Every possible combos for an island in Hashi game - php

Question

Here's the game : Hashiwokakero.
To solve it, I need to find all possible combinations of links + islands around every island.
Constraints are, 1 or 2 links, and one combination is enough links created for the targeted island.
For example, I have a island ['A' => 3], which means it needs 3 links to be solved, and it has 3 neighbors ['B', 'C', 'D'].
I'd like to find an algorithm which would produce such an array :
[
['B' => 1, 'C' => 1, 'D' => 1],
['B' => 1, 'C' => 2],
['B' => 1, 'D' => 2],
['B' => 2, 'C' => 1],
['B' => 2, 'D' => 1],
['C' => 1, 'D' => 2],
['C' => 2, 'D' => 1]
];
Thanks.

Answer 1

If you want to find all combinations of links (0, 1, or 2) per neighbor, with a fixed total number of links, then you could use the following recursive function:
function getPossibleLinks($value, $neighbors) {
if ($value == 0) return [[]];
$max = min(2, $value);
$min = 2 - min(count($neighbors) * 2 - $value, 2);
if ($min > 2) {
throw new Exception('Not possible to assign that many links');
}
$results = [];
for ($count = $min; $count <= $max; $count++) {
$nextResults = getPossibleLinks($value - $count, array_slice($neighbors, 0, -1));
foreach($nextResults as $result) {
if ($count) $result[end($neighbors)] = $count;
$results[] = $result;
}
}
return $results;
}
You would need to pass it the number of links as first argument ($value), and the array of neighbors as an array of strings.
Here is an example call:
$results = getPossibleLinks(3, ["B", "C", "D"]);
After this call, $results will have this content:
[
['B' => 2, 'C' => 1],
['B' => 1, 'C' => 2],
['B' => 2, 'D' => 1],
['B' => 1, 'C' => 1, 'D' => 1],
['C' => 2, 'D' => 1],
['B' => 1, 'D' => 2],
['C' => 1, 'D' => 2]
]
See it run on eval.in.