Inplace rotate square matrix by 90 degrees

Inplace rotate square matrix by 90 degrees | Set 1

Difficulty Level : Hard
Last Updated : 06 Apr, 2021

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:

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
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.
So run a loop in each cycle from x to N – x – 1, loop counter is y
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)
Print the matrix.

C++

// 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;
}

Java

// 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

Python3

# 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

C#

// 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

PHP

<?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
?>

Javascript

<script>
// Javascript program to rotate a
// matrix by 90 degrees
 
    // An Inplace function to
    // rotate a N x N matrix
    // by 90 degrees in
    // anti-clockwise direction
    function rotateMatrix(N,mat)
    {
     
        // Consider all squares one by one
        for (let x = 0; x < N / 2; x++)
        {
         
            // Consider elements in group
            // of 4 in current square
            for (let y = x; y < N - x - 1; y++)
            {
             
                // Store current cell in
                // temp variable
                let 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(N,mat)
    {
        for (let i = 0; i < N; i++)
        {
            for (let j = 0; j < N; j++)
                document.write(
                    " " + mat[i][j]);
   
            document.write("<br>");
        }
        document.write("<br>");
    }
     
    /* Driver program to test above functions */
    let N = 4;
    let mat=[[1, 2, 3, 4],[ 5, 6, 7, 8 ],[9, 10, 11, 12 ],[13, 14, 15, 16]];
     
    // displayMatrix(mat);
    rotateMatrix(N, mat);
 
    // Print rotated matrix
    displayMatrix(N, mat);
     
    // This code is contributed by rag2127. 
</script>

Output :

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
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