# Check if a pair with given product exists in a Matrix

Given a NxM matrix and a product K. The task is to check if a pair with the given product 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}};
K = 42
Output: YES

Input: mat[N][M] = {{1, 2, 3, 4},
{5, 6, 7, 8}};
K = 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 the current element of the matrix is divisible by the given product and when the product K is divided by the current element, the dividend obtained is also present in the hash.
That is,

```(k % mat[i][j] == 0) && (mp[k / mat[i][j]] > 0)
```
• If present, then return true, else insert current elements 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:

## C++

 `// CPP code to check for pair with given product ` `// exists in the matrix or not ` `#include ` `using` `namespace` `std; ` ` `  `#define N 4 ` `#define M 4 ` ` `  `// Function to check if a pair with given ` `// product exists in the matrix ` `bool` `isPairWithProductK(``int` `mat[N][M], ``int` `k) ` `{ ` `    ``// 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` `((k % mat[i][j] == 0) && (s.find(k / 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 product ` `    ``int` `k = 42; ` ` `  `    ``if` `(isPairWithProductK(mat, k)) { ` `        ``cout << ``"YES"` `<< endl; ` `    ``} ` `    ``else` `        ``cout << ``"NO"` `<< endl; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java code to check for pair with given product ` `// exists in the matrix or not ` `import` `java.util.*; ` `class` `GFG ` `{ ` `     ``static` `final` `int` `N=``4``; ` `     ``static` `final` `int` `M=``4``; ` `      `  `    ``// Function to check if a pair with given ` `    ``// product exists in the matrix ` `    ``static` `boolean` `isPairWithProductK(``int` `mat[][], ``int` `k) ` `    ``{ ` `        ``// 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` `((k % mat[i][j] == ``0``) && s.contains(k / 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 product ` `        ``int` `k = ``42``; ` `     `  `        ``if` `(isPairWithProductK(mat, k)) { ` `            ``System.out.println(``"YES"``); ` `        ``} ` `        ``else` `            ``System.out.println(``"NO"``); ` `     `  `         `  `    ``} ` `     `  `    ``// This code is conributed by ihritik ` `} `

## Python 3

 `# Python 3 code to check for pair with  ` `# given product exists in the matrix or not ` `N ``=` `4` `M ``=` `4` ` `  `# Function to check if a pair with  ` `# given product exists in the matrix ` `def` `isPairWithProductK(mat, k): ` ` `  `    ``# hash to store elements ` `    ``s ``=` `[] ` ` `  `    ``# 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` `((k ``%` `mat[i][j] ``=``=` `0``) ``and`  `                ``(k ``/``/` `mat[i][j]) ``in` `s): ` `                ``return` `True` `             `  `            ``else` `: ` `                ``s.append(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 product ` `    ``k ``=` `42` ` `  `    ``if` `(isPairWithProductK(mat, k)): ` `        ``print``( ``"YES"``) ` `     `  `    ``else``: ` `        ``print``(``"NO"``) ` ` `  `# This code is contributed by ita_c `

## C#

 `// C# code to check for pair with given product ` `// exists in the matrix or not ` `using` `System; ` `using` `System.Collections.Generic; ` ` `  `class` `GFG ` `{ ` `    ``static` `readonly` `int` `N = 4; ` `    ``static` `readonly` `int` `M = 4; ` `     `  `    ``// Function to check if a pair with given ` `    ``// product exists in the matrix ` `    ``static` `bool` `isPairWithProductK(``int` `[,]mat, ``int` `k) ` `    ``{ ` `        ``// 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` `((k % mat[i, j] == 0) &&  ` `                    ``s.Contains(k / mat[i, j])) ` `                ``{ ` `                    ``return` `true``; ` `                ``} ` `                ``else`  `                ``{ ` `                    ``s.Add(mat[i, j]); ` `                ``} ` `            ``} ` `        ``} ` `     `  `        ``return` `false``; ` `    ``} ` `     `  `    ``// Driver code ` `    ``public` `static` `void` `Main() ` `    ``{ ` `     `  `        ``// Input matrix ` `        ``int` `[,]mat = { { 1, 2, 3, 4 }, ` `                        ``{ 5, 6, 7, 8 }, ` `                        ``{ 9, 10, 11, 12 }, ` `                        ``{ 13, 14, 15, 16 } }; ` `     `  `        ``// given product ` `        ``int` `k = 42; ` `     `  `        ``if` `(isPairWithProductK(mat, k))  ` `        ``{ ` `            ``Console.WriteLine(``"YES"``); ` `        ``} ` `        ``else` `            ``Console.WriteLine(``"NO"``); ` `    ``} ` `} ` ` `  `// This code has been contributed ` `// by PrinciRaj1992  `

Output:

```YES
```

Time Complexity: O(N*M)

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