Topological Sorting
Topological sorting produces a linear order of a directed acyclic graph (DAG) such that every directed edge u→v places u before v.
ابدأ بهذا النموذج الذهني
Topological sorting produces a linear order of a directed acyclic graph (DAG) such that every directed edge u→v places u before v.
كيف يعمل، بلا مصطلحات زائدة
Kahn's algorithm repeatedly removes zero-indegree vertices using a queue.
A DFS postorder approach is another common method.
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 Topological Sorting, the goal is to make the invariant visible rather than to memorize code.
function topoSort(graph) {
const indegree = new Map();
for (const u of Object.keys(graph)) {
indegree.set(u, indegree.get(u) ?? 0);
for (const v of graph[u]) indegree.set(v, (indegree.get(v) ?? 0) + 1);
}
const queue = [...indegree].filter(([, d]) => d === 0).map(([v]) => v);
const out = [];
for (let i = 0; i < queue.length; i++) {
const u = queue[i]; out.push(u);
for (const v of graph[u] ?? []) if (indegree.set(v, indegree.get(v) - 1).get(v) === 0) queue.push(v);
}
return out.length === indegree.size ? out : null;
}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Do not quote this complexity mechanically.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
- Trying it on a graph with a directed cycle.
- Forgetting that multiple valid topological orders may exist.
صيغة إجابة احترافية
Mention dependency scheduling and cycle detection. In Kahn's algorithm, processing fewer than V nodes proves a cycle exists.
What problem does Topological Sorting solve?
Topological sorting produces a linear order of a directed acyclic graph (DAG) such that every directed edge u→v places u before v.
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؟
Trying it on a graph with a directed cycle.