Depth-First Search (Recursive)

Visit a start vertex, then recurse into its first unvisited neighbour all the way down before backtracking. A visited set prevents revisiting, and neighbour insertion order fixes the visit sequence.

Algorithm

On the canonical 6-vertex graph from graph-adjacency-list, starting at vertex 1, the deterministic visit order is [1, 2, 4, 3, 5, 6]. Calls unwind 6 -> 5 -> 4 -> 3 -> 2 -> 1 after all vertices are visited.

recursive descent Follow one branch to its end, then unwind and try the next neighbour.

Visual walkthrough

DFS follows the first unvisited neighbour as far as it can, then unwinds and tries the next branch.

Step 1 - First branch

Starting from 1, insertion order sends DFS to 2, then 4, then 3.

Step 2 - Full DFS order

The final order is [1, 2, 4, 3, 5, 6], then calls unwind 6 -> 5 -> 4 -> 3 -> 2 -> 1.

Basic Implementation

                            basic.php
                        

                            <?php
$adj = [1 => [2, 3], 2 => [1, 4], 3 => [1, 4], 4 => [2, 3, 5], 5 => [4, 6], 6 => [5]];
$visited = [];
$order = [];
$dfs = function ($v) use (&$dfs, &$adj, &$visited, &$order) {
	$visited[$v] = true;
	$order[] = $v;
	foreach ($adj[$v] as $nb) {
		if (!array_key_exists($nb, $visited)) {
			$dfs($nb);
		}
	}
};
$dfs(1);
echo "[" . implode(", ", $order) . "]\n";

                        

Complexity

Time: O(V + E)
Space: O(V) recursion depth

Implementation notes

PHP: a closure recurses via use (&$dfs, ...), sharing $visited and $order by reference.
The replay shows the current vertex, the visited set, the running visit order, and the call stack after each entry, matching the lesson spec.