java 37 lines · 7 steps

Breadth-first search on an adjacency-list graph

An undirected graph backed by a HashMap, traversed level by level with a queue.

Explained by highlit

Intermediate graph-traversal bfs adjacency-list queue visited-set

1import java.util.ArrayDeque;
2import java.util.ArrayList;
3import java.util.HashMap;
4import java.util.HashSet;
5import java.util.List;
6import java.util.Map;
7import java.util.Queue;
8import java.util.Set;
9 
10public class Graph {
11    private final Map<Integer, List<Integer>> adjacency = new HashMap<>();
12 
13    public void addEdge(int from, int to) {
14        adjacency.computeIfAbsent(from, k -> new ArrayList<>()).add(to);
15        adjacency.computeIfAbsent(to, k -> new ArrayList<>()).add(from);
16    }
17 
18    public List<Integer> bfs(int start) {
19        List<Integer> order = new ArrayList<>();
20        Set<Integer> visited = new HashSet<>();
21        Queue<Integer> queue = new ArrayDeque<>();
22 
23        queue.add(start);
24        visited.add(start);
25 
26        while (!queue.isEmpty()) {
27            int node = queue.poll();
28            order.add(node);
29            for (int neighbor : adjacency.getOrDefault(node, List.of())) {
30                if (visited.add(neighbor)) {
31                    queue.add(neighbor);
32                }
33            }
34        }
35        return order;
36    }
37}

01 / 01

STEP 01

Walkthrough

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Three takeaways

1An adjacency map of node to neighbor list is a compact, flexible way to represent sparse graphs.
2BFS visits nodes in distance order by processing a FIFO queue and marking nodes the moment they're enqueued.
3Set.add returning a boolean lets you check membership and record it in one branchless step.

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