# Inplace rotate square matrix by 90 degrees | Set 1

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.
```

## Recommended: Please solve it on “PRACTICE” first, before moving on to the solution.

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++ 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 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 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# 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 `

 ` `

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

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