Matrix Layer Rotation

You are given a 2D matrix of dimension  and a positive integer . You have to rotate the matrix  times and print the resultant matrix. Rotation should be in anti-clockwise direction.

Rotation of a  matrix is represented by the following figure. Note that in one rotation, you have to shift elements by one step only.

It is guaranteed that the minimum of m and n will be even.

As an example rotate the Start matrix by 2:

Start         First           Second
 1 2 3 4        2  3  4  5      3  4  5  6
12 1 2 5  ->   1  2  3  6 ->   2  3  4  7
11 4 3 6      12  1  4  7       1  2  1  8
10 9 8 7      11 10  9  8     12 11 10  9

Function Description

Complete the matrixRotation function in the editor below. It should print the resultant 2D integer array and return nothing.

matrixRotation has the following parameter(s):

• matrix: a 2D array of integers
• r: an integer that represents the rotation factor

Input Format

The first line contains three space separated integers, , , and , the number of rows and columns in , and the required rotation.
The next  lines contain  space-separated integers representing the elements of a row of .

Constraints

Output Format

Print each row of the rotated matrix as space-separated integers on separate lines.

Sample Input

Sample Input #01

4 4 2
1 2 3 4
5 6 7 8
9 10 11 12
13 14 15 16

Sample Output #01

3 4 8 12
2 11 10 16
1 7 6 15
5 9 13 14

Explanation #01

The matrix is rotated through two rotations.

 1  2  3  4      2  3  4  8      3  4  8 12
 5  6  7  8      1  7 11 12      2 11 10 16
 9 10 11 12  ->  5  6 10 16  ->  1  7  6 15
13 14 15 16      9 13 14 15      5  9 13 14

Sample Input #02

5 4 7
1 2 3 4
7 8 9 10
13 14 15 16
19 20 21 22
25 26 27 28

Sample Output #02

28 27 26 25
22 9 15 19
16 8 21 13
10 14 20 7
4 3 2 1

Explanation 02

The various states through 7 rotations:

1  2  3  4      2  3  4 10    3  4 10 16    4 10 16 22
7  8  9 10      1  9 15 16    2 15 21 22    3 21 20 28
13 14 15 16 ->  7  8 21 22 -> 1  9 20 28 -> 2 15 14 27 ->
19 20 21 22    13 14 20 28    7  8 14 27    1  9  8 26
25 26 27 28    19 25 26 27    13 19 25 26   7 13 19 25

10 16 22 28    16 22 28 27    22 28 27 26    28 27 26 25
 4 20 14 27    10 14  8 26    16  8  9 25    22  9 15 19
 3 21  8 26 ->  4 20  9 25 -> 10 14 15 19 -> 16  8 21 13
 2 15  9 25     3 21 15 19     4 20 21 13    10 14 20  7
 1  7 13 19     2  1  7 13     3  2  1  7     4  3  2  1

Sample Input #03

2 2 3
1 1
1 1

Sample Output #03

1 1
1 1

Explanation #03

All of the elements are the same, so any rotation will repeat the same matrix.

php

<?php

function Rotationlayer($ay, $ro) {

$len = count($ay);

$r = $ro%$len;

for($i = 0; $i < $r; $i++) {

$temp = $ay[0];

for($j =0; $j < $len; $j++) {

if($j == $len - 1) {

$ay[$j] = $temp;

} else {

$ay[$j] = $ay[$j+1];

}

}

}

return $ay;

}

// Complete the matrixRotation function below.

function matrixRotation($matrix, $ro) {

$n = count($matrix);

$m = count($matrix[0]);

$rot = array();

for($i =0; $i <min($n,$m)/2;$i++ ) {

$ar = array();

for($r = $i; $r < $m - $i -1; $r++) {

$ar[] = $matrix[$i][$r];

}

for($c = $i; $c < $n- $i -1; $c++) {

$ar[] = $matrix[$c][$m- $i - 1];

}

for($r = $m - $i -1; $r >= $i+1 ; $r--) {

$ar[] = $matrix[$n - $i - 1][$r];

}

for($c = $n - $i -1; $c >= $i+1 ; $c--) {

$ar[] = $matrix[$c][$i];

}

$rot[] = $ar;

}

$roa = array();

foreach($rot as $roi) {

$roa[] = Rotationlayer($roi, $ro);

}

$mt = array();

for($i =0; $i <min($n,$m)/2;$i++ ) {

$idx = 0;

$roay = $roa[$i];

for($r = $i; $r < $m - $i -1; $r++) {

$mt[$i][$r] = $roay[$idx];

$idx++;

}

for($c = $i; $c < $n- $i -1; $c++) {

$mt[$c][$m- $i - 1] = $roay[$idx];

$idx++;

}

for($r = $m - $i -1; $r >= $i+1 ; $r--) {

$mt[$n - $i - 1][$r] = $roay[$idx];

$idx++;

}

for($c = $n - $i -1; $c >= $i+1 ; $c--) {

$mt[$c][$i] = $roay[$idx];

$idx++;

}

}

$mta = array();

foreach($mt as $it) {

ksort($it);

$mta[] = $it;

}

foreach($mta as $item) {

foreach($item as $itm) {

echo $itm;

echo ' ';

}

echo "\n";

}

}

$mnr = explode(' ', rtrim(fgets(STDIN)));

$m = intval($mnr[0]);

$n = intval($mnr[1]);

$r = intval($mnr[2]);

$matrix == array();

for ($i = 0; $i < $m; $i++) {

$matrix_temp = rtrim(fgets(STDIN));

$matrix[] = array_map('intval',

preg_split('/ /', $matrix_temp, -1, PREG_SPLIT_NO_EMPTY));

}

matrixRotation($matrix, $r);