Two Sum-Pairs with 0 Sum Problem in Java

3 May 2025 | 4 min read

The Two Sum - Pairs with Zero Sum is another algorithmic problem referred to as a problem of identifying pairs of integers in an array that sum up to zero. This problem is quite common among coding interviews and competitive programming since it requires not only mathematic computation but also good manipulation with data structures.

Solving this problem as quickly as possible will allow us to understand how to address other problems that arise in connection with pairs, sums, and sets of unique solutions.

Problem Statement

Suppose we are given now an array of integer values, the problem is to find out all possible pairs of integers (a, b) for which a + b = 0. It means that for every positive integer in the array there should be another negative integer in the same array.

The problem is to achieve this in a way that requires as little time and space as possible to find these pairs. The solution also must consider the fact that pairs can be repeated in the input array, so that each such pair is reported only once.

Solution to Solve the Problem

This can be solved through several approaches with the most prominent solutions being; employ the sort the array and use, and hash set for lookup and. Both methods will, however, be explained below.

Method 1: Using a Hash Set

It uses a hash set to seize elements as the array will be processed by a method, which will be considered later on. For each element we have the check for its opposite exists in a set that will do for a valid pair.

File Name: TwoSumZero.java

Output:

 
Pairs with zero sum:
Pair: -3,3
Pair: -1,1
Pair: -2,2

Method 2: Using Sorting and Two Pointers

This method is simpler and reduces the size of the array after sorting it; then the use of two pointers in finding the two-sums equal to zero. Such an approach is efficient and the removal of duplicates occur automatically as the elements are sorted in the array.

File Name: TwoSumZero.java

Output:

 
Pairs with zero sum:
Pair: -3,3
Pair: -1,1
Pair: -2,2

Complexity Analysis

Time Complexity

Hash Set Method: O(N) on average for insertion and lookup operations.
Sorting and Two Pointers Method: O(NlogN) due to sorting, followed by O(N) for the two-pointer traversal.

Space Complexity

Hash Set Method: O(N) for storing elements in the hash set.
Sorting and Two Pointers Method: O(1) additional space if we ignore the input array's space.

Conclusion

They can find distinctive pairs of integers which constitute a sum zero result appropriately. The decision between them is in situations where some features are needed for example, time and memory requirements. Owing to the time complexity of the hash set method being linear, it is normally faster compared to the other method in unsorted arrays.

On the other hand, the sorting and two-pointer technique give a clear organization, and the similar pairs are excluded automatically. Not only does understanding these methods improve one's problem-solving skills, but it also prepares you for more advanced scenarios using the Combination/Sums in Arrays. Such techniques can greatly enhance a candidate or a participant's performance during a technical interview or a coding competition.

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