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Java Program for Diagonally Dominant Matrix

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  • Last Updated : 25 May, 2022
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In mathematics, a square matrix is said to be diagonally dominant if for every row of the matrix, the magnitude of the diagonal entry in a row is larger than or equal to the sum of the magnitudes of all the other (non-diagonal) entries in that row. More precisely, the matrix A is diagonally dominant if 
 

For example, The matrix 
 

is diagonally dominant because 
|a11| ≥ |a12| + |a13| since |+3| ≥ |-2| + |+1| 
|a22| ≥ |a21| + |a23| since |-3| ≥ |+1| + |+2| 
|a33| ≥ |a31| + |a32| since |+4| ≥ |-1| + |+2|
Given a matrix A of n rows and n columns. The task is to check whether matrix A is diagonally dominant or not.
Examples : 
 

Input : A = { { 3, -2, 1 },
              { 1, -3, 2 },
              { -1, 2, 4 } };
Output : YES
Given matrix is diagonally dominant
because absolute value of every diagonal
element is more than sum of absolute values
of corresponding row.

Input : A = { { -2, 2, 1 },
              { 1, 3, 2 },
              { 1, -2, 0 } };
Output : NO

 

The idea is to run a loop from i = 0 to n-1 for the number of rows and for each row, run a loop j = 0 to n-1 find the sum of non-diagonal element i.e i != j. And check if diagonal element is greater than or equal to sum. If for any row, it is false, then return false or print “No”. Else print “YES”. 
 

Java




// JAVA Program to check whether given matrix
// is Diagonally Dominant Matrix.
import java.util.*;
 
class GFG {
     
    // check the given  matrix is Diagonally
    // Dominant Matrix or not.
    static boolean isDDM(int m[][], int n)
    {
        // for each row
        for (int i = 0; i < n; i++)
        {       
      
            // for each column, finding
            //sum of each row.
            int sum = 0;
            for (int j = 0; j < n; j++)            
                sum += Math.abs(m[i][j]);       
      
            // removing the diagonal element.
            sum -= Math.abs(m[i][i]);
      
            // checking if diagonal element is less
            // than sum of non-diagonal element.
            if (Math.abs(m[i][i]) < sum)
                return false;
        
        }
 
        return true;
    }
 
    /* Driver program to test above function */
    public static void main(String[] args)
    {
        int n = 3;
        int m[][] = { { 3, -2, 1 },
                      { 1, -3, 2 },
                      { -1, 2, 4 } };
      
        if (isDDM(m, n))
             System.out.println("YES") ;
        else 
            System.out.println("NO");
     
    }
}
 
// This code is contributed by  Arnav Kr. Mandal.


Output : 

YES

Time Complexity: O(N2)

Auxiliary Space: O(1)

Please refer complete article on Diagonally Dominant Matrix for more details!


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