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.
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 <bits/stdc++.h>using namespace std;#define N 2#define M 2// Function that returns true if the matrix// is strictly increasingbool 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 codeint main(){ int a[N][M] = { { 2, 10 }, { 11, 20 } }; if (isMatrixInc(a)) cout << "Yes"; else cout << "No"; return 0;} |
Java
// Java implementation of the approachimport java.io.*;class GFG {static int N = 2;static int M = 2;// Function that returns true if the matrix// is strictly increasingstatic 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 codepublic 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 approachusing System; class GFG {static int N = 2;static int M = 2;// Function that returns true if the matrix// is strictly increasingstatic 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 codepublic 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 |
Javascript
<script>// Java Script implementation of the approachlet N = 2;let M = 2;// Function that returns true if the matrix// is strictly increasingfunction isMatrixInc(a){ // Check if the matrix // is strictly increasing for (let i = 0; i < N; i++) { for (let 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 let a = [[2, 10 ], [ 11, 20 ]]; if (isMatrixInc(a)) document.write( "Yes"); else document.write( "No");// This code is contributed by sravan kumar</script> |
Output:
Yes
Time Complexity: O(N*M)
Auxiliary Space: O(1)
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