Why does duplications happen in Heap's algorithm - php

Question

I want to get all permutations from elements of array. Source array is very simple:
$arr = [ 1,2,3,4 ];
I wrote the code for implement Heap's algorithm,
private function mixture( $size, array $collection ) {
$permutations = [];
$offset = $size - 1;
if ( 1 === $size ) {
$permutations[] = implode( '-', $collection );
return $permutations;
}
for ( $i = 0; $i < $offset; $i++ ) {
$permutations = array_merge( $permutations, $this->mixture( $offset, $collection ) );
$j = ( 0 == $size % 2 ) ? $i : 0;
$tmp_el = $collection[ $offset ];
$collection[ $offset ] = $collection[ $j ];
$collection[ $j ] = $tmp_el;
}
$permutations = array_merge( $permutations, $this->mixture( $offset, $collection ) );
return $permutations;
}
The result of works has a many of duplications
array (size=24)
0 => '1-2-3-4' << same 4
1 => '2-1-3-4' << same 5
2 => '3-2-1-4'
3 => '2-3-1-4'
4 => '1-2-3-4' << same 0
5 => '2-1-3-4' < same 1
6 => '4-2-3-1'
7 => '2-4-3-1'
8 => '3-2-4-1'
9 => '2-3-4-1'
10 => '4-2-3-1'
11 => '2-4-3-1'
12 => '4-1-3-2'
13 => '1-4-3-2'
14 => '3-1-4-2'
15 => '1-3-4-2'
16 => '4-1-3-2'
17 => '1-4-3-2'
18 => '4-1-2-3'
19 => '1-4-2-3'
20 => '2-1-4-3'
21 => '1-2-4-3'
22 => '4-1-2-3'
23 => '1-4-2-3'
Please, help me to understand a reason for this and fix the code. I want to remove any duplication from the result.
Thanks

Answer 1

Your only problem is that you need to pass the $collection by reference because PHP creates an array copy by default:
mixture( $size, array &$collection )
https://3v4l.org/7Vn2p
<?php
$arr = [ 1,2,3,4 ];
$expected = [
'1-2-3-4',
'2-1-3-4',
'3-1-2-4',
'1-3-2-4',
'2-3-1-4',
'3-2-1-4',
'4-2-1-3',
'2-4-1-3',
'1-4-2-3',
'4-1-2-3',
'2-1-4-3',
'1-2-4-3',
'1-3-4-2',
'3-1-4-2',
'4-1-3-2',
'1-4-3-2',
'3-4-1-2',
'4-3-1-2',
'4-3-2-1',
'3-4-2-1',
'2-4-3-1',
'4-2-3-1',
'3-2-4-1',
'2-3-4-1',
];
function mixture( $size, array &$collection ) {
$permutations = [];
$offset = $size - 1;
if ( 1 === $size ) {
$permutations[] = implode( '-', $collection );
return $permutations;
}
for ( $i = 0; $i < $offset; $i++ ) {
$permutations = array_merge( $permutations, mixture( $offset, $collection ) );
$j = ( 0 == $size % 2 ) ? $i : 0;
$tmp_el = $collection[ $offset ];
$collection[ $offset ] = $collection[ $j ];
$collection[ $j ] = $tmp_el;
}
$permutations = array_merge( $permutations, mixture( $offset, $collection ) );
return $permutations;
}
print_r($permutations = mixture( count($arr), $arr ));
if ($expected == $permutations) {
echo 'PASS'.PHP_EOL;
} else {
echo 'FAIL'.PHP_EOL;
echo 'missing: '.PHP_EOL;
print_r(array_diff($expected, array_unique($permutations)));
}