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Find a triplet such that sum of two equals to third element
• Difficulty Level : Medium
• Last Updated : 11 Jul, 2019

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)

Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

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 ``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

 `= 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)

This article is contributed by Mandeep Singh. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.