Finding maximum path of a complex array - php

Question

I have an array:
$data = array(
1 => array(
"time" => 1,
"parent" => array(4)
),
2 => array(
"time" => 3,
"parent" => array(4, 5)
),
3 => array(
"time" => 2,
"parent" => array(6)
),
4 => array(
"time" => 1,
"parent" => array(6)
),
5 => array(
"time" => 1,
"parent" => array(4)
),
6 => array(
"time" => 1,
"parent" => array()
)
);
Key is the ID of an element, parent is an array of elements, which refers to element id and time is just an integer.
This is an illustrated example of a given array:
Schema
The integer on the bottom-left is the "id" and the integer in the middle is "time".
My goal here is find the most time-consuming path of this array. In the given example, the path would be 2->5->4->6 (id wise) resulting in 6 "time" overall. It looks pretty easy on paper, however I can't really seem to code an algorythm to get the elements of the most time-consuming path. I would appreciate any kind of help.
I think the algorythm should be kind of bruteforce-ish and check through all of the options available. Thus with the given array it would go like:
1 -> 4 -> 6 = 3
2 -> 4 -> 6 = 5
2 -> 5 -> 4 -> 6 = 6
3 -> 6 = 3
4 -> 6 = 2
5 -> 4 -> 6 = 3
Thanks in advance.

Answer 1

Note that this will only work if there are no loops in the array.
// Note: built this in the SO editor, might have bugs
$cached = [];
$arrays = []; // Do this yourself
function get_path($num) {
global $arrays, $cached;
if (isset($cached[$num])) return $cached[$num];
$array = $arrays[$num];
$maxtime = $array['time'];
$bestpath = array($num);
foreach ($array['parent'] as $i) {
$path = get_path($i);
if ($path['time']+$array['time'] > $maxtime) {
$maxtime = $path['time'] + $array['time'];
$bestpath = array_merge(array($num),$path['path']);
}
}
$cached[$num] = array('path' => $bestpath, 'time' => $maxtime);
return $cached[$num];
}
var_dump(get_path(5));
Not really a bruteforce way, should be close enough to O(n). The basic idea is that you just cache the paths it can take.
Note: I used a bit of C-style syntax here, but ideally you wouldn't actually write the code like this