Graphs

Build a Graph as an Adjacency List

Represent an undirected graph as a per-vertex list of neighbours. For every edge (u, v), append v to adj[u] and u to adj[v]. Neighbour lists keep insertion order so the graph is a stable, deterministic fixture for the search lessons.

Algorithm

Basic Implementation

basic.rb 
edges = [[1, 2], [1, 3], [2, 4], [3, 4], [4, 5], [5, 6]]
adj = {}
edges.each do |u, v|
	adj[u] ||= []
	adj[v] ||= []
	adj[u] << v
	adj[v] << u
end
parts = []
adj.keys.sort.each do |v|
	parts << "#{v}: [#{adj[v].join(", ")}]"
end
puts "{" + parts.join(", ") + "}"

The graph fixture is pinned once, then the adjacency list writes each undirected edge in both directions.

Step 1 - Pinned graph fixture

The six vertices and six undirected edges are the shared fixture for BFS and DFS.

Graph with edges (1,2), (1,3), (2,4), (3,4), (4,5), (5,6).123456

Step 2 - Final adjacency list

Each row lists neighbours in the same insertion order used by the lesson.

Adjacency list after all six undirected edges are inserted.vertexneighbours1[2, 3]2[1, 4]3[1, 4]4[2, 3, 5]5[4, 6]6[5]

Complexity

  • Build: O(V + E)
  • Space: O(V + E)

Implementation notes

  • Ruby: a Hash maps each vertex to an Array of neighbours; keys are sorted before printing for a stable order.
  • The replay shows the adjacency list after each edge is added, matching the lesson spec.
adjacency list Each edge adds two directed entries, one in each direction.