How to Generate All Permutations of Numbers 0-8 Using PHP?

Calculating Permutations of Numbers

Given a set of numbers from 0 to 8, the task is to generate all possible permutations of these numbers. In a permutation, each number can only appear once.

To grasp this problem, let's delve into the mathematical concept of permutations. The permutations formula states that the total number of permutations of 'n' elements taken 'k' at a time is given by:

nPk = n!/(n-k)!

In our case, we want to permute all 9 numbers, so k = n = 9. This results in 9! = 362880 possible permutations.

PHP Implementation

PHP provides capabilities for generating permutations. The pc_permute() function can be employed for this purpose, as demonstrated in the following code:

function pc_permute($items, $perms = array()) {
    if (empty($items)) { 
        echo join(' ', $perms) . "\n";
    }  else {
        for ($i = count($items) - 1; $i >= 0; $i--) {
             $newitems = $items;
             $newperms = $perms;
             list($foo) = array_splice($newitems, $i, 1);
             array_unshift($newperms, $foo);
             pc_permute($newitems, $newperms);
         }
    }
}

Example Output

Utilizing the pc_permute() function, we can output all the permutations of the numbers 0 to 8:

pc_permute(array(0, 1, 2, 3, 4, 5, 7, 8));

This will generate the following output:

0 1 2 3 4 5 6 7 8
0 1 2 3 4 5 6 8 7
0 1 2 3 4 5 7 6 8
0 1 2 3 4 5 7 8 6
0 1 2 3 4 6 5 7 8
0 1 2 3 4 6 7 8 5
0 1 2 3 4 7 5 6 8
0 1 2 3 4 7 5 8 6
0 1 2 3 4 7 6 5 8
0 1 2 3 4 7 6 8 5
0 1 2 3 4 7 8 5 6
0 1 2 3 4 7 8 6 5
0 1 2 3 4 8 5 6 7
0 1 2 3 4 8 5 7 6
0 1 2 3 4 8 6 5 7
0 1 2 3 4 8 6 7 5
0 1 2 3 4 8 7 5 6
0 1 2 3 4 8 7 6 5
0 1 2 3 5 4 6 7 8
0 1 2 3 5 4 6 8 7
0 1 2 3 5 4 7 6 8
0 1 2 3 5 4 7 8 6
0 1 2 3 5 4 8 6 7
0 1 2 3 5 4 8 7 6
0 1 2 3 5 6 4 7 8
0 1 2 3 5 6 4 8 7
0 1 2 3 5 6 7 4 8
0 1 2 3 5 6 7 8 4
0 1 2 3 5 6 8 4 7
0 1 2 3 5 6 8 7 4
0 1 2 3 5 7 4 6 8
0 1 2 3 5 7 4 8 6
0 1 2 3 5 7 6 4 8
0 1 2 3 5 7 6 8 4
0 1 2 3 5 7 8 4 6
0 1 2 3 5 7 8 6 4
0 1 2 3 5 8 4 6 7
0 1 2 3 5 8 4 7 6
0 1 2 3 5 8 6 4 7
0 1 2 3 5 8 6 7 4
0 1 2 3 5 8 7 4 6
0 1 2 3 5 8 7 6 4
0 1 2 3 6 4 5 7 8
0 1 2 3 6 4 5 8 7
0 1 2 3 6 4 7 5 8
0 1 2 3 6 4 7 8 5
0 1 2 3 6 4 8 5 7
0 1 2 3 6 4 8 7 5
0 1 2 3 6 5 4 7 8
0 1 2 3 6 5 4 8 7
0 1 2 3 6 5 7 4 8
0 1 2 3 6 5 7 8 4
0 1 2 3 6 5 8 4 7
0 1 2 3 6 5 8 7 4
0 1 2 3 6 7 4 5 8
0 1 2 3 6 7 4 8 5
0 1 2 3 6 7 5 4 8
0 1 2 3 6 7 5 8 4
0 1 2 3 6 7 8 4 5
0 1 2 3 6 7 8 5 4
0 1 2 3 6 8 4 5 7
0 1 2 3 6 8 4 7 5
0 1 2 3 6 8 5 4 7
0 1 2 3 6 8 5 7 4
0 1 2 3 6 8 7 4 5
0 1 2 3 6 8 7 5 4
0 1 2 3 7 4 5 6 8
0 1 2 3 7 4 5 8 6
0 1 2 3 7 4 6 5 8
0 1 2 3 7 4 6 8 5
0 1 2 3 7 4 8 5 6
0 1 2 3 7 4 8 6 5

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