# Check if the given matrix is increasing row and column wise

Given a matrix mat[][], the task is to check if the given matrix is strictly increasing or not. A matrix is said to be strictly increasing if all of its rows as well as all of its columns are strictly increasing.

Examples:

Input: mat[][] = {{2, 10}, {11, 20}}
Output: Yes
All the rows and columns are strictly increasing.

Input: mat[][] = {{2, 1}, {11, 20}}
Output: No
First row doesn’t satisfy the required condition.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Linearly traverse for every element and check if there are increasing row-wise and column-wise or not. The two conditions are (a[i][j] > a[i – 1][j]) and (a[i][j] > a[i][j – 1]) . If any of the two conditions fail, then the matrix is not strictly increasing.

Below is the implementation of the above approach:

## C++

 `// C++ implementation of the approach ` `#include ` `using` `namespace` `std; ` `#define N 2 ` `#define M 2 ` ` `  `// Function that returns true if the matrix ` `// is strictly increasing ` `bool` `isMatrixInc(``int` `a[N][M]) ` `{ ` ` `  `    ``// Check if the matrix ` `    ``// is strictly increasing ` `    ``for` `(``int` `i = 0; i < N; i++) { ` `        ``for` `(``int` `j = 0; j < M; j++) { ` ` `  `            ``// Out of bound condition ` `            ``if` `(i - 1 >= 0) { ` `                ``if` `(a[i][j] <= a[i - 1][j]) ` `                    ``return` `false``; ` `            ``} ` ` `  `            ``// Out of bound condition ` `            ``if` `(j - 1 >= 0) { ` `                ``if` `(a[i][j] <= a[i][j - 1]) ` `                    ``return` `false``; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `a[N][M] = { { 2, 10 }, ` `                    ``{ 11, 20 } }; ` ` `  `    ``if` `(isMatrixInc(a)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation of the approach ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` ` `  `static` `int` `N = ``2``; ` `static` `int` `M = ``2``; ` ` `  `// Function that returns true if the matrix ` `// is strictly increasing ` `static` `boolean` `isMatrixInc(``int` `a[][]) ` `{ ` ` `  `    ``// Check if the matrix ` `    ``// is strictly increasing ` `    ``for` `(``int` `i = ``0``; i < N; i++)  ` `    ``{ ` `        ``for` `(``int` `j = ``0``; j < M; j++)  ` `        ``{ ` ` `  `            ``// Out of bound condition ` `            ``if` `(i - ``1` `>= ``0``) ` `            ``{ ` `                ``if` `(a[i][j] <= a[i - ``1``][j]) ` `                    ``return` `false``; ` `            ``} ` ` `  `            ``// Out of bound condition ` `            ``if` `(j - ``1` `>= ``0``)  ` `            ``{ ` `                ``if` `(a[i][j] <= a[i][j - ``1``]) ` `                    ``return` `false``; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver code ` ` `  `public` `static` `void` `main (String[] args)  ` `{ ` `     `  `    ``int` `a[][] = { { ``2``, ``10` `}, ` `                    ``{ ``11``, ``20` `} }; ` `     `  `    ``if` `(isMatrixInc(a)) ` `        ``System.out.print( ``"Yes"``); ` `    ``else` `        ``System.out.print( ``"No"``); ` `} ` `} ` ` `  `// This code is contributed by anuj_67.. `

## Python3

 `# Python3 implementation of the approach  ` ` `  `N, M ``=` `2``, ``2` ` `  `# Function that returns true if the matrix  ` `# is strictly increasing  ` `def` `isMatrixInc(a) :  ` ` `  `    ``# Check if the matrix  ` `    ``# is strictly increasing  ` `    ``for` `i ``in` `range``(N) : ` `        ``for` `j ``in` `range``(M) : ` ` `  `            ``# Out of bound condition  ` `            ``if` `(i ``-` `1` `>``=` `0``) : ` `                ``if` `(a[i][j] <``=` `a[i ``-` `1``][j]) :  ` `                    ``return` `False``;  ` ` `  `            ``# Out of bound condition  ` `            ``if` `(j ``-` `1` `>``=` `0``) :  ` `                ``if` `(a[i][j] <``=` `a[i][j ``-` `1``]) : ` `                    ``return` `False``;  ` `                     `  `    ``return` `True``; ` ` `  ` `  `# Driver code  ` `if` `__name__ ``=``=` `"__main__"` `:  ` ` `  `    ``a ``=` `[ [ ``2``, ``10` `],  ` `        ``[``11``, ``20` `] ];  ` ` `  `    ``if` `(isMatrixInc(a)) : ` `        ``print``(``"Yes"``);  ` `    ``else` `: ` `        ``print``(``"No"``);  ` `         `  `# This code is contributed by AnkitRai01 `

## C#

 `// C# implementation of the approach ` `using` `System;  ` `     `  `class` `GFG  ` `{ ` ` `  `static` `int` `N = 2; ` `static` `int` `M = 2; ` ` `  `// Function that returns true if the matrix ` `// is strictly increasing ` `static` `Boolean isMatrixInc(``int` `[,]a) ` `{ ` ` `  `    ``// Check if the matrix ` `    ``// is strictly increasing ` `    ``for` `(``int` `i = 0; i < N; i++)  ` `    ``{ ` `        ``for` `(``int` `j = 0; j < M; j++)  ` `        ``{ ` ` `  `            ``// Out of bound condition ` `            ``if` `(i - 1 >= 0) ` `            ``{ ` `                ``if` `(a[i,j] <= a[i - 1,j]) ` `                    ``return` `false``; ` `            ``} ` ` `  `            ``// Out of bound condition ` `            ``if` `(j - 1 >= 0)  ` `            ``{ ` `                ``if` `(a[i,j] <= a[i,j - 1]) ` `                    ``return` `false``; ` `            ``} ` `        ``} ` `    ``} ` ` `  `    ``return` `true``; ` `} ` ` `  `// Driver code ` `public` `static` `void` `Main (String[] args)  ` `{ ` `     `  `    ``int` `[,]a = { { 2, 10 }, ` `                    ``{ 11, 20 } }; ` `     `  `    ``if` `(isMatrixInc(a)) ` `        ``Console.WriteLine( ``"Yes"``); ` `    ``else` `        ``Console.WriteLine( ``"No"``); ` `} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:

```Yes
```

My Personal Notes arrow_drop_up Striver(underscore)79 at Codechef and codeforces D

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Improved By : AnkitRai01, vt_m, princi singh