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 Matrixdef 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 checkm = [ [ 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!
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