# Find three elements in an array that sum to a zero.

**Objective**: Given an array of integers write an algorithm to find 3 elements that sum to a zero. In short a+b+c = 0.

**Example**

int [] = { 3,-1,-7,-4,-5,9,10}; Elements are -4 9 -5

**Approach: Brute Force**

Use 3 nested loops and find the 3 elements which sum to 0.

Time Complexity: O(n^3)

**Code:**

**Approach: Sorting**

- Sort the array.
- Use the other loop to fix the one element at a time, say its ‘a’.
- Now the problem is reduced to “Find a pair of numbers from an array whose sum equals to K“

Time Complexity: **O(n^2)**

**Code:**

**Approach: Use Hashing**

- Use the other loop to fix the one element at a time.
- Now required_sum is (with two elements) = -fixed element.
- Create a HashSet, Iterate through the rest of the array.
- For current_element, remain_value = required_sum – current_element.
- Check if remain_value in the HashSet, we have found our triplets else add current_element to the HashSet.

Time Complexity: O(n^2)

**Code:**

**Output**:

Found 3 elements whose sum is = 0 Elements are -4 9 -5

Improvement 1:

Loop at line number 8 can be improved to execute till i < x.length – 1

Improvement 2:

Return statement at line number 18 should be removed to find other possible triplets in the array