Question

This is a code that I got from the site here and I’d like to know whether this implementation of A* is correct. I have looked at it and compare it with the wikipedia page and it seems valid.. The reason why I ask is because in the site it says there is still a bug in this code, I tried finding it but can’t find any. I want to change it though so that it takes an origin and destination as input parameter

<?php

class AStarSolver
{
    function solve(&$s)
    {
        include_once('PQueue.class.php');
        $o = new PQueue();
        $l = array();
        $c = array();
        $p = array();
        $a = $s->getStartIndex();
        $z = $s->getGoalIndex();
        $d = $s->goalDistance($a);

        $n0 = array('g'=>0, 'h'=>$d, 'i'=>$a, 'p'=>NULL, 'f'=>$d);
        $o->push($n0, -$d);
        $l[$a] = TRUE;

        while (! $o->isEmpty())
        {
            $n = $o->pop();

            if ($n['i'] == $z)
            {
                while ($n)
                {
                    $p[] = $n['i'];
                    $n = $n['p'];
                }
                break;
            }

            foreach ($s->getNeighbors($n['i']) as $j => $w)
            {
                if ((isset($l[$j]) || isset($c[$j])) && isset($m) && $m['g'] <= $n['g']+$w)
                    continue;

                $d = $s->goalDistance($j);
                $m = array('g'=>$n['g']+$w, 'h'=>$d, 'i'=>$j, 'p'=>$n, 'f'=>$n['g']+$w+$d);

                if (isset($c[$j]))
                    unset($c[$j]);

                if (! isset($l[$j]))
                {
                    $o->push($m, -$m['f']);
                    $l[$j] = TRUE;
                }
            }
            $c[$n['i']] = $n;
        }
        return $p;
    }

}

?>

The code to the Pqueue can be found here

Answer 1

The site suggests that the bug might be in the PQueue class.

In PQueue::pop this

$j+1 < $m

is a test whether the heap node at $i has one child (at $j) or two (at $j and $j+1).

But $m here is count($h) only on the first iteration through the loop, since the --$m in the loop condition is evaluated every time.

Move that --$m next to the array_pop where it belongs, and that will be one less bug.

---

Now for AStarSolver.

The variables are (relative to Wikipedia pseudocode):

• $o – open set as priority queue;
• $l – open set as map keyed by index;
• $c – closed set as map keyed by index;
• $n – current node (x);
• $m – neighbour node (y) ?;
• $j – neighbour node index.

Problems that I see:

• $n = $o->pop() isn’t followed by unset($l[$n['i']]). Since both $o and $l represent the same set, they should be kept in sync.

• According to Wikipedia the closed set is only used if the heuristic is monotone (and I think a distance heuristic is monotone), and in that case, once a node is added to the closed set, it is never visited again. This code seems to implement some other pseudocode, which does remove nodes from the closed set. I think this defeats the purpose of the closed set, and the first condition in the inner loop should be

  if (isset($c[$j]) || isset($l[$j]) && isset($m) && $m['g'] <= $n['g']+$w)

  Then we can remove the unset($c[$j]).

• $m['g'] in this condition should be the g-score of the current neighbour indexed by $j. But $m has whatever value is left over from the previous loop: the node corresponding to $j on a previous iteration.

  What we need is a way to find a node and its g-score by node index. We can store the node in the $l array: instead of $l[$j] = TRUE we do $l[$j] = $m and the above condition becomes

  if (isset($c[$j]) || isset($l[$j]) && $l[$j]['g'] <= $n['g']+$w)

• Now the tricky bit. If the node we just found is not in the open set, we add it there (that’s the $o->push and $l[$j] =).

  However, if it is in the open set we just found a better path to it, so we must update it. The code doesn’t do this and it’s tricky because the priority queue doesn’t provide a routine for increasing the priority of an element. However, we can rebuild the priority queue completely and the last bit of code in the inner loop becomes

  if (! isset($l[$j])) {
   $o->push($m, -$m['f']);
   $l[$j] = $m; // add a new element
} else {
   $l[$j] = $m; // replace existing element
   $o = new PQueue();
   foreach ($l as $m)
      $o->push($m, -$m['f']);
}

  This is not terribly efficient, but it’s a starting point. Changing an element in a priority queue isn’t efficient anyway, because you first have to find it.

---

Even without these changes the algorithm does find a path, just not the best path. You can see it in the mentioned mazes:

• In the crazy maze in the third inner circuit: the taken upper path around is slightly longer than the lower path would have been because of the obstacles on the left.

• In the big maze in the upper-right part of the path there’s an unnecessary loop up.

---

Since this was on my mind, I implemented my own version of the algorithm and posted it in an answer to your previous question.