Given an array of integers you have to find three numbers such that sum of two elements equals the third element.

**Examples:**

Input : {5, 32, 1, 7, 10, 50, 19, 21, 2} Output : 21, 2, 19 Input : {5, 32, 1, 7, 10, 50, 19, 21, 0} Output : no such triplet exist

Question source : Arcesium Interview Experience | Set 7 (On campus for Internship)

**Simple approach:** Run three loops and check if there exists a triplet such that sum of two elements equals the third element.

**Time complexity**: O(n^3)

**Efficient approach :** The idea is similar to Find a triplet that sum to a given value.

- Sort the given array first.
- Start fixing the greatest element of three from back and traverse the array to find other two numbers which sum upto the third element.
- Take two pointers j(from front) and k(initially i-1) to find the smallest of the two number and from i-1 to find the largest of the two remaining numbers
- If the addition of both the numbers is still less than A[i], then we need to increase the value of the summation of two numbers, thereby increase the j pointer, so as to increase the value of
**A[j] + A[k]**. - If the addition of both the numbers is more than A[i], then we need to decrease the value of the summation of two numbers, thereby decrease the k pointer so as to decrease the overall value of
**A[j] + A[k]**.

Below image is a dry run of the above approach:

Below is the implementation of the above approach:

## C++

`// CPP program to find three numbers` `// such that sum of two makes the` `// third element in array` `#include <bits/stdc++.h>` `using` `namespace` `std;` ` ` `// Utility function for finding` `// triplet in array` `void` `findTriplet(` `int` `arr[], ` `int` `n)` `{` ` ` `// sort the array` ` ` `sort(arr, arr + n);` ` ` ` ` `// for every element in arr` ` ` `// check if a pair exist(in array) whose` ` ` `// sum is equal to arr element` ` ` `for` `(` `int` `i = n - 1; i >= 0; i--) {` ` ` `int` `j = 0;` ` ` `int` `k = i - 1;` ` ` ` ` `// Iterate forward and backward to find` ` ` `// the other two elements` ` ` `while` `(j < k) {` ` ` ` ` `// If the two elements sum is` ` ` `// equal to the third element` ` ` `if` `(arr[i] == arr[j] + arr[k]) {` ` ` ` ` `// pair found` ` ` `cout << ` `"numbers are "` `<< arr[i] << ` `" "` ` ` `<< arr[j] << ` `" "` `<< arr[k] << endl;` ` ` `return` `;` ` ` `}` ` ` ` ` `// If the element is greater than` ` ` `// sum of both the elements, then try` ` ` `// adding a smaller number to reach the` ` ` `// equality` ` ` `else` `if` `(arr[i] > arr[j] + arr[k])` ` ` `j += 1;` ` ` ` ` `// If the element is smaller, then` ` ` `// try with a smaller number` ` ` `// to reach equality, so decrease K` ` ` `else` ` ` `k -= 1;` ` ` `}` ` ` `}` ` ` ` ` `// No such triplet is found in array` ` ` `cout << ` `"No such triplet exists"` `;` `}` ` ` `// driver program` `int` `main()` `{` ` ` `int` `arr[] = { 5, 32, 1, 7, 10, 50, 19, 21, 2 };` ` ` `int` `n = ` `sizeof` `(arr) / ` `sizeof` `(arr[0]);` ` ` ` ` `findTriplet(arr, n);` ` ` `return` `0;` `}` |

## Java

`// Java program to find three numbers` `// such that sum of two makes the` `// third element in array` `import` `java.util.Arrays;` ` ` `public` `class` `GFG {` ` ` ` ` `// utility function for finding` ` ` `// triplet in array` ` ` `static` `void` `findTriplet(` `int` `arr[], ` `int` `n)` ` ` `{` ` ` `// sort the array` ` ` `Arrays.sort(arr);` ` ` ` ` `// for every element in arr` ` ` `// check if a pair exist(in array) whose` ` ` `// sum is equal to arr element` ` ` `for` `(` `int` `i = n - ` `1` `; i >= ` `0` `; i--) {` ` ` `int` `j = ` `0` `;` ` ` `int` `k = i - ` `1` `;` ` ` `while` `(j < k) {` ` ` `if` `(arr[i] == arr[j] + arr[k]) {` ` ` ` ` `// pair found` ` ` `System.out.println(` `"numbers are "` `+ arr[i] + ` `" "` ` ` `+ arr[j] + ` `" "` `+ arr[k]);` ` ` ` ` `return` `;` ` ` `}` ` ` `else` `if` `(arr[i] > arr[j] + arr[k])` ` ` `j += ` `1` `;` ` ` `else` ` ` `k -= ` `1` `;` ` ` `}` ` ` `}` ` ` ` ` `// no such triplet is found in array` ` ` `System.out.println(` `"No such triplet exists"` `);` ` ` `}` ` ` ` ` `// driver program` ` ` `public` `static` `void` `main(String args[])` ` ` `{` ` ` `int` `arr[] = { ` `5` `, ` `32` `, ` `1` `, ` `7` `, ` `10` `, ` `50` `, ` `19` `, ` `21` `, ` `2` `};` ` ` `int` `n = arr.length;` ` ` `findTriplet(arr, n);` ` ` `}` `}` `// This code is contributed by Sumit Ghosh` |

## Python

`# Python program to find three numbers` `# such that sum of two makes the` `# third element in array` ` ` `# utility function for finding` `# triplet in array` `def` `findTriplet(arr, n):` ` ` ` ` `# sort the array` ` ` `arr.sort()` ` ` ` ` `# for every element in arr` ` ` `# check if a pair exist(in array) whose` ` ` `# sum is equal to arr element` ` ` `i ` `=` `n ` `-` `1` ` ` `while` `(i >` `=` `0` `):` ` ` `j ` `=` `0` ` ` `k ` `=` `i ` `-` `1` ` ` `while` `(j < k):` ` ` `if` `(arr[i] ` `=` `=` `arr[j] ` `+` `arr[k]):` ` ` ` ` `# pair found` ` ` `print` `"numbers are "` `, arr[i], arr[j], arr[k]` ` ` `return` ` ` `elif` `(arr[i] > arr[j] ` `+` `arr[k]):` ` ` `j ` `+` `=` `1` ` ` `else` `:` ` ` `k ` `-` `=` `1` ` ` `i ` `-` `=` `1` ` ` ` ` `# no such triplet is found in array` ` ` `print` `"No such triplet exists"` ` ` `# driver program` `arr ` `=` `[ ` `5` `, ` `32` `, ` `1` `, ` `7` `, ` `10` `, ` `50` `, ` `19` `, ` `21` `, ` `2` `]` `n ` `=` `len` `(arr)` `findTriplet(arr, n)` ` ` `# This code is contributed by Sachin Bisht` |

## C#

`// C# program to find three numbers` `// such that sum of two makes the` `// third element in array` `using` `System;` ` ` `public` `class` `GFG {` ` ` ` ` `// utility function for finding` ` ` `// triplet in array` ` ` `static` `void` `findTriplet(` `int` `[] arr, ` `int` `n)` ` ` `{` ` ` ` ` `// sort the array` ` ` `Array.Sort(arr);` ` ` ` ` `// for every element in arr` ` ` `// check if a pair exist(in` ` ` `// array) whose sum is equal` ` ` `// to arr element` ` ` `for` `(` `int` `i = n - 1; i >= 0; i--) {` ` ` `int` `j = 0;` ` ` `int` `k = i - 1;` ` ` `while` `(j < k) {` ` ` `if` `(arr[i] == arr[j] + arr[k]) {` ` ` ` ` `// pair found` ` ` `Console.WriteLine(` `"numbers are "` ` ` `+ arr[i] + ` `" "` `+ arr[j]` ` ` `+ ` `" "` `+ arr[k]);` ` ` ` ` `return` `;` ` ` `}` ` ` `else` `if` `(arr[i] > arr[j] + arr[k])` ` ` `j += 1;` ` ` `else` ` ` `k -= 1;` ` ` `}` ` ` `}` ` ` ` ` `// no such triplet is found in array` ` ` `Console.WriteLine(` `"No such triplet exists"` `);` ` ` `}` ` ` ` ` `// driver program` ` ` `public` `static` `void` `Main()` ` ` `{` ` ` `int` `[] arr = { 5, 32, 1, 7, 10, 50,` ` ` `19, 21, 2 };` ` ` `int` `n = arr.Length;` ` ` ` ` `findTriplet(arr, n);` ` ` `}` `}` ` ` `// This code is contributed by vt_m.` |

## PHP

`<?php` `// PHP program to find three` `// numbers such that sum of ` `// two makes the third` `// element in array` ` ` `// utility function for ` `// finding triplet in array` `function` `findTriplet(` `$arr` `, ` `$n` `)` `{` ` ` `// sort the array` ` ` `sort(` `$arr` `);` ` ` ` ` `// for every element in ` ` ` `// arr check if a pair ` ` ` `// exist(in array) whose` ` ` `// sum is equal to arr element` ` ` `for` `(` `$i` `= ` `$n` `- 1; ` `$i` `>= 0; ` `$i` `--)` ` ` `{` ` ` `$j` `= 0;` ` ` `$k` `= ` `$i` `- 1;` ` ` `while` `(` `$j` `< ` `$k` `) ` ` ` `{` ` ` `if` `(` `$arr` `[` `$i` `] == ` `$arr` `[` `$j` `] + ` `$arr` `[` `$k` `]) ` ` ` `{` ` ` ` ` `// pair found` ` ` `echo` `"numbers are "` `, ` `$arr` `[` `$i` `], ` `" "` `, ` ` ` `$arr` `[` `$j` `], ` `" "` `, ` ` ` `$arr` `[` `$k` `];` ` ` `return` `;` ` ` `} ` ` ` `else` `if` `(` `$arr` `[` `$i` `] > ` `$arr` `[` `$j` `] + ` ` ` `$arr` `[` `$k` `])` ` ` `$j` `+= 1;` ` ` `else` ` ` `$k` `-= 1;` ` ` `}` ` ` `}` ` ` ` ` `// no such triplet ` ` ` `// is found in array` ` ` `echo` `"No such triplet exists"` `;` `}` ` ` `// Driver Code` `$arr` `= ` `array` `(5, 32, 1, 7, 10, ` ` ` `50, 19, 21, 2 );` `$n` `= ` `count` `(` `$arr` `);` ` ` `findTriplet(` `$arr` `, ` `$n` `);` ` ` `// This code is contributed by anuj_67.` `?>` |

**Output:**

numbers are 21 2 19

**Time complexity**: O(N^2)

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