PHP Program for Markov matrix

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.

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. 

<?php
// PHP code to check Markov Matrix

function checkMarkov($m)
{
    $n = 3;
    
    // outer loop to access rows
    // and inner to access columns
    for ($i = 0; $i <$n; $i++) 
    {

        // Find sum of current row
        $sum = 0;
        for ($j = 0; $j < $n; $j++)
            $sum = $sum + $m[$i][$j];

        if ($sum != 1)
        return false;
    }

    return true;
}

    // Driver Code
    // Matrix to check
    $m = array(array(0, 0, 1),
               array(0.5, 0, 0.5),
               array(1, 0, 0));


    // calls the function check()
    if (checkMarkov($m))
        echo " yes ";
    else
        echo " no ";

// This code is contributed by nitin mittal.
?>

 yes 

Complexity Analysis:

• Time Complexity: O(m*n), Here m is the number of rows and n is the number of columns.
• Auxiliary Space: O(1), As constant extra space is used.

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