# Check whether a matrix is Markov matrix in C++

In this tutorial, we will learn how to **check whether a matrix is a Markov matrix or not in C++** with Example, Algorithm, and a program.

Markov matrix is a matrix in which the sum of each row is exactly equal to one.

## How to check whether a matrix is Markov matrix or not in C++

To check a Markov matrix we need to find the sum of each row and check whether the sum is equal to 1 or not.

**Example 1: **

Consider a matrix of 4*3 input matrix: 0.5 0.5 0 0.5 0.3 0.2 0 0.6 0.4 1 0 0 Sum of first row: 0.5 + 0.5 + 0 =1sum of second row: 0.5 + 0.3 + 0.2 =1sum of third row: 1 + 0 + 0 =1since, the sum of each rows is equal to 1, Therefore, the matrix is Markov matrix.

**Example 2: **

Consider a matrix of 3*3 input matrix: 1 0 0 0 1 0 1 1 1 sum of first row: 1 + 0 + 0 = 1 sum of second row: 0 + 1 +0 = 1 sum of third row: 1 + 1 + 1 = 3 since, the sum of each rows is not equal to 3, Therefore, the matrix is not a Markov matrix.

## Algorithm to check whether a matrix is Markov matrix

- declare and initialize a matrix of size
**m*n**. (where n and m are the lengths of row and column of matrix) - Declare a variable “rowsum” and initialize it with zero.
- Find the sum of each
**ith**row element and save to**rowsum.** - check whether the
**rowsum**is equal to one. if yes, then check for the remaining row. else print “Not markov matrix” - if all the row sum is equal to one, then print “Markov matrix”.

## C++ program to check whether a matrix is Markov matrix

#include <bits/stdc++.h> using namespace std; //function to check Markov matrix int isMarkov(float matrix[50][50], int m, int n){ for(int i = 0; i < m; i++) { //variable to store sum of each row float rowsum = 0; for(int j = 0; j < n; j++) rowsum += matrix[i][j]; if(rowsum != 1) return 0; } return 1; } int main(){ float matrix[50][50]; int n, m; //taking input in m and n for length of row and column cout<<"Enter the length of row of the matrix: "; cin >> m; cout<<"Enter the length of column of the matrix: "; cin >> n; //taking input in the matrix cout << "\nInput the element of matrix: \n"; for(int i = 0; i < m; i++) for(int j = 0; j < n; j++) cin>>matrix[i][j]; if (isMarkov(matrix, m, n)) cout << "The matrix is a markov matrix"; else cout << "The matrix is Not a markov matrix"; return 0; }

**Output: **

Enter the length of row of the matrix: 4 Enter the length of column of the matrix: 3 Input the element of matrix: 0.5 0.5 0 0.5 0.3 0.2 0 0.6 0.4 1 0 0 The matrix is a markov matrix.

**Time Complexity: **O(m*n), where m and n are lengths of row and column respectively

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