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

The canonical fixture is 6 vertices [1..6] with undirected edges (1,2), (1,3), (2,4), (3,4), (4,5), (5,6) inserted in that order. The final adjacency list is {1: [2, 3], 2: [1, 4], 3: [1, 4], 4: [2, 3, 5], 5: [4, 6], 6: [5]}. This same graph drives graph-bfs, graph-dfs, and graph-shortest-path-bfs.

Basic Implementation

basic.swift

let edges = [[1, 2], [1, 3], [2, 4], [3, 4], [4, 5], [5, 6]]
var adj: [Int: [Int]] = [:]
for e in edges {
	adj[e[0], default: []].append(e[1])
	adj[e[1], default: []].append(e[0])
}
var parts: [String] = []
for v in adj.keys.sorted() {
	let nbrs = adj[v]!.map { String($0) }.joined(separator: ", ")
	parts.append("\(v): [\(nbrs)]")
}
print("{" + parts.joined(separator: ", ") + "}")

Complexity

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

Implementation notes

Swift: a [Int: [Int]] dictionary stores neighbours via subscript-with-default; keys are sorted before printing because dictionary order is unspecified.
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.