Check if a pair with given product exists in a Matrix

Given an 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

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 <bits/stdc++.h>
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<Integer> s=new HashSet<Integer>();
     
        // 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 contributed 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

Javascript

<script>
// Javascript code to check for pair with given product
// exists in the matrix or not
     
    
    let N = 4;
    let M = 4;
     
    function isPairWithProductK(mat,k)
    {
        // hash to store elements
        let s=new Set();
       
        // looping through elements
        // if present in the matrix
        // return true, else push
        // the element in matrix
        for (let i = 0; i < N; i++) {
            for (let j = 0; j < M; j++) {
                if ((k % mat[i][j] == 0) && s.has(Math.floor(k / mat[i][j]))) {
                    return true;
                }
                else {
                    s.add(mat[i][j]);
                }
            }
        }
       
        return false;
    }
     
    // Driver code
     
    // Input matrix
    let mat = [[ 1, 2, 3, 4 ],
                    [ 5, 6, 7, 8] ,
                    [ 9, 10, 11, 12] ,
                    [13, 14, 15, 16]] ;
 
    // given product
 
    let k = 42;
   
    if (isPairWithProductK(mat, k))
    {
        document.write("YES");
    }
    else
        document.write("NO");
     
 
// This code is contributed by rag2127
</script>