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Check if it is possible to make two martices strictly increasing by swapping corresponding values only
• Last Updated : 05 Oct, 2020

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``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

 ` 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``?>`
Output:
```Yes

```

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