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.dart 
void main() {
  final edges = [[1, 2], [1, 3], [2, 4], [3, 4], [4, 5], [5, 6]];
  final adj = <int, List<int>>{};
  for (final e in edges) {
    adj.putIfAbsent(e[0], () => []).add(e[1]);
    adj.putIfAbsent(e[1], () => []).add(e[0]);
  }
  final parts = <String>[];
  for (final v in adj.keys) {
    parts.add('$v: [${adj[v]!.join(', ')}]');
  }
  print('{${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

  • Dart: a Map<int, List<int>> (LinkedHashMap) preserves insertion order; putIfAbsent appends neighbours in edge 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.