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Solved 2024 Thory Paper ISC Computer Science

Class 12 - ISC Computer Science Solved Theory Papers

Doubly Markov Matrix Program - ISC 2024 Theory

Write a program to declare a square matrix M[][] of order ‘N’. Check if the matrix is a Doubly Markov matrix or not. A matrix which satisfies the following conditions is Doubly Markov Matrix:

(i) All elements are >= 0


(ii) Sum of each row = 1
(iii) Sum of each column = 1

 

Accept ‘N’ from the user where 3 <= N <= 9. Display an appropriate error message if ‘N’ is not in the given range or the entered numbers are negative. Allow the user to create a matrix and check whether the created matrix is a Doubly Markov Matrix or not.

Test your program for the following data and some random data:

Example 1
INPUT: N = 3
Enter elements in the matrix: 0.5, 0.25, 0.25, 0.25, 0.75, 0.0, 0.25, 0.0, 0.75
OUTPUT: FORMED MATRIX

0.5

0.25

0.25

0.25

0.75

0.0

0.25

0.0

0.75

IT IS A DOUBLY MARKOV MATRIX

Example 2
INPUT: N = 3
Enter elements in the matrix: 1.5, 3, 0.15, 0.25, 4, 1.0, 0.25, 1.0, 3
OUTPUT: FORMED MATRIX

1.5

3

0.15

0.25

4

1.0

0.25

1.0

3

IT IS NOT A DOUBLY MARKOV MATRIX

Example 3
INPUT: N = 3
Enter elements in the matrix: 0.8, -4.0, 0.9, 3.5, 0.25, 0.25, 0.5, 0.0, 0.5
OUTPUT: NEGATIVE NUMBERS ENTERED. INVALID ENTRY

 

Example 4
INPUT: N = 12
OUTPUT: SIZE IS OUT OF RANGE. INVALID ENTRY

Java 
import java.util.Scanner;
class DoublyMarkov{
    public static void main(String[] args){
        Scanner in = new Scanner(System.in);
        System.out.print("N = ");
        int n = Integer.parseInt(in.nextLine());
        if(n < 3 || n > 9){
            System.out.println("SIZE IS OUT OF RANGE. INVALID ENTRY");
            return;
        }
        double m[][] = new double[n][n];
        boolean isNegative = false;
        System.out.println("Enter elements in the matrix:");
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++){
                m[i][j] = Double.parseDouble(in.nextLine());
                if(m[i][j] < 0)
                    isNegative = true;
            }
        }
        if(isNegative){
            System.out.println("NEGATIVE NUMBERS ENTERED. INVALID ENTRY");
            return;
        }
        System.out.println("FORMED MATRIX");
        for(int i = 0; i < n; i++){
            for(int j = 0; j < n; j++)
                System.out.print(m[i][j] + "\t");
            System.out.println();
        }
        boolean isMarkov = true;
        for(int i = 0; i < n; i++){
            double rowSum = 0.0;
            double colSum = 0.0;
            for(int j = 0; j < n; j++){
                rowSum += m[i][j];
                colSum += m[j][i];
            }
            if(rowSum != 1)
                isMarkov = false;
            if(colSum != 1)
                isMarkov = false;
        }
        if(isMarkov)
            System.out.println("IT IS A DOUBLY MARKOV MATRIX");
        else
            System.out.println("IT IS NOT A DOUBLY MARKOV MATRIX");
    }
}

Output

 
OUTPUT 1:
N = 3
Enter elements in the matrix:
0.5
0.25
0.25
0.25
0.75
0.0
0.25
0.0
0.75
FORMED MATRIX
0.5 0.25    0.25    
0.25    0.75    0.0 
0.25    0.0 0.75    
IT IS A DOUBLY MARKOV MATRIX

OUTPUT 2:

N = 3
Enter elements in the matrix:
1.5
3
0.15
0.25
4
1.0
0.25
1.0
3
FORMED MATRIX
1.5 3.0 0.15    
0.25    4.0 1.0 
0.25    1.0 3.0 
IT IS NOT A DOUBLY MARKOV MATRIX


OUTPUT 3:

N = 3
Enter elements in the matrix:
0.8
-4.0
0.9
3.5
0.25
0.25
0.5
0.0
0.5
NEGATIVE NUMBERS ENTERED. INVALID ENTRY

OUTPUT 4:
N = 12
SIZE IS OUT OF RANGE. INVALID ENTRY
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