Why should you care?

Grid problems, social “degrees”, and serialization often reduce to BFS.

See it live — copy this example

Run snippets in a .NET console app, LINQPad, or https://dotnetfiddle.net. Write Big O above every solution.

void Bfs(Dictionary<int, List<int>> g, int start) {
  var q = new Queue<int>();
  var seen = new HashSet<int> { start };
  q.Enqueue(start);
  while (q.Count > 0) {
    int u = q.Dequeue();
    Console.WriteLine(u);
    foreach (var v in g.GetValueOrDefault(u, new()))
      if (seen.Add(v)) q.Enqueue(v);
  }
}

What happened?

• Queue stores frontier.
• HashSet prevents revisits.
• Add returns false if already present.

Practice next

1. Build a tiny adjacency list.
2. Run BFS from node 1.
3. Track distance dictionary.
4. Return parent pointers to reconstruct path.
5. Multi-source BFS warm-up.

Remember

BFS = queue + visited. Unweighted shortest paths. Model the graph first.

Shortest hops

Friend-of-friend distance.

Outcome: BFS levels equal hop count.