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.
Implementation:
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. |
Java
// Java code to check Markov Matrix import java.io.*; public class markov { static boolean checkMarkov(double m[][]) { // outer loop to access rows // and inner to access columns for (int i = 0; i < m.length; i++) { // Find sum of current row double sum = 0; for (int j = 0; j < m[i].length; j++) sum = sum + m[i][j]; if (sum != 1) return false; } return true; } public static void main(String args[]) { // Matrix to check double m[][] = { { 0, 0, 1 }, { 0.5, 0, 0.5 }, { 1, 0, 0 } }; // calls the function check() if (checkMarkov(m)) System.out.println(" yes "); else System.out.println(" no "); } } |
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. |
C#
// C# code to check // Markov Matrix using System; class GFG { static bool checkMarkov(double [,]m) { // outer loop to access // rows and inner to // access columns for (int i = 0; i < m.GetLength(0); i++) { // Find sum of // current row double sum = 0; for (int j = 0; j < m.GetLength(1); j++) sum = sum + m[i, j]; if (sum != 1) return false; } return true; } // Driver Code static void Main() { // Matrix to check double [,]m = new double[,]{{ 0, 0, 1}, {0.5, 0, 0.5}, {1, 0, 0}}; // calls the // function check() if (checkMarkov(m)) Console.WriteLine(" yes "); else Console.WriteLine(" no "); } } // This code is contributed by // Manish Shaw(manishshaw1) |
PHP
<?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. ?> |
Javascript
<script> // Javascript code to check Markov Matrix let n = 3 function checkMarkov( m) { // outer loop to access rows // and inner to access columns for (let i = 0; i <n; i++) { // Find sum of current row let sum = 0; for (let j = 0; j < n; j++) sum = sum + m[i][j]; if (sum != 1) return false; } return true; } // driver code // Matrix to check let m = [ [ 0, 0, 1 ], [ 0.5, 0, 0.5 ], [ 1, 0, 0 ] ]; // calls the function check() if (checkMarkov(m)) document.write(" yes "); else document.write(" no "); </script> |
Output
yes
Time Complexity: O(n2)
Auxiliary Space: O(1), since no extra space has been taken.
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