# Pair with given sum in matrix

Given a NxM matrix and a sum S. The task is to check if a pair with given Sum exists in the matrix or not.

Examples:

```Input: mat[N][M] = {{1, 2, 3, 4},
{5, 6, 7, 8},
{9, 10, 11, 12},
{13, 14, 15, 16}};
sum = 31
Output: YES

Input: mat[N][M] = {{1, 2, 3, 4},
{5, 6, 7, 8}};
sum = 150
Output: NO
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach:

• Take a hash to store all elements of the matrix in the hash.
• Start traversing through the matrix, and while traversing check if abs(sum-matrix_element) is present in the hash.
• If present, then return true, else insert the current matrix element into the hash.
• If all elements of the matrix are traversed and no pair is found, return false.

Below is the implementation of the above approach:

 `// CPP code to check for pair with given sum ` `#include ` `using` `namespace` `std; ` ` `  `#define N 4 ` `#define M 4 ` ` `  `// Function to check if a pair with given sum ` `// exists in the matrix ` `bool` `isPairWithSum(``int` `mat[N][M], ``int` `sum) ` `{ ` `    ``// hash to store elements ` `    ``unordered_set<``int``> s; ` ` `  `    ``// looping through elements ` `    ``// if present in the matrix ` `    ``// return true, else push ` `    ``// the element in matrix ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``for` `(``int` `j = 0; j < M; j++) { ` `            ``if` `(s.find(sum - mat[i][j]) != s.end()) { ` `                ``return` `true``; ` `            ``} ` `            ``else` `{ ` `                ``s.insert(mat[i][j]); ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `false``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``// Input matrix ` `    ``int` `mat[N][M] = { { 1, 2, 3, 4 }, ` `                      ``{ 5, 6, 7, 8 }, ` `                      ``{ 9, 10, 11, 12 }, ` `                      ``{ 13, 14, 15, 16 } }; ` ` `  `    ``// given sum ` `    ``int` `sum = 11; ` ` `  `    ``if` `(isPairWithSum(mat, sum)) { ` `        ``cout << ``"YES"` `<< endl; ` `    ``} ` `    ``else` `        ``cout << ``"NO"` `<< endl; ` ` `  `    ``return` `0; ` `} `

 `// Java code to check for pair ` `// with given sum ` `import` `java.util.*; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to check if a pair with  ` `// given sum exists in the matrix ` `static` `final` `int` `N = ``4``; ` `static` `final` `int` `M = ``4``; ` `static` `boolean` `isPairWithSum(``int` `[][]mat,  ` `                             ``int` `sum) ` `{ ` `    ``// hash to store elements ` `    ``Set s = ``new` `HashSet(); ` ` `  `    ``// looping through elements ` `    ``// if present in the matrix ` `    ``// return true, else push ` `    ``// the element in matrix ` `    ``for` `(``int` `i = ``0``; i < N; i++)  ` `    ``{ ` `        ``for` `(``int` `j = ``0``; j < M; j++) ` `        ``{ ` `            ``if` `(s.contains(sum - mat[i][j]))  ` `            ``{ ` `                ``return` `true``; ` `            ``} ` `            ``else`  `            ``{ ` `                ``s.add(mat[i][j]); ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `false``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `main(String []args) ` `{ ` ` `  `    ``// Input matrix ` `    ``int` `[][]mat = { { ``1``, ``2``, ``3``, ``4` `}, ` `                    ``{ ``5``, ``6``, ``7``, ``8` `}, ` `                    ``{ ``9``, ``10``, ``11``, ``12` `}, ` `                    ``{ ``13``, ``14``, ``15``, ``16` `} }; ` ` `  `    ``// given sum ` `    ``int` `sum = ``11``; ` ` `  `    ``if` `(isPairWithSum(mat, sum))  ` `    ``{ ` `        ``System.out.println(``"YES"``); ` `    ``} ` `    ``else` `        ``System.out.println(``"NO"``); ` `} ` `} ` ` `  `// This code is contributed by ihritik  `

 `// C# code to check for pair ` `// with given sum ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` `     `  `// Function to check if a pair with  ` `// given sum exists in the matrix ` `static` `readonly` `int` `N = 4; ` `static` `readonly` `int` `M = 4; ` `static` `bool` `isPairWithSum(``int` `[,]mat,  ` `                            ``int` `sum) ` `{ ` `    ``// hash to store elements ` `    ``HashSet<``int``> s = ``new` `HashSet<``int``>(); ` ` `  `    ``// looping through elements ` `    ``// if present in the matrix ` `    ``// return true, else push ` `    ``// the element in matrix ` `    ``for` `(``int` `i = 0; i < N; i++)  ` `    ``{ ` `        ``for` `(``int` `j = 0; j < M; j++) ` `        ``{ ` `            ``if` `(s.Contains(sum - mat[i, j]))  ` `            ``{ ` `                ``return` `true``; ` `            ``} ` `            ``else` `            ``{ ` `                ``s.Add(mat[i, j]); ` `            ``} ` `        ``} ` `    ``} ` `    ``return` `false``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main(String []args) ` `{ ` ` `  `    ``// Input matrix ` `    ``int` `[,]mat = { { 1, 2, 3, 4 }, ` `                    ``{ 5, 6, 7, 8 }, ` `                    ``{ 9, 10, 11, 12 }, ` `                    ``{ 13, 14, 15, 16 } }; ` ` `  `    ``// given sum ` `    ``int` `sum = 11; ` ` `  `    ``if` `(isPairWithSum(mat, sum))  ` `    ``{ ` `        ``Console.WriteLine(``"YES"``); ` `    ``} ` `    ``else` `        ``Console.WriteLine(``"NO"``); ` `} ` `} ` ` `  `// This code contributed by Rajput-Ji `

 `# python code to check for pair with given sum ` ` `  `N``=` `4` `M``=` `4` ` `  `# Function to check if a pair with given sum ` `# exists in the matrix ` `def` `isPairWithSum(mat, ``sum``): ` `    ``# hash to store elements ` `    ``s ``=` `set``() ` ` `  `    ``# looping through elements ` `    ``# if present in the matrix ` `    ``# return true, else push ` `    ``# the element in matrix ` `    ``for` `i ``in` `range``(N): ` `        ``for` `j ``in` `range``(M): ` `            ``if` `(``sum` `-` `mat[i][j]) ``in` `s : ` `                ``return` `True` `             `  `            ``else` `: ` `                ``s.add(mat[i][j]) ` `             `  `    ``return` `False` ` `  ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``:  ` ` `  `    ``# Input matrix ` `    ``mat ``=` `[[ ``1``, ``2``, ``3``, ``4` `], ` `                    ``[ ``5``, ``6``, ``7``, ``8``] , ` `                    ``[ ``9``, ``10``, ``11``, ``12``] , ` `                    ``[``13``, ``14``, ``15``, ``16``]]   ` ` `  `    ``# given sum ` `    ``sum` `=` `11` ` `  `    ``if` `(isPairWithSum(mat, ``sum``)) : ` `        ``print``(``"YES"``) ` `     `  `    ``else``: ` `        ``print``(``"NO"``) ` ` `  `     `  `# This code is contributed by AbhiThakur `

 ` `

Output:
```YES
```

Time Complexity: O(N*M)

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