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Sort the minor diagonal elements of a matrix

The problem is to sort the minor diagonal elements of a given square matrix in ascending order. The minor diagonal of a matrix consists of elements from the top-right corner to the bottom-left corner. The objective is to rearrange these diagonal elements in such a way that they are in ascending order.

Example

Consider the following matrix:

4  2  6  7  5
3  1  7  3  2
1  5  9  4  6
8  1  9  2  6
7  6  2  2  5

After sorting the minor diagonal elements, the matrix becomes:

4  2  6  7  1
3  1  7  3  2
1  5  5  4  6
8  7  9  2  6
9  6  2  2  5

Idea to Solve the Problem

To solve this problem, we can traverse the minor diagonal of the matrix and for each diagonal element, find the minimum element in the remaining diagonal elements and swap them. This way, we can gradually sort the minor diagonal elements in ascending order.

Algorithm

  1. For each element on the minor diagonal (from matrix[0][N-1] to matrix[N-1][0]), do the following: a. Find the minimum element in the remaining diagonal elements. b. Swap the current element with the found minimum element.
  2. Display the matrix after sorting the minor diagonal.

Pseudocode

swap_node(i, j, matrix):
    // Swap diagonal elements of given location
    temp = matrix[N-1-i][i]
    matrix[N-1-i][i] = matrix[N-1-j][j]
    matrix[N-1-j][j] = temp

change_element(matrix, k):
    // Set the minimum value on a given location
    min = k
    for i from k to 0:
        if matrix[N-1-min][min] > matrix[N-1-i][i]:
            min = i
    // Set the minimum element of [k][N-1-k] position
    swap_node(k, min, matrix)

sort_minor(matrix):
    for k from N-1 to 0:
        change_element(matrix, k)
    show_data(matrix)

main:
    matrix = ...  // Define the matrix
    sort_minor(matrix)

Code Solution

// C Program
// Sort the minor diagonal elements of a matrix
#include <stdio.h>
#define N 5

//Display matrix elements
void show_data(int matrix[N][N])
{
    for (int i = 0; i < N; ++i)
    {
        for (int j = 0; j < N; ++j)
        {
            printf("  %d", matrix[i][j]);
        }
        printf("\n");
    }
    printf("\n");
}

// Swap diagonal elements of given location
void swap_node(int i, int j, int matrix[N][N])
{
    int temp = matrix[N-1-i][i];

    matrix[N-1-i][i] = matrix[N-1-j][j];
    
    matrix[N-1-j][j] = temp;
}

// Set the minimum value on a given location
void change_element(int matrix[N][N], int k)
{
    int min = k;

    for (int i = k; i >= 0 ; --i)
    {
        if (matrix[N-1-min][min] > matrix[N-1-i][i])
        {
            min = i;
        }
    }
    // Set the maximum element of [k][N-k] position
    swap_node(k, min, matrix);
}

// Sort the minor diagonal of a matrix
void sort_minor(int matrix[N][N])
{
    for (int k = N-1; k >=0; --k)
    {
        change_element(matrix, k);
    }
    show_data(matrix);
}
int main()
{
    // Test Case
    int matrix[N][N] = 
    {
        {4 , 2 , 6 , 7 , 5} ,
        {3 , 1 , 7 , 3,  2} ,
        {1 , 5 , 9 , 4,  6},
        {8 , 1 , 9 , 2,  6},
        {7 , 6 , 2 , 2,  5}
    };
    sort_minor(matrix);
    return 0;
}

Output

  4  2  6  7  1
  3  1  7  3  2
  1  5  5  4  6
  8  7  9  2  6
  9  6  2  2  5
/* 
  Java Program
  Sort the minor diagonal elements of a matrix
*/
class MyMatrix
{

    //Display matrix elements
    public void show_data(int[][] matrix,int size)
    {

        for (int i = 0; i < size; ++i)
        {
            for (int j = 0; j < size; ++j)
            {
                System.out.print("  " + matrix[i][j] );
            }
            System.out.print("\n");
        }
        System.out.print("\n");
    }
    // Swap diagonal elements of given location
    public void swap_node(int i, int j,int size, int[][] matrix)
    {
        int temp = matrix[size - 1 - i][i];
        matrix[size - 1 - i][i] = matrix[size - 1 - j][j];
        matrix[size - 1 - j][j] = temp;
    }
    // Set the minimum value on a given location
    public void change_element(int[][] matrix, int k, int size)
    {
        int min = k;

        for (int i = k; i >= 0; --i)
        {
            if (matrix[size - 1 - min][min] > matrix[size - 1 - i][i])
            {
                min = i;
            }
        }
        // Set the maximum element of [k][size-k] position
        swap_node(k, min,size, matrix);
    }
    // Sort the minor diagonal of a matrix
    public void sort_minor(int[][] matrix)
    {
        int size = matrix.length;

        if(matrix[0].length != size || size == 0)
        {
            // Not square matrix
            return;
        }
      	// Display matrix element
      	System.out.print("  Before Sort Minor Diagonal Element\n");
        show_data(matrix,size);
     
        for (int k = size - 1; k >= 0; --k)
        {
            change_element(matrix, k,size);
        }
      	// Display matrix element
      	System.out.print("  After Sort Minor Diagonal Element\n");
        show_data(matrix,size);
    }

    public static void main(String[] args) 
    {

        MyMatrix obj = new MyMatrix();
        // Case 1
        // Define matrix of integer elements
        int[][] matrix1 =  
        {
            {4 , 2 , 6 , 7 , 5} ,
            {3 , 1 , 7 , 3,  2} ,
            {1 , 5 , 9 , 4,  6},
            {8 , 1 , 9 , 2,  6},
            {7 , 6 , 2 , 2,  5}
        };
        obj.sort_minor(matrix1);

        // Case 2
        // Define matrix of integer elements
        int[][] matrix2  = 
        {
            { 1 , 9 , 8 , 3 , 2 } , 
            { 3 , -1 , 5 , 3 , 8} , 
            { 1 , 3 , 5 , 6 , 11} , 
            { 0 , 8 , 8 , 6 , 2 } , 
            { 1 , 3 , 4 , 5 , 10},
        };

        obj.sort_minor(matrix2);
    }
}

Output

  Before Sort Minor Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  9  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Minor Diagonal Element
  4  2  6  7  1
  3  1  7  3  2
  1  5  5  4  6
  8  7  9  2  6
  9  6  2  2  5

  Before Sort Minor Diagonal Element
  1  9  8  3  2
  3  -1  5  3  8
  1  3  5  6  11
  0  8  8  6  2
  1  3  4  5  10

  After Sort Minor Diagonal Element
  1  9  8  3  1
  3  -1  5  2  8
  1  3  3  6  11
  0  5  8  6  2
  8  3  4  5  10
// Include header file
#include <iostream>
#define N 5
using namespace std;
/*
  C++ Program
  Sort the minor diagonal elements of a matrix
*/
class MyMatrix
{
    public:
        // Display matrix elements
        void show_data(int matrix[N][N])
        {
            for (int i = 0; i < N; ++i)
            {
                for (int j = 0; j < N; ++j)
                {
                    cout << "  " << matrix[i][j];
                }
                cout << "\n";
            }
            cout << "\n";
        }
    //  Swap diagonal elements of given location
    void swap_node(int i, int j, int matrix[N][N])
    {
        int temp = matrix[N - 1 - i][i];
        matrix[N - 1 - i][i] = matrix[N - 1 - j][j];
        matrix[N - 1 - j][j] = temp;
    }
    //  Set the minimum value on a given location
    void change_element(int matrix[N][N], int k)
    {
        int min = k;
        for (int i = k; i >= 0; --i)
        {
            if (matrix[N - 1 - min][min] > matrix[N - 1 - i][i])
            {
                min = i;
            }
        }
        //  Set the maximum element of [k][N-k] position
        this->swap_node(k, min, matrix);
    }
    //  Sort the minor diagonal of a matrix
    void sort_minor(int matrix[N][N])
    {
       
        //  Display matrix element
        cout << "  Before Sort Minor Diagonal Element\n";
        this->show_data(matrix);
        for (int k = N - 1; k >= 0; --k)
        {
            this->change_element(matrix, k);
        }
        //  Display matrix element
        cout << "  After Sort Minor Diagonal Element\n";
        this->show_data(matrix);
    }
};
int main()
{
    MyMatrix obj = MyMatrix();
    //  Define matrix of integer elements
    int matrix[N][N] =     
    {
        {4 , 2 , 6 , 7 , 5} ,
        {3 , 1 , 7 , 3,  2} ,
        {1 , 5 , 9 , 4,  6},
        {8 , 1 , 9 , 2,  6},
        {7 , 6 , 2 , 2,  5}
    };
    obj.sort_minor(matrix);
  
    return 0;
}

Output

  Before Sort Minor Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  9  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Minor Diagonal Element
  4  2  6  7  1
  3  1  7  3  2
  1  5  5  4  6
  8  7  9  2  6
  9  6  2  2  5
// Include namespace system
using System;
/* 
  C# Program
  Sort the minor diagonal elements of a matrix
*/
public class MyMatrix
{
	// Display matrix elements
	public void show_data(int[,] matrix, int size)
	{
		for (int i = 0; i < size; ++i)
		{
			for (int j = 0; j < size; ++j)
			{
				Console.Write("   " + matrix[i,j]);
			}
			Console.Write("\n");
		}
		Console.Write("\n");
	}
	//  Swap diagonal elements of given location
	public void swap_node(int i, int j, int size, int[,] matrix)
	{
		int temp = matrix[size - 1 - i,i];
		matrix[size - 1 - i,i] = matrix[size - 1 - j,j];
		matrix[size - 1 - j,j] = temp;
	}
	//  Set the minimum value on a given location
	public void change_element(int[,] matrix, int k, int size)
	{
		int min = k;
		for (int i = k; i >= 0; --i)
		{
			if (matrix[size - 1 - min,min] > matrix[size - 1 - i,i])
			{
				min = i;
			}
		}
		//  Set the maximum element of [k,size-k] position
		swap_node(k, min, size, matrix);
	}
	//  Sort the minor diagonal of a matrix
	public void sort_minor(int[,] matrix)
	{
		int size = matrix.GetLength(0);

		if (matrix.GetLength(1) != size || size == 0)
		{
		        //  Not square matrix
			return;
		}
		//  Display matrix element
		Console.Write("  Before Sort Minor Diagonal Element\n");
		show_data(matrix, size);
		for (int k = size - 1; k >= 0; --k)
		{
			change_element(matrix, k, size);
		}
		//  Display matrix element
		Console.Write("  After Sort Minor Diagonal Element\n");
		show_data(matrix, size);
	}
	public static void Main(String[] args)
	{
		MyMatrix obj = new MyMatrix();
		//  Case 1
		//  Define matrix of integer elements
		int[,] matrix1 = 
        {
            {4 , 2 , 6 , 7 , 5} ,
            {3 , 1 , 7 , 3,  2} ,
            {1 , 5 , 9 , 4,  6},
            {8 , 1 , 9 , 2,  6},
            {7 , 6 , 2 , 2,  5}
        };
		obj.sort_minor(matrix1);
		//  Case 2
		//  Define matrix of integer elements
		int[,] matrix2 = 
        {
            { 1 , 9 , 8 , 3 , 7 } , 
            { 3 , -1 , 5 , 3 , 8} , 
            { 1 , 3 , 5 , 6 , 11} , 
            { 0 , 9 , 8 , 6 , 2 } , 
            { 1 , 3 , 4 , 5 , 10}
        };

		obj.sort_minor(matrix2);
	}
}

Output

  Before Sort Minor Diagonal Element
   4   2   6   7   5
   3   1   7   3   2
   1   5   9   4   6
   8   1   9   2   6
   7   6   2   2   5

  After Sort Minor Diagonal Element
   4   2   6   7   1
   3   1   7   3   2
   1   5   5   4   6
   8   7   9   2   6
   9   6   2   2   5

  Before Sort Minor Diagonal Element
   1   9   8   3   7
   3   -1   5   3   8
   1   3   5   6   11
   0   9   8   6   2
   1   3   4   5   10

  After Sort Minor Diagonal Element
   1   9   8   3   1
   3   -1   5   3   8
   1   3   5   6   11
   0   7   8   6   2
   9   3   4   5   10
<?php
/* 
  Php Program
  Sort the minor diagonal elements of a matrix
*/
class MyMatrix
{
	// Display matrix elements
	public	function show_data( & $matrix, $size)
	{
		for ($i = 0; $i < $size; ++$i)
		{
			for ($j = 0; $j < $size; ++$j)
			{
				echo "  ". $matrix[$i][$j];
			}
			echo "\n";
		}
		echo "\n";
	}
	//  Swap diagonal elements of given location
	public	function swap_node($i, $j, $size, & $matrix)
	{
		$temp = $matrix[$size - 1 - $i][$i];
		$matrix[$size - 1 - $i][$i] = $matrix[$size - 1 - $j][$j];
		$matrix[$size - 1 - $j][$j] = $temp;
	}
	//  Set the minimum value on a given location
	public	function change_element( & $matrix, $k, $size)
	{
		$min = $k;
		for ($i = $k; $i >= 0; --$i)
		{
			if ($matrix[$size - 1 - $min][$min] > $matrix[$size - 1 - $i][$i])
			{
				$min = $i;
			}
		}
		//  Set the maximum element of [k][size-k] position
		$this->swap_node($k, $min, $size, $matrix);
	}
	//  Sort the minor diagonal of a matrix
	public	function sort_minor( & $matrix)
	{
		$size = count($matrix);

		if (count($matrix[0]) != $size || $size == 0)
		{
		      //  Not square matrix
			return;
		}
		//  Display matrix element
		echo "  Before Sort Minor Diagonal Element\n";
		$this->show_data($matrix, $size);
		for ($k = $size - 1; $k >= 0; --$k)
		{
			$this->change_element($matrix, $k, $size);
		}
		//  Display matrix element
		echo "  After Sort Minor Diagonal Element\n";
		$this->show_data($matrix, $size);
	}
}

function main()
{
	$obj = new MyMatrix();
	//  Case 1
	//  Define matrix of integer elements
	$matrix1 = array(
      array(4, 2, 6, 7, 5), 
      array(3, 1, 7, 3, 2), 
      array(1, 5, 9, 4, 6), 
      array(8, 1, 9, 2, 6), 
      array(7, 6, 2, 2, 5)
    );
	$obj->sort_minor($matrix1);
	//  Case 2
	//  Define matrix of integer elements
	$matrix2 = array(
      array(1, 9, 8, 3, 2), 
      array(3, -1, 5, 3, 8), 
      array(1, 3, 5, 6, 11), 
      array(0, 8, 8, 6, 2), 
      array(1, 3, 4, 5, 10)
    );
	$obj->sort_minor($matrix2);
}
main();

Output

  Before Sort Minor Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  9  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Minor Diagonal Element
  4  2  6  7  1
  3  1  7  3  2
  1  5  5  4  6
  8  7  9  2  6
  9  6  2  2  5

  Before Sort Minor Diagonal Element
  1  9  8  3  2
  3  -1  5  3  8
  1  3  5  6  11
  0  8  8  6  2
  1  3  4  5  10

  After Sort Minor Diagonal Element
  1  9  8  3  1
  3  -1  5  2  8
  1  3  3  6  11
  0  5  8  6  2
  8  3  4  5  10
/* 
  Node Js Program
  Sort the minor diagonal elements of a matrix
*/
class MyMatrix
{
	// Display matrix elements
	show_data(matrix, size)
	{
		for (var i = 0; i < size; ++i)
		{
			for (var j = 0; j < size; ++j)
			{
				process.stdout.write("  " + matrix[i][j]);
			}
			process.stdout.write("\n");
		}
		process.stdout.write("\n");
	}
	//  Swap diagonal elements of given location
	swap_node(i, j, size, matrix)
	{
		var temp = matrix[size - 1 - i][i];
		matrix[size - 1 - i][i] = matrix[size - 1 - j][j];
		matrix[size - 1 - j][j] = temp;
	}
	//  Set the minimum value on a given location
	change_element(matrix, k, size)
	{
		var min = k;
		for (var i = k; i >= 0; --i)
		{
			if (matrix[size - 1 - min][min] > matrix[size - 1 - i][i])
			{
				min = i;
			}
		}
		//  Set the maximum element of [k][size-k] position
		this.swap_node(k, min, size, matrix);
	}
	//  Sort the minor diagonal of a matrix
	sort_minor(matrix)
	{
		var size = matrix.length;

		if (matrix[0].length != size || size == 0)
		{
		        //  Not square matrix
			return;
		}
		//  Display matrix element
		process.stdout.write("  Before Sort Minor Diagonal Element\n");
		this.show_data(matrix, size);
		for (var k = size - 1; k >= 0; --k)
		{
			this.change_element(matrix, k, size);
		}
		//  Display matrix element
		process.stdout.write("  After Sort Minor Diagonal Element\n");
		this.show_data(matrix, size);
	}
}

function main()
{
	var obj = new MyMatrix();
	//  Case 1
	//  Define matrix of integer elements
	var matrix1 = [
        [4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] , 
        [1, 5, 9, 4, 6] , 
        [8, 1, 9, 2, 6] , 
        [7, 6, 2, 2, 5]
	];
	obj.sort_minor(matrix1);
	//  Case 2
	//  Define matrix of integer elements
	var matrix2 = [
		[1, 9, 8, 3, 2] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 8, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	];
	obj.sort_minor(matrix2);
}
main();

Output

  Before Sort Minor Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  9  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Minor Diagonal Element
  4  2  6  7  1
  3  1  7  3  2
  1  5  5  4  6
  8  7  9  2  6
  9  6  2  2  5

  Before Sort Minor Diagonal Element
  1  9  8  3  2
  3  -1  5  3  8
  1  3  5  6  11
  0  8  8  6  2
  1  3  4  5  10

  After Sort Minor Diagonal Element
  1  9  8  3  1
  3  -1  5  2  8
  1  3  3  6  11
  0  5  8  6  2
  8  3  4  5  10
#   Python 3 Program
#   Sort the minor diagonal elements of a matrix

class MyMatrix :
	#  Display matrix elements
	def show_data(self, matrix, size) :
		i = 0
		while (i < size) :
			j = 0
			while (j < size) :
				print("  ", matrix[i][j], end = "")
				j += 1
			
			print("\n", end = "")
			i += 1
		
		print("\n", end = "")
	
	#   Swap diagonal elements of given location
	def swap_node(self, i, j, size, matrix) :
		temp = matrix[size - 1 - i][i]
		matrix[size - 1 - i][i] = matrix[size - 1 - j][j]
		matrix[size - 1 - j][j] = temp
	
	#   Set the minimum value on a given location
	def change_element(self, matrix, k, size) :
		min = k
		i = k
		while (i >= 0) :
			if (matrix[size - 1 - min][min] > matrix[size - 1 - i][i]) :
				min = i
			
			i -= 1
		
		#   Set the maximum element of [k][size-k] position
		self.swap_node(k, min, size, matrix)
	
	#   Sort the minor diagonal of a matrix
	def sort_minor(self, matrix) :
		size = len(matrix)
		#   Not square matrix
		if (len(matrix[0]) != size or size == 0) :
		       #   Not square matrix
			return
		
		#   Display matrix element
		print("  Before Sort Minor Diagonal Element\n", end = "")
		self.show_data(matrix, size)
		k = size - 1
		while (k >= 0) :
			self.change_element(matrix, k, size)
			k -= 1
		
		#   Display matrix element
		print("  After Sort Minor Diagonal Element\n", end = "")
		self.show_data(matrix, size)
	

def main() :
	obj = MyMatrix()
	#   Case 1
	#   Define matrix of integer elements
	matrix1 = [
		[4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] , 
        [1, 5, 9, 4, 6] , 
        [8, 1, 9, 2, 6] , 
        [7, 6, 2, 2, 5]
	]
	obj.sort_minor(matrix1)
	#   Case 2
	#   Define matrix of integer elements
	matrix2 = [
		[1, 9, 8, 3, 2] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 8, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	]
	obj.sort_minor(matrix2)

if __name__ == "__main__": main()

Output

  Before Sort Minor Diagonal Element
   4   2   6   7   5
   3   1   7   3   2
   1   5   9   4   6
   8   1   9   2   6
   7   6   2   2   5

  After Sort Minor Diagonal Element
   4   2   6   7   1
   3   1   7   3   2
   1   5   5   4   6
   8   7   9   2   6
   9   6   2   2   5

  Before Sort Minor Diagonal Element
   1   9   8   3   2
   3   -1   5   3   8
   1   3   5   6   11
   0   8   8   6   2
   1   3   4   5   10

  After Sort Minor Diagonal Element
   1   9   8   3   1
   3   -1   5   2   8
   1   3   3   6   11
   0   5   8   6   2
   8   3   4   5   10
#   Ruby Program
#   Sort the minor diagonal elements of a matrix

class MyMatrix 
	#  Display matrix elements
	def show_data(matrix, size) 
		i = 0
		while (i < size) 
			j = 0
			while (j < size) 
				print("   ", matrix[i][j])
				j += 1
			end

			print("\n")
			i += 1
		end

		print("\n")
	end

	#   Swap diagonal elements of given location
	def swap_node(i, j, size, matrix) 
		temp = matrix[size - 1 - i][i]
		matrix[size - 1 - i][i] = matrix[size - 1 - j][j]
		matrix[size - 1 - j][j] = temp
	end

	#   Set the minimum value on a given location
	def change_element(matrix, k, size) 
		min = k
		i = k
		while (i >= 0) 
			if (matrix[size - 1 - min][min] > matrix[size - 1 - i][i]) 
				min = i
			end

			i -= 1
		end

		#   Set the maximum element of [k][size-k] position
		self.swap_node(k, min, size, matrix)
	end

	#   Sort the minor diagonal of a matrix
	def sort_minor(matrix) 
		size = matrix.length
		
		if (matrix[0].length != size || size == 0) 
			#   Not square matrix
                       return
		end

		#   Display matrix element
		print("  Before Sort Minor Diagonal Element\n")
		self.show_data(matrix, size)
		k = size - 1
		while (k >= 0) 
			self.change_element(matrix, k, size)
			k -= 1
		end

		#   Display matrix element
		print("  After Sort Minor Diagonal Element\n")
		self.show_data(matrix, size)
	end

end

def main() 
	obj = MyMatrix.new()
	#   Case 1
	#   Define matrix of integer elements
	matrix1 = [
		[4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] , 
        [1, 5, 9, 4, 6] , 
        [8, 1, 9, 2, 6] , 
        [7, 6, 2, 2, 5]
	]
	obj.sort_minor(matrix1)
	#   Case 2
	#   Define matrix of integer elements
	matrix2 = [
		[1, 9, 8, 3, 2] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 8, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	]
	obj.sort_minor(matrix2)
end

main()

Output

  Before Sort Minor Diagonal Element
   4   2   6   7   5
   3   1   7   3   2
   1   5   9   4   6
   8   1   9   2   6
   7   6   2   2   5

  After Sort Minor Diagonal Element
   4   2   6   7   1
   3   1   7   3   2
   1   5   5   4   6
   8   7   9   2   6
   9   6   2   2   5

  Before Sort Minor Diagonal Element
   1   9   8   3   2
   3   -1   5   3   8
   1   3   5   6   11
   0   8   8   6   2
   1   3   4   5   10

  After Sort Minor Diagonal Element
   1   9   8   3   1
   3   -1   5   2   8
   1   3   3   6   11
   0   5   8   6   2
   8   3   4   5   10

/* 
  Scala Program
  Sort the minor diagonal elements of a matrix
*/
class MyMatrix
{
	//  Display matrix elements
	def show_data(matrix: Array[Array[Int]], size: Int): Unit = {
		var i: Int = 0;
		while (i < size)
		{
			var j: Int = 0;
			while (j < size)
			{
				print("  " + matrix(i)(j));
				j += 1;
			}
			print("\n");
			i += 1;
		}
		print("\n");
	}
	//   Swap diagonal elements of given location
	def swap_node(i: Int, j: Int, size: Int, matrix: Array[Array[Int]]): Unit = {
		var temp: Int = matrix(size - 1 - i)(i);
		matrix(size - 1 - i)(i) = matrix(size - 1 - j)(j);
		matrix(size - 1 - j)(j) = temp;
	}
	//   Set the minimum value on a given location
	def change_element(matrix: Array[Array[Int]], k: Int, size: Int): Unit = {
		var min: Int = k;
		var i: Int = k;
		while (i >= 0)
		{
			if (matrix(size - 1 - min)(min) > matrix(size - 1 - i)(i))
			{
				min = i;
			}
			i -= 1;
		}
		//   Set the maximum element of [k][size-k] position
		this.swap_node(k, min, size, matrix);
	}
	//   Sort the minor diagonal of a matrix
	def sort_minor(matrix: Array[Array[Int]]): Unit = {
		var size: Int = matrix.length;
		
		if (matrix(0).length != size || size == 0)
		{
                       //   Not square matrix
			return;
		}
		//   Display matrix element
		print("  Before Sort Minor Diagonal Element\n");
		this.show_data(matrix, size);
		var k: Int = size - 1;
		while (k >= 0)
		{
			this.change_element(matrix, k, size);
			k -= 1;
		}
		//   Display matrix element
		print("  After Sort Minor Diagonal Element\n");
		this.show_data(matrix, size);
	}
}
object Main
{
	def main(args: Array[String]): Unit = {
		var obj: MyMatrix = new MyMatrix();
		//   Case 1
		//   Define matrix of integer elements
		var matrix1: Array[Array[Int]] = Array(
            Array(4, 2, 6, 7, 5), 
            Array(3, 1, 7, 3, 2), 
            Array(1, 5, 9, 4, 6), 
            Array(8, 1, 9, 2, 6), 
            Array(7, 6, 2, 2, 5)
        );
		obj.sort_minor(matrix1);
		//   Case 2
		//   Define matrix of integer elements
		var matrix2: Array[Array[Int]] = Array(
            Array(1, 9, 8, 3, 2), 
            Array(3, -1, 5, 3, 8),
            Array(1, 3, 5, 6, 11), 
            Array(0, 8, 8, 6, 2), 
            Array(1, 3, 4, 5, 10)
        );
		obj.sort_minor(matrix2);
	}
}

Output

  Before Sort Minor Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  9  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Minor Diagonal Element
  4  2  6  7  1
  3  1  7  3  2
  1  5  5  4  6
  8  7  9  2  6
  9  6  2  2  5

  Before Sort Minor Diagonal Element
  1  9  8  3  2
  3  -1  5  3  8
  1  3  5  6  11
  0  8  8  6  2
  1  3  4  5  10

  After Sort Minor Diagonal Element
  1  9  8  3  1
  3  -1  5  2  8
  1  3  3  6  11
  0  5  8  6  2
  8  3  4  5  10
/* 
  Swift 4 Program
  Sort the minor diagonal elements of a matrix
*/
class MyMatrix
{
	//  Display matrix elements
	func show_data(_ matrix: [[Int]], _ size: Int)
	{
		var i: Int = 0;
		while (i < size)
		{
			var j: Int = 0;
			while (j < size)
			{
				print("  ", matrix[i][j], terminator: "");
				j += 1;
			}
			print("\n", terminator: "");
			i += 1;
		}
		print("\n", terminator: "");
	}
	//   Swap diagonal elements of given location
	func swap_node(_ i: Int, _ j: Int, _ size: Int, _ matrix: inout[[Int]])
	{
		let temp: Int = matrix[size - 1 - i][i];
		matrix[size - 1 - i][i] = matrix[size - 1 - j][j];
		matrix[size - 1 - j][j] = temp;
	}
	//   Set the minimum value on a given location
	func change_element(_ matrix: inout[[Int]], _ k: Int, _ size: Int)
	{
		var min: Int = k;
		var i: Int = k;
		while (i >= 0)
		{
			if (matrix[size - 1 - min][min] > matrix[size - 1 - i][i])
			{
				min = i;
			}
			i -= 1;
		}
		//   Set the maximum element of [k][size-k] position
		self.swap_node(k, min, size, &matrix);
	}
	//   Sort the minor diagonal of a matrix
	func sort_minor(_ matrix: inout[[Int]])
	{
		let size: Int = matrix.count;
	
		if (matrix[0].count != size || size == 0)
		{
	              //   Not square matrix
			return;
		}
		//   Display matrix element
		print("  Before Sort Minor Diagonal Element");
		self.show_data(matrix, size);
		var k: Int = size - 1;
		while (k >= 0)
		{
			self.change_element(&matrix, k, size);
			k -= 1;
		}
		//   Display matrix element
		print("  After Sort Minor Diagonal Element");
		self.show_data(matrix, size);
	}
}
func main()
{
	let obj: MyMatrix = MyMatrix();
	//   Case 1
	//   Define matrix of integer elements
	var matrix1: [
		[Int]
	] = [
		[4, 2, 6, 7, 5] , 
        [3, 1, 7, 3, 2] ,
        [1, 5, 9, 4, 6] , 
        [8, 1, 9, 2, 6] , 
        [7, 6, 2, 2, 5]
	];
	obj.sort_minor(&matrix1);
	//   Case 2
	//   Define matrix of integer elements
	var matrix2: [[Int]] = [
		[1, 9, 8, 3, 2] , 
        [3, -1, 5, 3, 8] , 
        [1, 3, 5, 6, 11] , 
        [0, 8, 8, 6, 2] , 
        [1, 3, 4, 5, 10]
	];
	obj.sort_minor(&matrix2);
}
main();

Output

  Before Sort Minor Diagonal Element
   4   2   6   7   5
   3   1   7   3   2
   1   5   9   4   6
   8   1   9   2   6
   7   6   2   2   5

  After Sort Minor Diagonal Element
   4   2   6   7   1
   3   1   7   3   2
   1   5   5   4   6
   8   7   9   2   6
   9   6   2   2   5

  Before Sort Minor Diagonal Element
   1   9   8   3   2
   3   -1   5   3   8
   1   3   5   6   11
   0   8   8   6   2
   1   3   4   5   10

  After Sort Minor Diagonal Element
   1   9   8   3   1
   3   -1   5   2   8
   1   3   3   6   11
   0   5   8   6   2
   8   3   4   5   10
/* 
  Kotlin Program
  Sort the minor diagonal elements of a matrix
*/
class MyMatrix
{
	//  Display matrix elements
	fun show_data(matrix: Array <Array<Int>> , size: Int): Unit
	{
		var i: Int = 0;
		while (i < size)
		{
			var j: Int = 0;
			while (j < size)
			{
				print("  " + matrix[i][j]);
				j += 1;
			}
			print("\n");
			i += 1;
		}
		print("\n");
	}
	//   Swap diagonal elements of given location
	fun swap_node(i: Int, j: Int, size: Int, matrix: Array<Array<Int>> ): Unit
	{
		var temp: Int = matrix[size - 1 - i][i];
		matrix[size - 1 - i][i] = matrix[size - 1 - j][j];
		matrix[size - 1 - j][j] = temp;
	}
	//   Set the minimum value on a given location
	fun change_element(matrix: Array <Array<Int>> , k: Int, size: Int): Unit
	{
		var min: Int = k;
		var i: Int = k;
		while (i >= 0)
		{
			if (matrix[size - 1 - min][min] > matrix[size - 1 - i][i])
			{
				min = i;
			}
			i -= 1;
		}
		//   Set the maximum element of [k][size-k] position
		this.swap_node(k, min, size, matrix);
	}
	//   Sort the minor diagonal of a matrix
	fun sort_minor(matrix: Array <Array<Int>> ): Unit
	{
		var size: Int = matrix.count();
		
		if (matrix[0].count() != size || size == 0)
		{
          	// Not square matrix
			return;
		}
		//   Display matrix element
		print("  Before Sort Minor Diagonal Element\n");
		this.show_data(matrix, size);
		var k: Int = size - 1;
		while (k >= 0)
		{
			this.change_element(matrix, k, size);
			k -= 1;
		}
		//   Display matrix element
		print("  After Sort Minor Diagonal Element\n");
		this.show_data(matrix, size);
	}
}
fun main(args: Array <String> ): Unit
{
	var obj: MyMatrix = MyMatrix();
	//   Case 1
	//   Define matrix of integer elements
	var matrix1: Array <Array<Int>> = arrayOf(
        arrayOf(4, 2, 6, 7, 5), 
        arrayOf(3, 1, 7, 3, 2), 
        arrayOf(1, 5, 9, 4, 6), 
        arrayOf(8, 1, 9, 2, 6), 
        arrayOf(7, 6, 2, 2, 5)
    );
	obj.sort_minor(matrix1);
	//   Case 2
	//   Define matrix of integer elements
	var matrix2: Array <Array<Int>> = arrayOf(
        arrayOf(1, 9, 8, 3, 2), 
        arrayOf(3, -1, 5, 3, 8), 
        arrayOf(1, 3, 5, 6, 11), 
        arrayOf(0, 8, 8, 6, 2), 
        arrayOf(1, 3, 4, 5, 10)
    );
	obj.sort_minor(matrix2);
}

Output

  Before Sort Minor Diagonal Element
  4  2  6  7  5
  3  1  7  3  2
  1  5  9  4  6
  8  1  9  2  6
  7  6  2  2  5

  After Sort Minor Diagonal Element
  4  2  6  7  1
  3  1  7  3  2
  1  5  5  4  6
  8  7  9  2  6
  9  6  2  2  5

  Before Sort Minor Diagonal Element
  1  9  8  3  2
  3  -1  5  3  8
  1  3  5  6  11
  0  8  8  6  2
  1  3  4  5  10

  After Sort Minor Diagonal Element
  1  9  8  3  1
  3  -1  5  2  8
  1  3  3  6  11
  0  5  8  6  2
  8  3  4  5  10

Output Explanation

The mentioned C code implements the above algorithm to sort the minor diagonal elements of the matrix. It traverses the minor diagonal and swaps elements to sort them. The output displays the matrix after sorting the minor diagonal.

Time Complexity

The time complexity of the sorting process is O(N^2), where N is the number of rows (or columns) in the matrix. This is because for each element on the minor diagonal, we find the minimum element among the remaining diagonal elements, which requires traversing a portion of the matrix. Overall, the algorithm has a quadratic time complexity.





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