Inplace rotate square matrix by 90 degrees | Set 1

3.5

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

Examples:

Input
 1  2  3
 4  5  6
 7  8  9

Output:
 3  6  9 
 2  5  8 
 1  4  7 

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

An approach that requires extra space is already discussed here.

How to do without extra space?
Below are some important observations.

First row of source –> First column of destination, elements filled in opposite order

Second row of source –> Second column of destination, elements filled in opposite order

so … on

Last row of source –> Last column of destination, elements filled in opposite order.

An N x N matrix will have floor(N/2) square 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, we 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. We use nothing but a temporary variable to achieve this.

Below steps demonstrate the idea

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

Below is the implementation of above idea.

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


Output:

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

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

Asked in: Microsoft

Related QA Topic : http://qa.geeksforgeeks.org/4493/rotate-the-matrix-inplace

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