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

Given a square matrix, turn it by 90 degrees in an 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.

Approach:

To solve the question without any extra space, rotate the array in the ,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, to 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.

 Below is the implementation of the above approach:

<?php 
// PHP program to rotate a 
// matrix by 90 degrees
$N = 4;

// An Inplace function to 
// rotate a N x N matrix
// by 90 degrees in 
// anti-clockwise direction
function rotateMatrix(&$mat)
{
    global $N;
    
    // Consider all 
    // squares one by one
    for ($x = 0; $x < $N / 2; $x++)
    {
        // Consider elements 
        // in group of 4 in 
        // current square
        for ($y = $x; 
             $y < $N - $x - 1; $y++)
        {
            // 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
function displayMatrix(&$mat)
{
    global $N;
    for ($i = 0; $i < $N; $i++)
    {
        for ($j = 0; $j < $N; $j++)
            echo $mat[$i][$j] . " ";

        echo "
";
    }
    echo "
";
}

// Driver code

// Test Case 1
$mat =  array(array(1, 2, 3, 4),
              array(5, 6, 7, 8),
              array(9, 10, 11, 12),
              array(13, 14, 15, 16));

// Tese Case 2
/* $mat = array(array(1, 2, 3),
                array(4, 5, 6),
                array(7, 8, 9));
*/

// Tese Case 3
/*$mat = array(array(1, 2),
               array(4, 5));*/

// displayMatrix($mat);
rotateMatrix($mat);

// Print rotated matrix
displayMatrix($mat);

// This code is contributed 
// by ChitraNayal
?>

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

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