237. 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)

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)

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)

Output:

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