Python 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.

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. 

Python3

# Python 3 code to check Markov Matrix

def checkMarkov(m) :

    # Outer loop to access rows
    # and inner to access columns
    for i in range(0, len(m)) :

        # Find sum of current row
        sm = 0
        for j in range(0, len(m[i])) :
            sm = sm + m[i][j]

        if (sm != 1) :
            return False

    return True

# Matrix to check
m = [ [ 0, 0, 1 ],
      [ 0.5, 0, 0.5 ],
      [ 1, 0, 0 ]      ]

# Calls the function check()
if (checkMarkov(m)) :
    print(" yes ")
else :
    print(" no ")


# This code is contributed by Nikita Tiwari.

Output

 yes 

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!