Minimum number of steps to convert a given matrix into Diagonally Dominant Matrix

Given a matrix of order NxN, the task is to find the minimum number of steps to convert given matrix into Diagonally Dominant Matrix. In each step, the only operation allowed is to decrease or increase any element by 1.

Examples:

Input: mat[][] = {{3, 2, 4}, {1, 4, 4}, {2, 3, 4}}
Output: 5
Sum of the absolute values of elements of row 1 except
the diagonal element is 3 more than abs(arr[0][0]).
1 more than abs(arr[1][1]) in the second row
and 1 more than abs(arr[2][2]) in the third row.
Hence, 3 + 1 + 1 = 5

Input: mat[][] = {{1, 2, 4, 0}, {1, 3, 4, 2}, {3, 3, 4, 2}, {-1, 0, 1, 4}}
Output: 13

Approach:



Below is the implementation of the above approach:

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
#define N 3
  
// Function to return the minimum steps
// required to convert the given matrix
// to a Diagonally Dominant Matrix
int findStepsForDDM(int arr[][N])
{
    int result = 0;
  
    // For each row
    for (int i = 0; i < N; i++) {
  
        // To store the sum of the current row
        int sum = 0;
        for (int j = 0; j < N; j++)
            sum += abs(arr[i][j]);
  
        // Remove the element of the current row
        // which lies on the main diagonal
        sum -= abs(arr[i][i]);
  
        // Checking if the diagonal element is less
        // than the sum of non-diagonal element
        // then add their difference to the result
        if (abs(arr[i][i]) < abs(sum))
            result += abs(abs(arr[i][i]) - abs(sum));
    }
  
    return result;
}
  
// Driven code
int main()
{
    int arr[N][N] = { { 3, -2, 1 },
                      { 1, -3, 2 },
                      { -1, 2, 4 } };
  
    cout << findStepsForDDM(arr);
  
    return 0;
}
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java implementation of the approach 
class GFG 
{
      
    final static int N = 3 ;
      
    // Function to return the minimum steps 
    // required to convert the given matrix 
    // to a Diagonally Dominant Matrix 
    static int findStepsForDDM(int arr[][]) 
    
        int result = 0
      
        // For each row 
        for (int i = 0; i < N; i++) 
        
      
            // To store the sum of the current row 
            int sum = 0
            for (int j = 0; j < N; j++) 
                sum += Math.abs(arr[i][j]); 
      
            // Remove the element of the current row 
            // which lies on the main diagonal 
            sum -= Math.abs(arr[i][i]); 
      
            // Checking if the diagonal element is less 
            // than the sum of non-diagonal element 
            // then add their difference to the result 
            if (Math.abs(arr[i][i]) < Math.abs(sum)) 
                result += Math.abs(Math.abs(arr[i][i]) - Math.abs(sum)); 
        
      
        return result; 
    
      
    // Driven code 
    public static void main (String[] args) 
    {
          
        int arr[][] = { { 3, -2, 1 }, 
                        { 1, -3, 2 }, 
                        { -1, 2, 4 } }; 
      
        System.out.println(findStepsForDDM(arr)); 
    }
}
  
// This code is contributed by AnkitRai01
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python3 implementation of the approach
  
N = 3
  
# Function to return the minimum steps
# required to convert the given matrix
# to a Diagonally Dominant Matrix
def findStepsForDDM(arr):
  
    result = 0
  
    # For each row
    for i in range(N):
  
        # To store the sum of the current row
        sum = 0
        for j in range(N):
            sum += abs(arr[i][j])
  
        # Remove the element of the current row
        # which lies on the main diagonal
        sum -= abs(arr[i][i])
  
        # Checking if the diagonal element is less
        # than the sum of non-diagonal element
        # then add their difference to the result
        if (abs(arr[i][i]) < abs(sum)):
            result += abs(abs(arr[i][i]) - abs(sum))
  
    return result
  
# Driver code
  
arr= [ [ 3, -2, 1 ],
    [ 1, -3, 2 ],
    [ -1, 2, 4 ] ]
  
print(findStepsForDDM(arr))
  
# This code is contributed by mohit kumar 29
chevron_right

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# implementation of the approach
using System;
  
class GFG
{
          
    static int N = 3 ;
      
    // Function to return the minimum steps 
    // required to convert the given matrix 
    // to a Diagonally Dominant Matrix 
    static int findStepsForDDM(int [,]arr) 
    
        int result = 0; 
      
        // For each row 
        for (int i = 0; i < N; i++) 
        
      
            // To store the sum of the current row 
            int sum = 0; 
            for (int j = 0; j < N; j++) 
                sum += Math.Abs(arr[i,j]); 
      
            // Remove the element of the current row 
            // which lies on the main diagonal 
            sum -= Math.Abs(arr[i,i]); 
      
            // Checking if the diagonal element is less 
            // than the sum of non-diagonal element 
            // then add their difference to the result 
            if (Math.Abs(arr[i,i]) < Math.Abs(sum)) 
                result += Math.Abs(Math.Abs(arr[i,i]) - Math.Abs(sum)); 
        
      
        return result; 
    
      
    // Driven code 
    static public void Main ()
    {
      
        int [,]arr = { { 3, -2, 1 }, 
                        { 1, -3, 2 }, 
                        { -1, 2, 4 } }; 
      
        Console.WriteLine(findStepsForDDM(arr)); 
    }
}
  
// This code is contributed by ajit.
chevron_right

Output:
0

Time complexity: O(N2)

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.





Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.



Article Tags :
Practice Tags :