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

Basic Implementation

basic.scala

import scala.collection.mutable.{HashMap, HashSet, ArrayBuffer}
object Main {
	val adj = HashMap.empty[Int, List[Int]]
	val visited = HashSet.empty[Int]
	val order = ArrayBuffer.empty[Int]
	def dfs(v: Int): Unit = {
		visited += v
		order += v
		for (nb <- adj(v)) {
			if (!visited.contains(nb)) {
				dfs(nb)
			}
		}
	}
	def main(args: Array[String]): Unit = {
		adj(1) = List(2, 3)
		adj(2) = List(1, 4)
		adj(3) = List(1, 4)
		adj(4) = List(2, 3, 5)
		adj(5) = List(4, 6)
		adj(6) = List(5)
		dfs(1)
		println(order.mkString("[", ", ", "]"))
	}
}

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.

Complexity

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

Implementation notes

Scala: a recursive dfs over object-level adj, visited, and order; mkString renders the buffer.
The replay shows the current vertex, the visited set, and the running visit order after each entry, matching the lesson spec.

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