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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