Inplace rotate square matrix by 90 degrees | Set 1

Given a square matrix, turn it by 90 degrees in anti-clockwise direction without using any extra space.

Examples :

Input:
Matrix:
 1  2  3
 4  5  6
 7  8  9
Output:
 3  6  9 
 2  5  8 
 1  4  7 
The given matrix is rotated by 90 degree 
in anti-clockwise direction.

Input:
 1  2  3  4 
 5  6  7  8 
 9 10 11 12 
13 14 15 16 
Output:
 4  8 12 16 
 3  7 11 15 
 2  6 10 14 
 1  5  9 13
The given matrix is rotated by 90 degree 
in anti-clockwise direction.

An approach that requires extra space is already discussed here.

Approach: To solve the question without any extra space, rotate the array in form of squares, dividing the matrix into squares or cycles. For example,
A 4 X 4 matrix will have 2 cycles. The first cycle is formed by its 1st row, last column, last row and 1st column. The second cycle is formed by 2nd row, second-last column, second-last row and 2nd column. The idea is for each square cycle, swap the elements involved with the corresponding cell in the matrix in anti-clockwise direction i.e. from top to left, left to bottom, bottom to right and from right to top one at a time using nothing but a temporary variable to achieve this.

Demonstration:



First Cycle (Involves Red Elements)
 1  2  3 4 
 5  6  7 8 
 9 10 11 12 
 13 14 15 16 

Moving first group of four elements (First
elements of 1st row, last row, 1st column 
and last column) of first cycle in counter
clockwise. 
 4  2  3 16
 5  6  7 8 
 9 10 11 12 
 1 14  15 13 
 
Moving next group of four elements of 
first cycle in counter clockwise 
 4  8  3 16 
 5  6  7  15  
 2  10 11 12 
 1  14  9 13 

Moving final group of four elements of 
first cycle in counter clockwise 
 4  8 12 16 
 3  6  7 15 
 2 10 11 14 
 1  5  9 13 


Second Cycle (Involves Blue Elements)
 4  8 12 16 
 3  6 7  15 
 2  10 11 14 
 1  5  9 13 

Fixing second cycle
 4  8 12 16 
 3  7 11 15 
 2  6 10 14 
 1  5  9 13

Algorithm:

  1. There is N/2 squares or cycles in a matrix of side N. Process a square one at a time. Run a loop to traverse the matrix a cycle at a time, i.e loop from 0 to N/2 – 1, loop counter is i
  2. Consider elements in group of 4 in current square, rotate the 4 elements at a time. So the number of such groups in a cycle is N – 2*i.
  3. So run a loop in each cycle from x to N – x – 1, loop counter is y
  4. The elements in the current group is (x, y), (y, N-1-x), (N-1-x, N-1-y), (N-1-y, x), now rotate the these 4 elements, i.e (x, y) <- (y, N-1-x), (y, N-1-x)<- (N-1-x, N-1-y), (N-1-x, N-1-y)<- (N-1-y, x), (N-1-y, x)<- (x, y)
  5. Print the matrix.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to rotate a matrix
// by 90 degrees
#include <bits/stdc++.h>
#define N 4
using namespace std;
  
void displayMatrix(
    int mat[N][N]);
  
// An Inplace function to
// rotate a N x N matrix
// by 90 degrees in
// anti-clockwise direction
void rotateMatrix(int mat[][N])
{
    // Consider all squares one by one
    for (int x = 0; x < N / 2; x++) {
        // Consider elements in group
        // of 4 in current square
        for (int y = x; y < N - x - 1; y++) {
            // Store current cell in
            // temp variable
            int temp = mat[x][y];
  
            // Move values from right to top
            mat[x][y] = mat[y][N - 1 - x];
  
            // Move values from bottom to right
            mat[y][N - 1 - x]
                = mat[N - 1 - x][N - 1 - y];
  
            // Move values from left to bottom
            mat[N - 1 - x][N - 1 - y]
                = mat[N - 1 - y][x];
  
            // Assign temp to left
            mat[N - 1 - y][x] = temp;
        }
    }
}
  
// Function to print the matrix
void displayMatrix(int mat[N][N])
{
    for (int i = 0; i < N; i++) {
        for (int j = 0; j < N; j++)
            printf("%2d ", mat[i][j]);
  
        printf("\n");
    }
    printf("\n");
}
  
/* Driver program to test above functions */
int main()
{
    // Test Case 1
    int mat[N][N] = {
        { 1, 2, 3, 4 },
        { 5, 6, 7, 8 },
        { 9, 10, 11, 12 },
        { 13, 14, 15, 16 }
    };
  
    // Tese Case 2
    /* int mat[N][N] = {
                        {1, 2, 3},
                        {4, 5, 6},
                        {7, 8, 9}
                    };
     */
  
    // Tese Case 3
    /*int mat[N][N] = {
                    {1, 2},
                    {4, 5}
                };*/
  
    // displayMatrix(mat);
  
    rotateMatrix(mat);
  
    // Print rotated matrix
    displayMatrix(mat);
  
    return 0;
}

chevron_right






                        filter_none









Java














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// Java program to rotate a 


// matrix by 90 degrees 


import java.io.*; 


  


class GFG { 


    // An Inplace function to 


    // rotate a N x N matrix 


    // by 90 degrees in 


    // anti-clockwise direction 


    static void rotateMatrix( 


        int N, int mat[][]) 


    { 


        // Consider all squares one by one 


        for (int x = 0; x < N / 2; x++) { 


            // Consider elements in group 


            // of 4 in current square 


            for (int y = x; y < N - x - 1; y++) { 


                // Store current cell in 


                // temp variable 


                int temp = mat[x][y]; 


  


                // Move values from right to top 


                mat[x][y] = mat[y][N - 1 - x]; 


  


                // Move values from bottom to right 


                mat[y][N - 1 - x] 


                    = mat[N - 1 - x][N - 1 - y]; 


  


                // Move values from left to bottom 


                mat[N - 1 - x][N - 1 - y] = mat[N - 1 - y][x]; 


  


                // Assign temp to left 


                mat[N - 1 - y][x] = temp; 


            } 


        } 


    } 


  


    // Function to print the matrix 


    static void displayMatrix( 


        int N, int mat[][]) 


    { 


        for (int i = 0; i < N; i++) { 


            for (int j = 0; j < N; j++) 


                System.out.print( 


                    " " + mat[i][j]); 


  


            System.out.print("\n"); 


        } 


        System.out.print("\n"); 


    } 


  


    /* Driver program to test above functions */


    public static void main(String[] args) 


    { 


        int N = 4; 


  


        // Test Case 1 


        int mat[][] = { 


            { 1, 2, 3, 4 }, 


            { 5, 6, 7, 8 }, 


            { 9, 10, 11, 12 }, 


            { 13, 14, 15, 16 } 


        }; 


  


        // Tese Case 2 


        /* int mat[][] = { 


                            {1, 2, 3}, 


                            {4, 5, 6}, 


                            {7, 8, 9} 


                        }; 


         */


  


        // Tese Case 3 


        /*int mat[][] = { 


                        {1, 2}, 


                        {4, 5} 


                    };*/


  


        // displayMatrix(mat); 


  


        rotateMatrix(N, mat); 


  


        // Print rotated matrix 


        displayMatrix(N, mat); 


    } 


} 


  


// This code is contributed by Prakriti Gupta 



















                        chevron_right







                        filter_none









Python3














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















# Python3 program to rotate a matrix by 90 degrees 


N = 4


  


# An Inplace function to rotate  


# N x N matrix by 90 degrees in 


# anti-clockwise direction 


def rotateMatrix(mat): 


      


    # Consider all squares one by one 


    for x in range(0, int(N / 2)): 


          


        # Consider elements in group    


        # of 4 in current square 


        for y in range(x, N-x-1): 


              


            # store current cell in temp variable 


            temp = mat[x][y] 


  


            # move values from right to top 


            mat[x][y] = mat[y][N-1-x] 


  


            # move values from bottom to right 


            mat[y][N-1-x] = mat[N-1-x][N-1-y] 


  


            # move values from left to bottom 


            mat[N-1-x][N-1-y] = mat[N-1-y][x] 


  


            # assign temp to left 


            mat[N-1-y][x] = temp 


  


  


# Function to print the matrix 


def displayMatrix( mat ): 


      


    for i in range(0, N): 


          


        for j in range(0, N): 


              


            print (mat[i][j], end = ' ') 


        print ("") 


      


      


  


  


# Driver Code 


mat = [[0 for x in range(N)] for y in range(N)] 


  


# Test case 1 


mat = [ [1, 2, 3, 4 ], 


        [5, 6, 7, 8 ], 


        [9, 10, 11, 12 ], 


        [13, 14, 15, 16 ] ] 


          


''' 


# Test case 2 


mat = [ [1, 2, 3 ], 


        [4, 5, 6 ], 


        [7, 8, 9 ] ] 


  


# Test case 3 


mat = [ [1, 2 ], 


        [4, 5 ] ] 


          


'''


  


rotateMatrix(mat) 


  


# Print rotated matrix 


displayMatrix(mat) 


  


  


# This code is contributed by saloni1297 



















                        chevron_right







                        filter_none









C#














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















// C# program to rotate a 


// matrix by 90 degrees 


using System; 


  


class GFG { 


    // An Inplace function to 


    // rotate a N x N matrix 


    // by 90 degrees in anti- 


    // clockwise direction 


    static void rotateMatrix(int N, 


                             int[, ] mat) 


    { 


        // Consider all 


        // squares one by one 


        for (int x = 0; x < N / 2; x++) { 


            // Consider elements 


            // in group of 4 in 


            // current square 


            for (int y = x; y < N - x - 1; y++) { 


                // store current cell 


                // in temp variable 


                int temp = mat[x, y]; 


  


                // move values from 


                // right to top 


                mat[x, y] = mat[y, N - 1 - x]; 


  


                // move values from 


                // bottom to right 


                mat[y, N - 1 - x] = mat[N - 1 - x, 


                                        N - 1 - y]; 


  


                // move values from 


                // left to bottom 


                mat[N - 1 - x, 


                    N - 1 - y] 


                    = mat[N - 1 - y, x]; 


  


                // assign temp to left 


                mat[N - 1 - y, x] = temp; 


            } 


        } 


    } 


  


    // Function to print the matrix 


    static void displayMatrix(int N, 


                              int[, ] mat) 


    { 


        for (int i = 0; i < N; i++) { 


            for (int j = 0; j < N; j++) 


                Console.Write(" " + mat[i, j]); 


            Console.WriteLine(); 


        } 


        Console.WriteLine(); 


    } 


  


    // Driver Code 


    static public void Main() 


    { 


        int N = 4; 


  


        // Test Case 1 


        int[, ] mat = { 


            { 1, 2, 3, 4 }, 


            { 5, 6, 7, 8 }, 


            { 9, 10, 11, 12 }, 


            { 13, 14, 15, 16 } 


        }; 


  


        // Tese Case 2 


        /* int mat[][] =  


        { 


            {1, 2, 3}, 


            {4, 5, 6}, 


            {7, 8, 9} 


        }; 


        */


  


        // Tese Case 3 


        /*int mat[][] =  


        { 


            {1, 2}, 


            {4, 5} 


        };*/


  


        // displayMatrix(mat); 


  


        rotateMatrix(N, mat); 


  


        // Print rotated matrix 


        displayMatrix(N, mat); 


    } 


} 


  


// This code is contributed by ajit 



















                        chevron_right







                        filter_none









PHP














                                    filter_none




                                    edit

                                    close




                                    play_arrow




                                    link

                                    brightness_4

                                    code
                                




















<?php  


// PHP program to rotate a  


// matrix by 90 degrees 


$N = 4; 


  


// An Inplace function to  


// rotate a N x N matrix 


// by 90 degrees in  


// anti-clockwise direction 


function rotateMatrix(&$mat) 


{ 


    global $N; 


      


    // Consider all  


    // squares one by one 


    for ($x = 0; $x < $N / 2; $x++) 


    { 


        // Consider elements  


        // in group of 4 in  


        // current square 


        for ($y = $x;  


             $y < $N - $x - 1; $y++) 


        { 


            // store current cell 


            // in temp variable 


            $temp = $mat[$x][$y]; 


  


            // move values from 


            // right to top 


            $mat[$x][$y] = $mat[$y][$N - 1 - $x]; 


  


            // move values from 


            // bottom to right 


            $mat[$y][$N - 1 - $x] =  


                $mat[$N - 1 - $x][$N - 1 - $y]; 


  


            // move values from  


            // left to bottom 


            $mat[$N - 1 - $x][$N - 1 - $y] =  


                         $mat[$N - 1 - $y][$x]; 


  


            // assign temp to left 


            $mat[$N - 1 - $y][$x] = $temp; 


        } 


    } 


} 


  


// Function to  


// print the matrix 


function displayMatrix(&$mat) 


{ 


    global $N; 


    for ($i = 0; $i < $N; $i++) 


    { 


        for ($j = 0; $j < $N; $j++) 


            echo $mat[$i][$j] . " "; 


  


        echo "\n"; 


    } 


    echo "\n"; 


} 


  


// Driver code 


  


// Test Case 1 


$mat =  array(array(1, 2, 3, 4), 


              array(5, 6, 7, 8), 


              array(9, 10, 11, 12), 


              array(13, 14, 15, 16)); 


  


// Tese Case 2 


/* $mat = array(array(1, 2, 3), 


                array(4, 5, 6), 


                array(7, 8, 9)); 


*/


  


// Tese Case 3 


/*$mat = array(array(1, 2), 


               array(4, 5));*/


  


// displayMatrix($mat); 


rotateMatrix($mat); 


  


// Print rotated matrix 


displayMatrix($mat); 


  


// This code is contributed  


// by ChitraNayal 


?> 



















                        chevron_right







                        filter_none










Output :


 4  8 12 16 
 3  7 11 15 
 2  6 10 14 
 1  5  9 13 



Complexity Analysis:


    

  • Time Complexity: O(n*n), where n is side of array.
    
A single traversal of the matrix is needed.
    • 

  • Space Complexity: O(1).
    
As a constant space is needed
    • 



Exercise: Turn 2D matrix by 90 degrees in clockwise direction without using extra space.


Rotate a matrix by 90 degree without using any extra space | Set 2


This article is contributed by Aditya Goel. If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.


Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above


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.





    

        My Personal Notes
        arrow_drop_up
    

    

        
        

            
            
        

    


Recommended Posts: