Php 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:
- 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
- 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.
- So run a loop in each cycle from x to N – x – 1, loop counter is y
- 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)
- Print the matrix.
PHP
<?php
$N = 4;
function rotateMatrix(& $mat )
{
global $N ;
for ( $x = 0; $x < $N / 2; $x ++)
{
for ( $y = $x ;
$y < $N - $x - 1; $y ++)
{
$temp = $mat [ $x ][ $y ];
$mat [ $x ][ $y ] = $mat [ $y ][ $N - 1 - $x ];
$mat [ $y ][ $N - 1 - $x ] =
$mat [ $N - 1 - $x ][ $N - 1 - $y ];
$mat [ $N - 1 - $x ][ $N - 1 - $y ] =
$mat [ $N - 1 - $y ][ $x ];
$mat [ $N - 1 - $y ][ $x ] = $temp ;
}
}
}
function displayMatrix(& $mat )
{
global $N ;
for ( $i = 0; $i < $N ; $i ++)
{
for ( $j = 0; $j < $N ; $j ++)
echo $mat [ $i ][ $j ] . " " ;
echo "
";
}
echo "
";
}
$mat = array ( array (1, 2, 3, 4),
array (5, 6, 7, 8),
array (9, 10, 11, 12),
array (13, 14, 15, 16));
rotateMatrix( $mat );
displayMatrix( $mat );
?>
|
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!
Last Updated :
25 Oct, 2022
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