**Time Complexity of Optimal Solution:** The optimal solution traverses the array once and performs constant time operations with the HashSet. Therefore, it has a time complexity of O(n)

**Space Complexity of Optimal Solution:** The optimal solution uses additional space to store elements in the HashSet, and the space complexity is O(n).

If you love coding and want to know about some interview’s frequently asked popular algorithm check out my previous post.

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