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# Inplace rotate square matrix by 90 degrees | Set 1

• Difficulty Level : Hard
• Last Updated : 25 Sep, 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:

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++

 `// C++ program to rotate a matrix``// by 90 degrees``#include ``#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

 ``

## Javascript

 ``
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

Easy  to understand and apply

Another Approach:

1.Reverse every individual  row

2. Perform Transpose

## C++

 `// C++ program to rotate a matrix``// by 90 degrees``#include ``#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])``{ ``//REVERSE every row ``  ``for``(``int` `i=0;i
Output
``` 4  8 12 16
3  7 11 15
2  6 10 14
1  5  9 13

```

Complexity Analysis:

Time Complexity: O(n*n) + 0(n*n)   where n is size of array.
Auxiliary Space: 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