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# Python3 Program to Inplace rotate square matrix by 90 degrees | Set 1

• Last Updated : 25 Oct, 2022

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.

## 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`

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 size of array.
A single traversal of the matrix is needed.
• Space Complexity: O(1).
As a constant space is needed

Please refer complete article on Inplace rotate square matrix by 90 degrees | Set 1 for more details!

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