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

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


int a [] = { 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 problem is reduced to “Find a pair of numbers from an array whose sum equals -a”

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 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)



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

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If you find anything incorrect or you feel that there is any better approach to solve the above problem, please write comment.

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