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# 3 Sum - Leetcode #15 Short & Simple Solution

Updated: Jun 6, 2022

## Problem Statement

We solved the two sum problem in our earlier article, and this problem in some ways is a continuation of the two sum problem. So, if you have not yet solved the two sum problem we advice you to do so because it will help you understand the 3 sum problem better.

Given an array of integers, nums, return all the triplets in the given array nums[i], nums[j], nums[k] such that i != j, i != k, and j != k, and nums[i] + nums[j] + nums[k] == 0.

Notice: The solution set must not contain duplicate triplets.

## Example

Example 1:

```Input: nums = [-1,0,1,2,-1,-4]
Output: [[-1,-1,2],[-1,0,1]]```

Example 2:

```Input: nums = 
Output: []```

## Solution

Let us try to understand the problem statement. The first part of the problem statement is clear, we are asked to find out all the triplets in the given array whose sum is equal to zero. A triplet is nothing but a set of three numbers in the given array. For example, if nums=[1,2, 3,4] is the given array, [1,2,3] [2,3,4] [1,3,4] etc are its triplets.

What does the condition i != j, i != k, and j != k mean?

It means that we are not allowe