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Find three element from different three arrays such that a + b + c = sum
• Difficulty Level : Medium
• Last Updated : 08 Jun, 2021

Given three integer arrays and a “sum”, the task is to check if there are three elements a, b, c such that a + b + c = sum and a, b and c belong to three different arrays.
Examples :

```Input : a1[] = { 1 , 2 , 3 , 4 , 5 };
a2[] = { 2 , 3 , 6 , 1 , 2 };
a3[] = { 3 , 2 , 4 , 5 , 6 };
sum = 9
Output : Yes
1  + 2  + 6 = 9  here 1 from a1[] and 2 from
a2[] and 6 from a3[]

Input : a1[] = { 1 , 2 , 3 , 4 , 5 };
a2[] = { 2 , 3 , 6 , 1 , 2 };
a3[] = { 3 , 2 , 4 , 5 , 6 };
sum = 20
Output : No```

A naive approach is to run three loops and check sum of three element form different arrays equal to given number if find then print exist and otherwise print not exist.

## C++

 `// C++ program to find three element``// from different three arrays such``// that a + b + c is equal to``// given sum``#include``using` `namespace` `std;` `// Function to check if there is``// an element from each array such``// that sum of the three elements``// is equal to given sum.``bool` `findTriplet(``int` `a1[], ``int` `a2[],``                 ``int` `a3[], ``int` `n1,``                 ``int` `n2, ``int` `n3, ``int` `sum)``{``    ``for` `(``int` `i = 0; i < n1; i++)``    ``for` `(``int` `j = 0; j < n2; j++)``        ``for` `(``int` `k = 0; k < n3; k++)``            ``if` `(a1[i] + a2[j] + a3[k] == sum)``            ``return` `true``;` `    ``return` `false``;``}` `// Driver Code``int` `main()``{``    ``int` `a1[] = { 1 , 2 , 3 , 4 , 5 };``    ``int` `a2[] = { 2 , 3 , 6 , 1 , 2 };``    ``int` `a3[] = { 3 , 2 , 4 , 5 , 6 };``    ``int` `sum = 9;``    ``int` `n1 = ``sizeof``(a1) / ``sizeof``(a1);``    ``int` `n2 = ``sizeof``(a2) / ``sizeof``(a2);``    ``int` `n3 = ``sizeof``(a3) / ``sizeof``(a3);``    ``findTriplet(a1, a2, a3, n1, n2, n3, sum)?``                ``cout << ``"Yes"` `: cout << ``"No"``;``    ``return` `0;``}`

## Java

 `// Java program to find three element``// from different three arrays such``// that a + b + c is equal to``// given sum``class` `GFG``{``        ` `    ``// Function to check if there is``    ``// an element from each array such``    ``// that sum of the three elements``    ``// is equal to given sum.``    ``static` `boolean` `findTriplet(``int` `a1[], ``int` `a2[],``                               ``int` `a3[], ``int` `n1,``                               ``int` `n2, ``int` `n3, ``int` `sum)``    ``{``        ``for` `(``int` `i = ``0``; i < n1; i++)``            ``for` `(``int` `j = ``0``; j < n2; j++)``                ``for` `(``int` `k = ``0``; k < n3; k++)``                    ``if` `(a1[i] + a2[j] + a3[k] == sum)``                    ``return` `true``;``    ` `        ``return` `false``;``    ``}``    ` `    ``// Driver code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `a1[] = { ``1` `, ``2` `, ``3` `, ``4` `, ``5` `};``        ``int` `a2[] = { ``2` `, ``3` `, ``6` `, ``1` `, ``2` `};``        ``int` `a3[] = { ``3` `, ``2` `, ``4` `, ``5` `, ``6` `};``        ``int` `sum = ``9``;``        ` `        ``int` `n1 = a1.length;``        ``int` `n2 = a2.length;``        ``int` `n3 = a3.length;``        ` `        ``if``(findTriplet(a1, a2, a3, n1, n2, n3, sum))``            ``System.out.print(``"Yes"``);``        ``else``            ``System.out.print(``"No"``);``    ``}``}` `// This code is contributed by Anant Agarwal.`

## Python3

 `# Python3 program to find``# three element from different``# three arrays such that``# a + b + c is equal to``# given sum` `# Function to check if there``# is an element from each``# array such that sum of the``# three elements is equal to``# given sum.``def` `findTriplet(a1, a2, a3,``                ``n1, n2, n3, ``sum``):` `    ``for` `i ``in` `range``(``0` `, n1):``        ``for` `j ``in` `range``(``0` `, n2):``            ``for` `k ``in` `range``(``0` `, n3):``                ``if` `(a1[i] ``+` `a2[j] ``+``                    ``a3[k] ``=``=` `sum``):``                    ``return` `True` `    ``return` `False` `# Driver Code``a1 ``=` `[ ``1` `, ``2` `, ``3` `, ``4` `, ``5` `]``a2 ``=` `[ ``2` `, ``3` `, ``6` `, ``1` `, ``2` `]``a3 ``=` `[ ``3` `, ``2` `, ``4` `, ``5` `, ``6` `]``sum` `=` `9``n1 ``=` `len``(a1)``n2 ``=` `len``(a2)``n3 ``=` `len``(a3)``print``(``"Yes"``) ``if` `findTriplet(a1, a2, a3,``                            ``n1, n2, n3,``                            ``sum``) ``else` `print``(``"No"``)` `# This code is contributed``# by Smitha`

## C#

 `// C# program to find three element``// from different three arrays such``// that a + b + c is equal to``// given sum``using` `System;` `public` `class` `GFG``{` `// Function to check if there is an``// element from each array such that``// sum of the three elements is``// equal to given sum.``static` `bool` `findTriplet(``int` `[]a1, ``int` `[]a2,``                        ``int` `[]a3, ``int` `n1,``                        ``int` `n2, ``int` `n3,``                        ``int` `sum)``{``    ` `    ``for` `(``int` `i = 0; i < n1; i++)``    ` `        ``for` `(``int` `j = 0; j < n2; j++)``        ` `            ``for` `(``int` `k = 0; k < n3; k++)``            ``if` `(a1[i] + a2[j] + a3[k] == sum)``            ``return` `true``;` `    ``return` `false``;``}` `    ``// Driver Code``    ``static` `public` `void` `Main ()``    ``{``        ``int` `[]a1 = {1 , 2 , 3 , 4 , 5};``        ``int` `[]a2 = {2 , 3 , 6 , 1 , 2};``        ``int` `[]a3 = {3 , 2 , 4 , 5 , 6};``        ``int` `sum = 9;``        ``int` `n1 = a1.Length;``        ``int` `n2 = a2.Length;``        ``int` `n3 = a3.Length;``        ``if``(findTriplet(a1, a2, a3, n1,``                       ``n2, n3, sum))``        ``Console.WriteLine(``"Yes"``);``        ``else``        ``Console.WriteLine(``"No"``);``    ``}``}` `// This code is contributed by vt_m.`

## PHP

 ``

## Javascript

 ``

Output :

`Yes`

Time complexity : O(n3
Space complexity : O(1)
An efficient solution is to store all elements of first array in hash table (unordered_set in C++) and calculate sum of two elements last two array elements one by one and substract from given number k and check in hash table if it’s exist in hash table then print exist and otherwise not exist.

```1. Store all elements of first array in hash table
2. Generate all pairs of elements from two arrays using
nested loop. For every pair (a1[i], a2[j]), check if
sum - (a1[i] + a2[j]) exists in hash table. If yes
return true.      ```

Below is the implementation of above idea.

## C++

 `// C++ program to find three element``// from different three arrays such``// that a + b + c is equal to``// given sum``#include``using` `namespace` `std;` `// Function to check if there is``// an element from each array such``// that sum of the three elements is``// equal to given sum.``bool` `findTriplet(``int` `a1[], ``int` `a2[],``                 ``int` `a3[], ``int` `n1,``                 ``int` `n2, ``int` `n3,``                 ``int` `sum)``{``    ``// Store elements of``    ``// first array in hash``    ``unordered_set <``int``> s;``    ``for` `(``int` `i = 0; i < n1; i++)``        ``s.insert(a1[i]);` `    ``// sum last two arrays``    ``// element one by one``    ``for` `(``int` `i = 0; i < n2; i++)``    ``{``        ``for` `(``int` `j = 0; j < n3; j++)``        ``{``            ``// Consider current pair and``            ``// find if there is an element``            ``// in a1[] such that these three``            ``// form a required triplet``            ``if` `(s.find(sum - a2[i] - a3[j]) !=``                                       ``s.end())``                ``return` `true``;``        ``}``    ``}` `    ``return` `false``;``}` `// Driver Code``int` `main()``{``    ``int` `a1[] = { 1 , 2 , 3 , 4 , 5 };``    ``int` `a2[] = { 2 , 3 , 6 , 1 , 2 };``    ``int` `a3[] = { 3 , 2 , 4 , 5 , 6 };``    ``int` `sum = 9;``    ``int` `n1 = ``sizeof``(a1) / ``sizeof``(a1);``    ``int` `n2 = ``sizeof``(a2) / ``sizeof``(a2);``    ``int` `n3 = ``sizeof``(a3) / ``sizeof``(a3);``    ``findTriplet(a1, a2, a3, n1, n2, n3, sum)?``    ``cout << ``"Yes"` `: cout << ``"No"``;` `    ``return` `0;``}`

## Java

 `// Java program to find three element``// from different three arrays such``// that a + b + c is equal to``// given sum``import` `java.util.*;` `class` `GFG``{` `    ``// Function to check if there is``    ``// an element from each array such``    ``// that sum of the three elements is``    ``// equal to given sum.``    ``static` `boolean` `findTriplet(``int` `a1[], ``int` `a2[], ``int` `a3[],``                                ``int` `n1, ``int` `n2, ``int` `n3,``                                ``int` `sum)``    ``{``        ``// Store elements of``        ``// first array in hash``        ``HashSet s = ``new` `HashSet();``        ``for` `(``int` `i = ``0``; i < n1; i++)``        ``{``            ``s.add(a1[i]);``        ``}` `        ``// sum last two arrays``        ``// element one by one``        ``ArrayList al = ``new` `ArrayList<>(s);``        ``for` `(``int` `i = ``0``; i < n2; i++)``        ``{``            ``for` `(``int` `j = ``0``; j < n3; j++)``            ``{``                ` `                ``// Consider current pair and``                ``// find if there is an element``                ``// in a1[] such that these three``                ``// form a required triplet``                ``if` `(al.contains(sum - a2[i] - a3[j]) &``                            ``al.indexOf(sum - a2[i] - a3[j])``                            ``!= al.get(al.size() - ``1``))``                ``{``                    ``return` `true``;``                ``}``            ``}``        ``}``        ``return` `false``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `a1[] = {``1``, ``2``, ``3``, ``4``, ``5``};``        ``int` `a2[] = {``2``, ``3``, ``6``, ``1``, ``2``};``        ``int` `a3[] = {``3``, ``2``, ``4``, ``5``, ``6``};``        ``int` `sum = ``9``;``        ``int` `n1 = a1.length;``        ``int` `n2 = a2.length;``        ``int` `n3 = a3.length;``        ``if` `(findTriplet(a1, a2, a3, n1, n2, n3, sum))``        ``{``            ``System.out.println(``"Yes"``);``        ``}``        ``else``        ``{``            ``System.out.println(``"No"``);``        ``}``    ``}``}` `// This code is contributed by 29AjayKumar`

## Python3

 `# Python3 program to find three element``# from different three arrays such``# that a + b + c is equal to``# given sum` `# Function to check if there is``# an element from each array such``# that sum of the three elements is``# equal to given sum.``def` `findTriplet(a1, a2, a3,``                ``n1, n2, n3, ``sum``):` `    ``# Store elements of first``    ``# array in hash``    ``s ``=` `set``()` `    ``# sum last two arrays element``    ``# one by one``    ``for` `i ``in` `range``(n1):``        ``s.add(a1[i])` `    ``for` `i ``in` `range``(n2):``        ``for` `j ``in` `range``(n3):` `            ``# Consider current pair and``            ``# find if there is an element``            ``# in a1[] such that these three``            ``# form a required triplet``            ``if` `sum` `-` `a2[i] ``-` `a3[j] ``in` `s:``                ``return` `True``    ``return` `False` `# Driver code``a1 ``=` `[``1``, ``2``, ``3``, ``4``, ``5``]``a2 ``=` `[``2``, ``3``, ``6``, ``1``, ``2``]``a3 ``=` `[``3``, ``24``, ``5``, ``6``]``n1 ``=` `len``(a1)``n2 ``=` `len``(a2)``n3 ``=` `len``(a3)``sum` `=` `9``if` `findTriplet(a1, a2, a3,``               ``n1, n2, n3, ``sum``) ``=``=` `True``:``    ``print``(``"Yes"``)``else``:``    ``print``(``"No"``)` `# This code is contributed by Shrikant13`

## C#

 `// C# program to find three element``// from different three arrays such``// that a + b + c is equal to``// given sum``using` `System;``using` `System.Collections.Generic;` `class` `GFG``{` `    ``// Function to check if there is``    ``// an element from each array such``    ``// that sum of the three elements is``    ``// equal to given sum.``    ``static` `bool` `findTriplet(``int` `[]a1, ``int` `[]a2, ``int` `[]a3,``                                ``int` `n1, ``int` `n2, ``int` `n3,``                                ``int` `sum)``    ``{``        ``// Store elements of``        ``// first array in hash``        ``HashSet<``int``> s = ``new` `HashSet<``int``>();``        ``for` `(``int` `i = 0; i < n1; i++)``        ``{``            ``s.Add(a1[i]);``        ``}` `        ``// sum last two arrays``        ``// element one by one``        ``List<``int``> al = ``new` `List<``int``>(s);``        ``for` `(``int` `i = 0; i < n2; i++)``        ``{``            ``for` `(``int` `j = 0; j < n3; j++)``            ``{``                ` `                ``// Consider current pair and``                ``// find if there is an element``                ``// in a1[] such that these three``                ``// form a required triplet``                ``if` `(al.Contains(sum - a2[i] - a3[j]) &``                            ``al.IndexOf(sum - a2[i] - a3[j])``                            ``!= al[al.Count - 1])``                ``{``                    ``return` `true``;``                ``}``            ``}``        ``}``        ``return` `false``;``    ``}` `    ``// Driver Code``    ``public` `static` `void` `Main(String[] args)``    ``{``        ``int` `[]a1 = {1, 2, 3, 4, 5};``        ``int` `[]a2 = {2, 3, 6, 1, 2};``        ``int` `[]a3 = {3, 2, 4, 5, 6};``        ``int` `sum = 9;``        ``int` `n1 = a1.Length;``        ``int` `n2 = a2.Length;``        ``int` `n3 = a3.Length;``        ``if` `(findTriplet(a1, a2, a3, n1, n2, n3, sum))``        ``{``            ``Console.WriteLine(``"Yes"``);``        ``}``        ``else``        ``{``            ``Console.WriteLine(``"No"``);``        ``}``    ``}``}` `// This code is contributed by PrinciRaj1992`

## Javascript

 ``

Output :

`Yes`

Time complexity : O(n2
Auxiliary Space : O(n)
References :
http://stackoverflow.com/questions/2070359/finding-three-elements-in-an-array-whose-sum-is-closest-to-a-given-number
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