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Program for Markov matrix
  • Difficulty Level : Basic
  • Last Updated : 26 Jul, 2018

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++

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// 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.

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Java

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// 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 ");
    }
}

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Python3

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# 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.

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C#

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// 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)

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PHP

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<?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.
?>

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Output :

yes

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