Posted on by Kalkicode
Code Matrix

Reverse the diamond elements in square matrix

The given problem involves reversing the elements in a diamond pattern within a square matrix. The goal is to create a function that takes a square matrix as input and rearranges its elements in a way that the elements along the diagonals form a diamond shape, and then reverse the order of those diamond elements.

Problem Statement

You are given a square matrix with odd dimensions. You need to reverse the diamond elements within the matrix. The diamond elements are the elements along the diagonals that form a diamond shape. For example, in a 5x5 matrix:


    1  2  3  4  5
    6  7  8  9  10
    11  12  13  15  16
    17  18  19  20  21
    22  23  24  25  26
  
  # Diamond of matrix
          3    
       7  8  9  
    11 12 13 15 16
       18 19 20  
          24   
  
  # When Reverse by row of diamond
          3    
       9  8  7 
    16 15 13 12 11  
       20 19 18 
          24 
  # Final result
  
    1  2  3  4  5
    6  9  8  7 10
   16 15 13 12 11
   17 20 19 18 21
   22 23 24 25 26

Solution Approach

To solve this problem, the code provides a function reverse_row that takes the matrix as input and performs the following steps:

  1. Check if the matrix is square and has odd dimensions. If it doesn't satisfy these conditions, the function will not proceed.
  2. Initialize a variable col_s to the middle column index.
  3. Loop through each row of the matrix: a. Call the change function to reverse the elements in the diamond shape for the current row. b. Decrease col_s for the first half of the rows and increase it for the second half.

The change function swaps the elements along the diagonal forming the diamond shape. It iterates through half of the row and swaps the elements with their corresponding elements on the opposite side of the diamond.

Pseudocode

function change(matrix, row_s, col_s):
        for i from col_s to (COL - 1) - col_s:
            swap matrix[row_s][i] with matrix[row_s][COL - 1 - i]
    
    function reverse_row(matrix):
        if ROW != COL or COL is even:
            print "This is not a perfect odd rows or columns matrix"
            return
        col_s = COL / 2
        for i from 0 to ROW - 1:
            call change(matrix, i, col_s)
            if i < ROW / 2:
                col_s = col_s - 1
            else:
                col_s = col_s + 1
    
    matrix = predefined square matrix
    show_data(matrix)
    reverse_row(matrix)
    show_data(matrix)

Algorithm Explanation

  1. The change function iterates through half of the row's elements from col_s to (COL - 1) - col_s.
  2. It swaps the current element with the element at the corresponding position on the opposite side of the diamond.
  3. The reverse_row function first checks if the matrix is square and has odd dimensions. If not, it prints an error message and returns.
  4. It initializes col_s to the middle column index.
  5. The loop in the reverse_row function iterates through each row of the matrix: a. It calls the change function to reverse the diamond elements in the current row. b. For the first half of the rows, col_s is decreased to move inward through the diamond shape. For the second half, it's increased to move outward.

Code Solution

/*
  C Program 
+ Reverse the diamond elements in square matrix
*/
#include <stdio.h>
//Size of matrix
#define ROW 5
#define COL 5

void change(int matrix[ROW][COL],int row_s,int col_s)
{
  int temp = 0;
  for (int i = col_s; i < (COL)-i; ++i)
  {
      //Swap element value
      temp=matrix[row_s][i];
      matrix[row_s][i] = matrix[row_s][(COL-1)-i];
      matrix[row_s][(COL-1)-i]=temp;
  }
}
//Reversing diamond position element in row wise
void reverse_row(int matrix[ROW][COL])
{
  if(ROW != COL || COL%2==0)
  {
    printf("\nThis is not a perfect odd rows or columns matrix");
    return;
  }

  int col_s = COL / 2;

  for (int i = 0; i < ROW; ++i)
  {
    change(matrix,i,col_s);
    
    if(i < ROW/2)
    {
      
      col_s--;
    }
    else
    { 
      col_s++;
    
    }
  }

}
//Display matrix elements
void show_data(int matrix[][COL])
{
  for (int i = 0; i < ROW; ++i)
  {
    for (int j = 0; j < COL; ++j)
    {
      printf("%3d",matrix[i][j] );
    }
    printf("\n");
  }
  printf("\n");
}
int main(){

  int matrix[ROW][COL] ={
    {1,  2,   3,  4,  5},
    {6,  7,   8,  9,  10},
    {11, 12, 13, 15,  16},
    {17, 18, 19, 20,  21},
    {22, 23, 24, 25,  26}

  }; 

  show_data(matrix);  
  
  reverse_row(matrix);

  show_data(matrix);  

  return 0;
}

Output

  1  2  3  4  5
  6  7  8  9 10
 11 12 13 15 16
 17 18 19 20 21
 22 23 24 25 26

  1  2  3  4  5
  6  9  8  7 10
 16 15 13 12 11
 17 20 19 18 21
 22 23 24 25 26

/*
 C++ Program
 Reverse the diamond elements in square matrix
*/
#include<iostream>
#define ROW 5
#define COL 5
using namespace std;

class MyMatrix {
	public:
	int rows;
	int cols;
	MyMatrix() {
		//Get the size of matrix
		this->rows = ROW;
		this->cols = COL;
	}
	void change(int matrix[][COL], int row_s, int col_s) {
		int temp = 0;
		for (int i = col_s; i < this->cols - i; ++i) {
			//Swap element value
			temp = matrix[row_s][i];
			matrix[row_s][i] = matrix[row_s][(this->cols - 1) - i];
			matrix[row_s][(this->cols - 1) - i] = temp;
		}
	}
	//Reversing diamond position element in row wise
	void reverse_row(int matrix[][COL]) {
		if (this->rows != this->cols || this->cols % 2 == 0) {
			cout << "\nThis is not a perfect odd rows or columns matrix";
			return;
		}
		int col_s = this->cols / 2;
		for (int i = 0; i < this->rows; ++i) {
			this->change(matrix, i, col_s);
			if (i < this->rows / 2) {
				col_s--;
			} else {
				col_s++;
			}
		}
	}
	//Display matrix elements
	void show_data(int matrix[][COL]) {
		for (int i = 0; i < this->rows; ++i) {
			for (int j = 0; j < this->cols; ++j) {
				cout << " " << matrix[i][j];
			}
			cout << "\n";
		}
		cout << "\n";
	}
};
int main() {
	int matrix[][COL] = {
		{
			1,
			2,
			3,
			4,
			5
		},
		{
			6,
			7,
			8,
			9,
			10
		},
		{
			11,
			12,
			13,
			15,
			16
		},
		{
			17,
			18,
			19,
			20,
			21
		},
		{
			22,
			23,
			24,
			25,
			26
		}
	};
	MyMatrix obj;
	obj.show_data(matrix);
	obj.reverse_row(matrix);
	obj.show_data(matrix);
	return 0;
}

Output

 1 2 3 4 5
 6 7 8 9 10
 11 12 13 15 16
 17 18 19 20 21
 22 23 24 25 26

 1 2 3 4 5
 6 9 8 7 10
 16 15 13 12 11
 17 20 19 18 21
 22 23 24 25 26

/*
  C# Program
  Reverse the diamond elements in square matrix
*/
using System;
public class MyMatrix {
	int rows;
	int cols;
	MyMatrix(int[,] matrix) {
		//Get the size of matrix
		rows = matrix.GetLength(0);
		cols = matrix.GetLength(1);
	}
	public void change(int[,] matrix, int row_s, int col_s) {
		int temp = 0;
		for (int i = col_s; i < cols - i; ++i) {
			//Swap element value
			temp = matrix[row_s,i];
			matrix[row_s,i] = matrix[row_s,(cols - 1) - i];
			matrix[row_s,(cols - 1) - i] = temp;
		}
	}
	//Reversing diamond position element in row wise
	public void reverse_row(int[,] matrix) {
		if (rows != cols || cols % 2 == 0) {
			Console.Write("\nThis is not a perfect odd rows or columns matrix");
			return;
		}
		int col_s = cols / 2;
		for (int i = 0; i < rows; ++i) {
			change(matrix, i, col_s);
			if (i < rows / 2) {
				col_s--;
			} else {
				col_s++;
			}
		}
	}
	//Display matrix elements
	public void show_data(int[,] matrix) {
		for (int i = 0; i < rows; ++i) {
			for (int j = 0; j < cols; ++j) {
				Console.Write(" " + matrix[i,j]);
			}
			Console.Write("\n");
		}
		Console.Write("\n");
	}
	public static void Main(String[] args) {
		int[,]
		//Define matrix 
		matrix = {
			{
				1,
				2,
				3,
				4,
				5
			},
			{
				6,
				7,
				8,
				9,
				10
			},
			{
				11,
				12,
				13,
				15,
				16
			},
			{
				17,
				18,
				19,
				20,
				21
			},
			{
				22,
				23,
				24,
				25,
				26
			}
		};
		MyMatrix obj = new MyMatrix(matrix);
		obj.show_data(matrix);
		obj.reverse_row(matrix);
		obj.show_data(matrix);
	}
}

Output

 1 2 3 4 5
 6 7 8 9 10
 11 12 13 15 16
 17 18 19 20 21
 22 23 24 25 26

 1 2 3 4 5
 6 9 8 7 10
 16 15 13 12 11
 17 20 19 18 21
 22 23 24 25 26

<?php
/*
  Php Program
  Reverse the diamond elements in square matrix
*/
class MyMatrix {
	public $rows;
	public $cols;

	function __construct($matrix) {
		//Get the size of matrix
		$this->rows = count($matrix);
		$this->cols = count($matrix[0]);
	}
	public 	function change(&$matrix, $row_s, $col_s) {
		$temp = 0;
		for ($i = $col_s; $i < $this->cols - $i; ++$i) {
			//Swap element value
			$temp = $matrix[$row_s][$i];
			$matrix[$row_s][$i] = $matrix[$row_s][($this->cols - 1) - $i];
			$matrix[$row_s][($this->cols - 1) - $i] = $temp;
		}
	}
	//Reversing diamond position element in row wise

	public 	function reverse_row(&$matrix) {
		if ($this->rows != $this->cols || $this->cols % 2 == 0) {
			echo("\nThis is not a perfect odd rows or columns matrix");
			return;
		}
		$col_s = intval($this->cols / 2);
		for ($i = 0; $i < $this->rows; ++$i) {
			$this->change($matrix, $i, $col_s);
			if ($i < intval($this->rows / 2)) {
				$col_s--;
			} else {
				$col_s++;
			}
		}
	}
	//Display matrix elements

	public 	function show_data($matrix) {
		for ($i = 0; $i < $this->rows; ++$i) {
			for ($j = 0; $j < $this->cols; ++$j) {
				echo(" ". $matrix[$i][$j]);
			}
			echo("\n");
		}
		echo("\n");
	}
};

function main() {
	//Define matrix 
	$matrix = array(
      array(1, 2, 3, 4, 5), 
      array(6, 7, 8, 9, 10),
      array(11, 12, 13, 15, 16), 
      array(17, 18, 19, 20, 21), 
      array(22, 23, 24, 25, 26)
    );
	$obj = new MyMatrix($matrix);
	$obj->show_data($matrix);
	$obj->reverse_row($matrix);
	$obj->show_data($matrix);

}
main();

Output

 1 2 3 4 5
 6 7 8 9 10
 11 12 13 15 16
 17 18 19 20 21
 22 23 24 25 26

 1 2 3 4 5
 6 9 8 7 10
 16 15 13 12 11
 17 20 19 18 21
 22 23 24 25 26

/*
 Node Js Program
 Reverse the diamond elements in square matrix
*/
class MyMatrix {
	;;
	constructor(matrix) {
		//Get the size of matrix
		this.rows = matrix.length;
		this.cols = matrix[0].length;
	}
	change(matrix, row_s, col_s) {
		var temp = 0;
		for (var i = col_s; i < this.cols - i; ++i) {
			//Swap element value
			temp = matrix[row_s][i];
			matrix[row_s][i] = matrix[row_s][(this.cols - 1) - i];
			matrix[row_s][(this.cols - 1) - i] = temp;
		}
	}

	//Reversing diamond position element in row wise
	reverse_row(matrix) {
		if (this.rows != this.cols || this.cols % 2 == 0) {
			process.stdout.write("\nThis is not a perfect odd rows or columns matrix");
			return;
		}
		var col_s = parseInt(this.cols / 2);
		for (var i = 0; i < this.rows; ++i) {
			this.change(matrix, i, col_s);
			if (i < parseInt(this.rows / 2)) {
				col_s--;
			} else {
				col_s++;
			}
		}
	}

	//Display matrix elements
	show_data(matrix) {
		for (var i = 0; i < this.rows; ++i) {
			for (var j = 0; j < this.cols; ++j) {
				process.stdout.write(" " + matrix[i][j]);
			}

			process.stdout.write("\n");
		}

		process.stdout.write("\n");
	}
}

function main(args) {
	//Define matrix 
	var matrix = [
		[1, 2, 3, 4, 5],
		[6, 7, 8, 9, 10],
		[11, 12, 13, 15, 16],
		[17, 18, 19, 20, 21],
		[22, 23, 24, 25, 26]
	];
	var obj = new MyMatrix(matrix);
	obj.show_data(matrix);
	obj.reverse_row(matrix);
	obj.show_data(matrix);
}
main();

Output

 1 2 3 4 5
 6 7 8 9 10
 11 12 13 15 16
 17 18 19 20 21
 22 23 24 25 26

 1 2 3 4 5
 6 9 8 7 10
 16 15 13 12 11
 17 20 19 18 21
 22 23 24 25 26

# Python 3 Program
# Reverse the diamond elements in square matrix
class MyMatrix :
	
	def __init__(self, matrix) :
		# Get the size of matrix
		self.rows = len(matrix)
		self.cols = len(matrix[0])
	
	def change(self, matrix, row_s, col_s) :
		temp = 0
		i = col_s
		while (i < self.cols - i) :
			# Swap element value
			temp = matrix[row_s][i]
			matrix[row_s][i] = matrix[row_s][(self.cols - 1) - i]
			matrix[row_s][(self.cols - 1) - i] = temp
			i += 1
		
	
	# Reversing diamond position element in row wise
	def reverse_row(self, matrix) :
		if (self.rows != self.cols or self.cols % 2 == 0) :
			print("\nThis is not a perfect odd rows or columns matrix", end = "")
			return
		
		col_s = int(self.cols / 2)
		i = 0
		while (i < self.rows) :
			self.change(matrix, i, col_s)
			if (i < int(self.rows / 2)) :
				col_s -= 1
			else :
				col_s += 1
			
			i += 1
		
	
	# Display matrix elements
	def show_data(self, matrix) :
		i = 0
		while (i < self.rows) :
			j = 0
			while (j < self.cols) :
				print(" ", matrix[i][j], end = "")
				j += 1
			
			print("\n", end = "")
			i += 1
		
		print("\n", end = "")
	

def main() :
	matrix = [
		[1, 2, 3, 4, 5],
		[6, 7, 8, 9, 10],
		[11, 12, 13, 15, 16],
		[17, 18, 19, 20, 21],
		[22, 23, 24, 25, 26]
	]
	obj = MyMatrix(matrix)
	obj.show_data(matrix)
	obj.reverse_row(matrix)
	obj.show_data(matrix)


if __name__ == "__main__":
	main()

Output

  1  2  3  4  5
  6  7  8  9  10
  11  12  13  15  16
  17  18  19  20  21
  22  23  24  25  26

  1  2  3  4  5
  6  9  8  7  10
  16  15  13  12  11
  17  20  19  18  21
  22  23  24  25  26

# Ruby Program 
# Reverse the diamond elements in square matrix
class MyMatrix 
	# Define the accessor and reader of class MyMatrix
    attr_reader :rows, :cols
    attr_accessor :rows, :cols
	def initialize(matrix) 
		# Get the size of matrix
		@rows = matrix.length
		@cols = matrix[0].length
	end
	def change(matrix, row_s, col_s) 
		temp = 0
		i = col_s
		while (i < @cols - i) 
			# Swap element value
			temp = matrix[row_s][i]
			matrix[row_s][i] = matrix[row_s][(@cols - 1) - i]
			matrix[row_s][(@cols - 1) - i] = temp
			i += 1
		end
	end
	# Reversing diamond position element in row wise
	def reverse_row(matrix) 
		if (@rows != @cols or @cols % 2 == 0) 
			print("\nThis is not a perfect odd rows or columns matrix")
			return
		end
		col_s = @cols / 2
		i = 0
		while (i < @rows) 
			self.change(matrix, i, col_s)
			if (i < @rows / 2) 
				col_s -= 1
			else 
				col_s += 1
			end
			i += 1
		end
	end
	# Display matrix elements
	def show_data(matrix) 
		i = 0
		while (i < @rows) 
			j = 0
			while (j < @cols) 
				print(" ", matrix[i][j])
				j += 1
			end
			print("\n")
			i += 1
		end
		print("\n")
	end
end
def main() 
	matrix = [
		[1, 2, 3, 4, 5],
		[6, 7, 8, 9, 10],
		[11, 12, 13, 15, 16],
		[17, 18, 19, 20, 21],
		[22, 23, 24, 25, 26]
	]
	obj = MyMatrix.new(matrix)
	obj.show_data(matrix)
	obj.reverse_row(matrix)
	obj.show_data(matrix)
end


main()

Output

 1 2 3 4 5
 6 7 8 9 10
 11 12 13 15 16
 17 18 19 20 21
 22 23 24 25 26

 1 2 3 4 5
 6 9 8 7 10
 16 15 13 12 11
 17 20 19 18 21
 22 23 24 25 26


/*
 Scala Program
 Reverse the diamond elements in square matrix
*/
class MyMatrix(var rows: Int,var cols: Int) {


	def this(matrix: Array[Array[Int]]) {
		//Get the size of matrix
		this(matrix.length,matrix(0).length);
	}
	def change(matrix: Array[Array[Int]], row_s: Int, col_s: Int): Unit = {
		var temp: Int = 0;
		var i: Int = col_s;
		while (i < this.cols - i) {
			//Swap element value
			temp = matrix(row_s)(i);
			matrix(row_s)(i) = matrix(row_s)((this.cols - 1) - i);
			matrix(row_s)((this.cols - 1) - i) = temp;
			i += 1;
		}
	}
	//Reversing diamond position element in row wise
	def reverse_row(matrix: Array[Array[Int]]): Unit = {
		if (this.rows != this.cols || this.cols % 2 == 0) {
			print("\nThis is not a perfect odd rows or columns matrix");

			return;
		}
		var col_s: Int = (this.cols / 2).toInt;
		var i: Int = 0;
		while (i < this.rows) {
			this.change(matrix, i, col_s);

			if (i < (this.rows / 2).toInt) {
				col_s -= 1;
			} else {
				col_s += 1;
			}
			i += 1;
		}
	}
	//Display matrix elements
	def show_data(matrix: Array[Array[Int]]): Unit = {
		var i: Int = 0;
		while (i < this.rows) {
			var j: Int = 0;
			while (j < this.cols) {
				print(" " + matrix(i)(j));
				j += 1;
			}
			print("\n");
			i += 1;
		}
		print("\n");
	}
}
object Main {
	def main(args: Array[String]): Unit = {
		val matrix: Array[Array[Int]] = Array(
			Array(1, 2, 3, 4, 5),
			Array(6, 7, 8, 9, 10),
			Array(11, 12, 13, 15, 16),
			Array(17, 18, 19, 20, 21),
			Array(22, 23, 24, 25, 26));
		val obj: MyMatrix = new MyMatrix(matrix);
		obj.show_data(matrix);
		obj.reverse_row(matrix);
		obj.show_data(matrix);
	}
}

Output

 1 2 3 4 5
 6 7 8 9 10
 11 12 13 15 16
 17 18 19 20 21
 22 23 24 25 26

 1 2 3 4 5
 6 9 8 7 10
 16 15 13 12 11
 17 20 19 18 21
 22 23 24 25 26

/*
  Swift 4 Program
  Reverse the diamond elements in square matrix
*/
class MyMatrix {
	var rows : Int;
	var cols : Int;
	init(_ matrix: [
		[Int]
	]) {
		//Get the size of matrix
		self.rows = matrix.count;
		self.cols = matrix[0].count;
	}
	func change(_ matrix: inout [[Int]], _ row_s: Int, _ col_s: Int) {
		var temp: Int = 0;
		var i: Int = col_s;
		while (i < self.cols - i) {
			//Swap element value
			temp = matrix[row_s][i];
			matrix[row_s][i] = matrix[row_s][(self.cols - 1) - i];
			matrix[row_s][(self.cols - 1) - i] = temp;
			i += 1;
		}
	}
	//Reversing diamond position element in row wise
	func reverse_row(_ matrix: inout [[Int]]) {
		if (self.rows != self.cols || self.cols % 2 == 0) {
			print("\nThis is not a perfect odd rows or columns matrix", terminator: "");
			return;
		}
		var col_s: Int = self.cols / 2;
		var i: Int = 0;
		while (i < self.rows) {
			self.change(&matrix, i, col_s);
			if (i < self.rows / 2) {
				col_s -= 1;
			} else {
				col_s += 1;
			}
			i += 1;
		}
	}
	//Display matrix elements
	func show_data(_ matrix: [
		[Int]
	]) {
		var i: Int = 0;
		while (i < self.rows) {
			var j: Int = 0;
			while (j < self.cols) {
				print(" ", matrix[i][j], terminator: "");
				j += 1;
			}
			print("\n", terminator: "");
			i += 1;
		}
		print("\n", terminator: "");
	}
}
func main() {
	var matrix: [[Int]] = [
		[1, 2, 3, 4, 5],
		[6, 7, 8, 9, 10],
		[11, 12, 13, 15, 16],
		[17, 18, 19, 20, 21],
		[22, 23, 24, 25, 26]
	];
	let obj: MyMatrix = MyMatrix(matrix);
	obj.show_data(matrix);
	obj.reverse_row(&matrix);
	obj.show_data(matrix);
}
main();

Output

  1  2  3  4  5
  6  7  8  9  10
  11  12  13  15  16
  17  18  19  20  21
  22  23  24  25  26

  1  2  3  4  5
  6  9  8  7  10
  16  15  13  12  11
  17  20  19  18  21
  22  23  24  25  26

Time Complexity

The change function has a time complexity of O(N), where N is the number of columns in the matrix. The reverse_row function iterates through each row and calls the change function, resulting in a time complexity of O(N^2), where N is the number of rows/columns in the matrix. The overall time complexity of the given code is O(N^2).

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