Rotate a matrix by 90 degree in clockwise direction without using any extra space

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

Examples:

Input:
1 2 3
4 5 6
7 8 9
Output:
7 4 1
8 5 2
9 6 3

Input:
1 2
3 4
Output:
3 1
4 2

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: The approach is similar to Inplace rotate square matrix by 90 degrees | Set 1. The only thing that is different is to print the elements of cycle in clockwise direction i.e. An N x N matrix will have floor(N/2) square cycles.
For example, a 3 X 3 matrix will have 1 cycle. The cycle is formed by its 1st row, last column, last row, and 1st column.
For each square cycle, we swap the elements involved with the corresponding cell in the matrix in the clockwise direction. We just need a temporary variable for this.

Explanation:

Let size of row and column be 3.
During first iteration –
a[i][j] = Element at first index (leftmost corner top)= 1.

a[j][n-1-i]= Rightmost corner top Element = 3.

a[n-1-i][n-1-j] = Righmost corner bottom element = 9.

a[n-1-j][i] = Leftmost corner bottom element = 7.

Move these elements in the clockwise direction.

During second iteration –

a[i][j] = 2.

a[j][n-1-j] = 6.

a[n-1-i][n-1-j] = 8.

a[n-1-j][i] = 4.
Similarly, move these elements in the clockwise direction.

Below is the implementation of above approach:

C++

 // C++ implementation of above approach #include using namespace std;    #define N 4    // Function to rotate the matrix 90 degree clockwise void rotate90Clockwise(int a[N][N]) {        // Traverse each cycle     for (int i = 0; i < N / 2; i++) {         for (int j = i; j < N - i - 1; j++) {                // Swap elements of each cycle             // in clockwise direction             int temp = a[i][j];             a[i][j] = a[N - 1 - j][i];             a[N - 1 - j][i] = a[N - 1 - i][N - 1 - j];             a[N - 1 - i][N - 1 - j] = a[j][N - 1 - i];             a[j][N - 1 - i] = temp;         }     } }    // Function for print matrix void printMatrix(int arr[N][N]) {     for (int i = 0; i < N; i++) {         for (int j = 0; j < N; j++)             cout << arr[i][j] << " ";         cout << '\n';     } }    // Driver code int main() {     int arr[N][N] = { { 1, 2, 3, 4 },                       { 5, 6, 7, 8 },                       { 9, 10, 11, 12 },                       { 13, 14, 15, 16 } };     rotate90Clockwise(arr);     printMatrix(arr);     return 0; }

Java

 // Java implementation of above approach import java.io.*;    class GFG  {        static int N = 4;    // Function to rotate the matrix 90 degree clockwise static void rotate90Clockwise(int a[][]) {        // Traverse each cycle     for (int i = 0; i < N / 2; i++)     {         for (int j = i; j < N - i - 1; j++)         {                // Swap elements of each cycle             // in clockwise direction             int temp = a[i][j];             a[i][j] = a[N - 1 - j][i];             a[N - 1 - j][i] = a[N - 1 - i][N - 1 - j];             a[N - 1 - i][N - 1 - j] = a[j][N - 1 - i];             a[j][N - 1 - i] = temp;         }     } }    // Function for print matrix static void printMatrix(int arr[][]) {     for (int i = 0; i < N; i++)     {         for (int j = 0; j < N; j++)         System.out.print( arr[i][j] + " ");         System.out.println();     } }    // Driver code        public static void main (String[] args)      {             int arr[][] = { { 1, 2, 3, 4 },                       { 5, 6, 7, 8 },                       { 9, 10, 11, 12 },                       { 13, 14, 15, 16 } };     rotate90Clockwise(arr);     printMatrix(arr);     } }    // This code has been contributed by inder_verma.

Python

 # Function to rotate the matrix # 90 degree clockwise def rotate90Clockwise(A):     N = len(A)     for i in range(N // 2):         for j in range(i, N - i - 1):             temp = A[i][j]             A[i][j] = A[N - 1 - j][i]             A[N - 1 - j][i] = A[N - 1 - i][N - 1 - j]             A[N - 1 - i][N - 1 - j] = A[j][N - 1 - i]             A[j][N - 1 - i] = temp    # Function to print the matrix def printMatrix(A):     N = len(A)     for i in range(N):         print(A[i])    # Driver code A = [[1, 2, 3, 4],      [5, 6, 7, 8],       [9, 10, 11, 12],       [13, 14, 15, 16]] rotate90Clockwise(A) printMatrix(A)    # This code was contributed  # by pk_tautolo

C#

 // C# implementation of above approach using System;     class GFG  { static int N = 4;    // Function to rotate the matrix  // 90 degree clockwise static void rotate90Clockwise(int[,] a) {        // Traverse each cycle     for (int i = 0; i < N / 2; i++)     {         for (int j = i; j < N - i - 1; j++)         {                // Swap elements of each cycle             // in clockwise direction             int temp = a[i, j];             a[i, j] = a[N - 1 - j, i];             a[N - 1 - j, i] = a[N - 1 - i, N - 1 - j];             a[N - 1 - i, N - 1 - j] = a[j, N - 1 - i];             a[j, N - 1 - i] = temp;         }     } }    // Function for print matrix static void printMatrix(int[,] arr) {     for (int i = 0; i < N; i++)     {         for (int j = 0; j < N; j++)         Console.Write( arr[i, j] + " ");         Console.Write("\n");     } }    // Driver code public static void Main ()      {     int [,]arr = {{1, 2, 3, 4},                   {5, 6, 7, 8},                   {9, 10, 11, 12},                   {13, 14, 15, 16}};     rotate90Clockwise(arr);     printMatrix(arr); } }    // This code is contributed  // by ChitraNayal

PHP



Output:

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

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