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

Given a 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:
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[``0``]) ` `    ``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[``0``]) ` `    ``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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