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Check if it is possible to make two matrices strictly increasing by swapping corresponding values only

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  • Last Updated : 22 Apr, 2022
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Given two n * m matrices A[][] and B[][], the task is to make both the matrices strictly increasing (both rows and columns) only by swapping two elements in different matrices if they are located in the corresponding position i.e. A[i][j] can only be swapped with B[i][j]. If possible then print Yes otherwise, No.
Examples: 

Input: 
A[][] = {{2, 10},      B[][] = {{9, 4},  
         {11, 5}}               {3, 12}}
Output: Yes
Swap 2 with 9 and 5 with 12 then the resulting 
matrices will be strictly increasing.

Input: 
A[][] = {{1, 3},       B[][] = {{3, 1}, 
         {2, 4},                {3, 6}, 
         {5, 10}}               {4, 8}}
Output: No

Approach: We can solve this problem using greedy technique. Swap A[i][j] with B[i][j] if A[i][j] > B[i][j]. At the end for every i and j we have A[i][j] ≤ B[i][j]
If the resultant matrices are strictly increasing then print Yes otherwise, print No.
Below is the implementation of the above approach: 

C++




#include<bits/stdc++.h>
using namespace std;
 
// Function to check whether the matrices
// can be made strictly increasing
// with the given operation
string Check(int a[][2], int b[][2], int n, int m)
{
 
    // Swap only when a[i][j] > b[i][j]
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m; j++)
            if (a[i][j] > b[i][j])
                swap(a[i][j], b[i][j]);
 
    // Check if rows are strictly increasing
    for (int i = 0; i < n; i++)
        for (int j = 0; j < m - 1; j++)
            if(a[i][j] >= a[i][j + 1] || b[i][j] >= b[i][j + 1])
                return "No";
 
    // Check if columns are strictly increasing
    for (int i = 0; i < n - 1; i++)
        for (int j = 0; j < m ;j++)
            if (a[i][j] >= a[i + 1][j] || b[i][j] >= b[i + 1][j])
                return "No";
 
    return "Yes";
}
 
// Driver code
int main()
{
    int n = 2, m = 2;
    int a[][2] = {{2, 10}, {11, 5}};
    int b[][2] = {{9, 4}, {3, 12}};
    cout << (Check(a, b,n,m));
}
 
// This code is contributed by chitranayal

Java




class GFG{
     
// Function to check whether the matrices
// can be made strictly increasing
// with the given operation
public static String Check(int a[][], int b[][],
                           int n, int m)
{
     
    // Swap only when a[i][j] > b[i][j]
    for(int i = 0; i < n; i++)
        for(int j = 0; j < m; j++)
            if (a[i][j] > b[i][j])
            {
                int temp = a[i][j];
                a[i][j] = b[i][j];
                b[i][j] = temp;
            }
  
    // Check if rows are strictly increasing
    for(int i = 0; i < n; i++)
        for(int j = 0; j < m - 1; j++)
            if (a[i][j] >= a[i][j + 1] ||
                b[i][j] >= b[i][j + 1])
                return "No";
  
    // Check if columns are strictly increasing
    for(int i = 0; i < n - 1; i++)
        for(int j = 0; j < m ;j++)
            if (a[i][j] >= a[i + 1][j] ||
                b[i][j] >= b[i + 1][j])
                return "No";
  
    return "Yes";
}  
 
// Driver code
public static void main(String[] args)
{
    int n = 2, m = 2;
    int a[][] = { { 2, 10 }, { 11, 5 } };
    int b[][] = { { 9, 4 }, { 3, 12 } };
     
    System.out.print(Check(a, b, n, m));
}
}
 
// This code is contributed by divyeshrabadiya07

Python3




# Function to check whether the matrices
# can be made strictly increasing
# with the given operation
def Check(a, b):
 
    # Swap only when a[i][j] > b[i][j]
    for i in range(n):
        for j in range(m):
            if a[i][j]>b[i][j]:
                a[i][j], b[i][j]= b[i][j], a[i][j]
 
    # Check if rows are strictly increasing
    for i in range(n):
        for j in range(m-1):
            if(a[i][j]>= a[i][j + 1] or b[i][j]>= b[i][j + 1]):
                return "No"
 
    # Check if columns are strictly increasing
    for i in range(n-1):
        for j in range(m):
            if (a[i][j]>= a[i + 1][j] or b[i][j]>= b[i + 1][j]):
                return "No"
 
    return "Yes"
 
# Driver code
if __name__=="__main__":
     
    n, m = 2, 2
    a =[[2, 10], [11, 5]]
    b =[[9, 4], [3, 12]]
    print(Check(a, b))

C#




// C# implementation of the
// above approach
using System;
using System.Collections;
class GfG{
      
// Function to check
// whether the matrices
// can be made strictly
// increasing with the
// given operation
static string Check(int [,]a, int [,]b,
                    int n, int m)
{
  // Swap only when
  // a[i][j] > b[i][j]
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m; j++)
      if (a[i, j] > b[i, j])
      {
        int tmp = a[i, j];
        a[i, j] = b[i, j];
        b[i, j] = tmp;
      }
 
  // Check if rows are
  // strictly increasing
  for (int i = 0; i < n; i++)
    for (int j = 0; j < m - 1; j++)
      if(a[i, j] >= a[i, j + 1] ||
         b[i, j] >= b[i, j + 1])
        return "No";
 
  // Check if columns are
  // strictly increasing
  for (int i = 0; i < n - 1; i++)
    for (int j = 0; j < m ; j++)
      if (a[i, j] >= a[i + 1, j] ||
          b[i, j] >= b[i + 1, j])
        return "No";
 
  return "Yes";
}
      
// Driver Code
public static void Main(string []arg)
{
  int n = 2, m = 2;
  int [,]a = {{2, 10}, {11, 5}};
  int [,]b = {{9, 4}, {3, 12}};
  Console.Write(Check(a, b, n, m));
}
}
 
// This code is contributed by Rutvik_56

PHP




<?php
// PHP implementation of the approach
 
// Function to check whether the matrices
// can be made strictly increasing
// with the given operation
function Check($a, $b, $n, $m)
{
 
    // Swap only when a[i][j] > b[i][j]
    for ($i = 0; $i < $n; $i++)
    {
        for ($j= 0; $j < $n; $j++)
        {
            if ($a[$i][$j] > $b[$i][$j])
            {
                $temp = $a[$i][$j];
                $a[$i][$j] = $b[$i][$j];
                $b[$i][$j] = $temp;
            }
        }
    }
             
 
    // Check if rows are strictly increasing
    for ($i = 0; $i < $n; $i++)
    {
        for ($j= 0;$j < $m-1 ; $j++)
        {
            if($a[$i][$j] >= $a[$i][$j + 1] or
               $b[$i][$j] >= $b[$i][$j + 1])
                return "No";
        }
    }
 
    // Check if columns are strictly increasing
    for ($i = 0; $i < $n - 1; $i++)
    {
        for ($j = 0; $j < $m; $j++)
        {
            if ($a[$i][$j] >= $a[$i + 1][$j] or
                $b[$i][$j] >= $b[$i + 1][$j])
                return "No";
        }
    }
    return "Yes";
}
 
// Driver code
$n = 2; $m = 2;
$a = array(array(2, 10), array(11, 5));
$b = array(array(9, 4), array(3, 12));
print(Check($a, $b, $n, $m));
 
// This code is contributed by AnkitRai01
?>

Javascript




<script>
  
// Function to check whether the matrices
// can be made strictly increasing
// with the given operation
function Check(a, b, n, m)
{
      
    // Swap only when a[i][j] > b[i][j]
    for(let i = 0; i < n; i++)
        for(let j = 0; j < m; j++)
            if (a[i][j] > b[i][j])
            {
                let temp = a[i][j];
                a[i][j] = b[i][j];
                b[i][j] = temp;
            }
   
    // Check if rows are strictly increasing
    for(let i = 0; i < n; i++)
        for(let j = 0; j < m - 1; j++)
            if (a[i][j] >= a[i][j + 1] ||
                b[i][j] >= b[i][j + 1])
                return "No";
   
    // Check if columns are strictly increasing
    for(let i = 0; i < n - 1; i++)
        for(let j = 0; j < m ;j++)
            if (a[i][j] >= a[i + 1][j] ||
                b[i][j] >= b[i + 1][j])
                return "No";
   
    return "Yes";
       
 
// Driver Code
 
        let n = 2, m = 2;
    let a = [[ 2, 10 ], [ 11, 5 ]];
    let b = [[ 9, 4 ],  [3, 12 ]];
      
    document.write(Check(a, b, n, m));
      
</script>

Output: 

Yes

 

Time Complexity: O(N*M), as we are traversing over the matrix.

Auxiliary Space: O(1), as we are not using any extra space.


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