I have numbers, from 0 to 8. I would like in result, all possible sets of those numbers, each set should use all numbers, each number can occur only once in a set.
I would like to see solution made in PHP that could print out result. Or, at least, I would like some refreshment in theory of combinatorics, as I have long forgotten it. What is the formula to calculate how many permutations will there be?
Example sets:
- 0-1-2-3-4-5-6-7-8
- 0-1-2-3-4-5-6-8-7
- 0-1-2-3-4-5-8-6-7
- 0-1-2-3-4-8-5-6-7
- 0-1-2-3-8-4-5-6-7
- 0-1-2-8-3-4-5-6-7
- and so on…
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Answer
You’re looking for the permutations formula:
nPk = n!/(n-k)!
In your case, you have 9 entries and you want to choose all of them, that’s 9P9 = 9! = 362880
You can find a PHP algorithm to permutate in recipe 4.26 of O’Reilly’s “PHP Cookbook”.
pc_permute(array(0, 1, 2, 3, 4, 5, 7, 8));
Copied in from O’Reilly:
function pc_permute($items, $perms = array( )) { if (empty($items)) { print 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); } } }