C++ Program to 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.

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 <bits/stdc++.h>
#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("
");
    }
    printf("
");
}

/* 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;
}

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