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

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:

Python

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# 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))

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PHP

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<?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
?>

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Output:

Yes


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Improved By : AnkitRai01



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