Build a Graph as an Adjacency List

Represent an undirected graph as a map from each vertex to its 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.cpp

#include <iostream>
#include <vector>
#include <map>

int main() {
    std::vector<std::pair<int, int>> edges = {
        {1, 2}, {1, 3}, {2, 4}, {3, 4}, {4, 5}, {5, 6}};
    std::map<int, std::vector<int>> adj;
    for (const auto& e : edges) {
        adj[e.first].push_back(e.second);
        adj[e.second].push_back(e.first);
    }
    std::cout << "{";
    bool first = true;
    for (const auto& kv : adj) {
        if (!first) std::cout << ", ";
        std::cout << kv.first << ": [";
        for (size_t i = 0; i < kv.second.size(); ++i) {
            if (i > 0) std::cout << ", ";
            std::cout << kv.second[i];
        }
        std::cout << "]";
        first = false;
    }
    std::cout << "}" << std::endl;
    return 0;
}

Complexity

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

Implementation notes

C++: a std::map<int, std::vector<int>> keeps vertices in sorted order, and each vector stores neighbours appended 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.