Graph Breadth-First Search
BFS explores a graph level by level using a queue. In an unweighted graph it finds shortest paths by number of edges.
ابدأ بهذا النموذج الذهني
BFS explores a graph level by level using a queue. In an unweighted graph it finds shortest paths by number of edges.
كيف يعمل، بلا مصطلحات زائدة
Enqueue the start and mark it visited.
Repeatedly dequeue one node and enqueue unseen neighbors.
اقرأ الخوارزمية كسلسلة من القرارات
Define directed/undirected and weighted/unweighted assumptions.
Choose the graph representation.
Track algorithm state and handle disconnected/cyclic cases explicitly.
Read a tiny input by hand and write down the state after every important operation. For Graph Breadth-First Search, the goal is to make the invariant visible rather than to memorize code.
function bfs(graph, start) {
const seen = new Set([start]);
const queue = [start];
let head = 0;
while (head < queue.length) {
const node = queue[head++];
for (const next of graph[node] ?? []) {
if (!seen.has(next)) {
seen.add(next);
queue.push(next);
}
}
}
return seen;
}لا تحفظ الصياغة. تتبع الحالة التي تتغير في كل سطر واربطها بالثابت الموضح أعلاه.
O(V+E)
Do not quote this complexity mechanically. Ask which operation or input dimension it describes, then derive the cost from the loops, recursion depth, data-structure operations and any preprocessing assumptions.
مناسب لـ
- Use the algorithm only when its graph assumptions match the problem.
ما الذي يسوء عادةً
- Forgetting disconnected components.
- Mixing weighted and unweighted shortest-path algorithms.
- Not protecting against revisits/cycles.
صيغة إجابة احترافية
The queue is not an implementation detail—it creates level order, which is exactly why unweighted shortest paths work.
What problem does Graph Breadth-First Search solve?
BFS explores a graph level by level using a queue. In an unweighted graph it finds shortest paths by number of edges.
ماذا يجب أن أذكر عن التعقيد؟
Its typical cost here is O(V+E), but a complete answer should connect that cost to the representation, input constraints and the dominant operations.
ما الخطأ الأكثر شيوعاً؟
Forgetting disconnected components.