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C++ Program for Markov matrix

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  • Last Updated : 18 Jan, 2022
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Given a m x n 2D matrix, check if it is a Markov Matrix.
Markov Matrix : The matrix in which the sum of each row is equal to 1.
 

Example of Markov Matrix

Examples: 
 

Input :
1    0   0
0.5  0  0.5
0    0   1
Output : yes

Explanation :
Sum of each row results to 1, 
therefore it is a Markov Matrix.

Input :
1 0 0
0 0 2
1 0 0
Output :
no

 

Approach : Initialize a 2D array, then take another single dimensional array to store the sum of each rows of the matrix, and check whether all the sum stored in this 1D array is equal to 1, if yes then it is Markov matrix else not. 
 

C++




// C++ code to check Markov Matrix
#include <iostream>
using namespace std;
  
#define n 3
  
bool checkMarkov(double m[][n])
{
    // outer loop to access rows
    // and inner to access columns
    for (int i = 0; i <n; i++) {
  
        // Find sum of current row
        double sum = 0;
        for (int j = 0; j < n; j++)
            sum = sum + m[i][j];
  
        if (sum != 1)
        return false;
    }
  
    return true;
}
  
// Driver Code
int main() 
{
    // Matrix to check
    double m[3][3] = { { 0, 0, 1 },
                    { 0.5, 0, 0.5 },
                    { 1, 0, 0 } };
  
    // calls the function check()
    if (checkMarkov(m))
        cout << " yes ";
    else
        cout << " no ";
}
  
// This code is contributed by Anant Agarwal.


Output : 

yes

Please refer complete article on Program for Markov matrix for more details!


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