알고리즘 읽기 노트

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.

유형알고리즘카테고리Graphs깊이고급일반적인 복잡도O(V+E)

짧은 면접 답변

이 멘탈 모델부터 시작하세요

Topological sorting produces a linear order of a directed acyclic graph (DAG) such that every directed edge u→v places u before v.

간단한 설명

불필요한 전문용어 없이 동작 방식 이해하기

Kahn's algorithm repeatedly removes zero-indegree vertices using a queue.

A DFS postorder approach is another common method.

실행

알고리즘을 연속된 의사결정으로 읽기

Define directed/undirected and weighted/unweighted assumptions.

Choose the graph representation.

Track algorithm state and handle disconnected/cyclic cases explicitly.

기억해 둘 작은 예제

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.

읽기 쉬운 JavaScript 구현JavaScript

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;
}

이 코드를 읽는 방법

문법을 외우지 마세요. 각 줄에서 바뀌는 상태를 따라가고 위에서 설명한 불변식과 연결하세요.

복잡도

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Do not quote this complexity mechanically.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.

언제 사용하는가

적합한 경우

Use the algorithm only when its graph assumptions match the problem.

흔한 실수

보통 어디에서 문제가 생기는가

Trying it on a graph with a directed cycle.
Forgetting that multiple valid topological orders may exist.

면접에서 설명하는 방법

전문적인 답변 구조

Mention dependency scheduling and cycle detection. In Kahn's algorithm, processing fewer than V nodes proves a cycle exists.

문제→핵심 아이디어→불변식 / 상태→Big-O→트레이드오프

빠른 면접 체크

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.

복잡도에 대해 무엇을 언급해야 하나요?

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.

가장 흔한 실수는 무엇인가요?

Trying it on a graph with a directed cycle.

계속 읽기Graph representationDFS/BFSPriority queues