PHP: Finding word in graph of letters recursively - php

Question

I'm having a graph like this:
Now, let's say I'm looking for a word CAT. I'm trying to make a nice code to walk this graph and find a word. I'd like it to find all existing positions of a word, not only first one.
The result for $graph->find('cat') should be:
return [
[1, 0, 6],
[1, 2, 3]
];
I have created such code in the past, but it was iterative. This time I'd like to try recursive.
Here's what I have so far:
I call it like this:
// LetterGraph is my own class
$graph = new LetterGraph($nodes);
$graph->find('cat');
And in my LetterGraph class I do the following:
public function find(string $word): array {
$result = [];
$firstLetter = mb_substr($word, 0, 1);
foreach ($this->letters as $node) {
if ($node->letter === $firstLetter) {
$result[] = $this->walk($word, [$node]);
}
}
return $result;
}
protected function walk(string $word, array $nodes): array {
$lastNode = end($nodes);
$letterToFind = mb_substr($word, count($nodes), 1);
foreach ($lastNode->neighbours as $neighbour) {
if ($neighbour->letter === $letterToFind) {
// is return okay here?
return $this->walk($word, array_merge($nodes, $neighbour);
}
}
}
Now, I'm not sure how to deal with recursive returns to make it give me the result I want.

Answer 1

It can be solved using Master theorem.
Assuming $node->id is the number you want to see in the resulting array, the recursion may look like
public function find(string $word, array $nodes = null): array
{
$firstLetter = mb_substr($word, 0, 1);
$rest = mb_substr($word, 1);
if (empty($nodes)) {
//top level call, start to search across all nodes
$nodes = $this->letters;
}
$result = [];
foreach ($nodes as $node) {
if ($node->letter === $firstLetter) {
if (empty($rest)) {
//exit recursion
$result[] = [$node->id];
} else {
//recursively search rest of the string
$branches = $this->find($rest, $node->neighbours);
if (!empty($branches)) {
foreach ($branches as $branch) {
$result[] = array_merge([$node->id], $branch);
}
}
}
}
}
return $result;
}