How to reconstruct paths from a multi-path Dijkstra?

Question

I am currently writing a PHP library for graphs. I have already implemented a single-path Dijkstra\'s algorithm successfully, but now struggle with implementing a multi-path ver

Answer 1

Actually, a modified DFS function I named "enumerate" solved this question. For posterity's sake, here is the code I used to turn the output of the multi-path Dijkstra into an array of paths:

/**
 * Returns all shortest paths to $dest from the origin vertex $this->start in the graph.
 *
 * @param string $dest ID of the destination vertex
 *
 * @return array An array containing the shortest path and distance
 */
public function get($dest)
{
    $this->paths = [];
    $this->enumerate($dest, $this->start);

    return array(
        'paths' => $this->paths,
        'dist' => $this->dist[$dest],
    );
}

/**
 * Enumerates the result of the multi-path Dijkstra as paths.
 *
 * @param string $source ID of the source vertex
 * @param string $dest   ID of the destination vertex
 */
private function enumerate($source, $dest)
{
    array_unshift($this->path, $source);
    $discovered[] = $source;

    if ($source === $dest) {
        $this->paths[] = $this->path;
    } else {
        if (!$this->prev[$source]) {
            return;
        }
        foreach ($this->prev[$source] as $child) {
            if (!in_array($child, $discovered)) {
                $this->enumerate($child, $dest);
            }
        }
    }

    array_shift($this->path);
    if (($key = array_search($source, $discovered)) !== false) {
        unset($discovered[$key]);
    }
}

Answer 2

Like this? (Pseudocode):

function output_paths(source, dest, tail) {

    if source == dest:
        output([dest] + tail)

    for each node in prev[dest]:
        output_paths(source, node, [dest] + tail)
}


output_paths(source=A, dest=J, tail=[])