Topological Sort (トポロジカルソート) (graph/others/topological-sort.hpp)

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• Last update: 2026-08-10 07:40:27+00:00
• Include: #include "graph/others/topological-sort.hpp"

DAG(閉路のない有向グラフ) が与えられたとき、トポロジカルソートする。

入次数 $0$ の頂点から消すことを繰り返す。

topological_sort

vector<int> topological_sort(const Graph<T>& g)

DAG g をトポロジカルソートして、その頂点の順序を返す。

計算量

$O(E + V)$

Depends on

• Graph Template (グラフテンプレート) (graph/graph-template.hpp)

Required by

• Offline Dag Reachability (DAGの到達可能性クエリ) (graph/others/offline-dag-reachability.hpp)

Verified with

• test/verify/aoj-0275.test.cpp

Code

#pragma once

#include <stack>
#include <vector>

#include "../graph-template.hpp"

/**
 * @brief Topological Sort(トポロジカルソート)
 *
 */
template <typename T>
std::vector<int> topological_sort(const Graph<T>& g) {
  const int N = (int)g.size();
  std::vector<int> deg(N);
  for (int i = 0; i < N; i++) {
    for (auto& to : g[i]) ++deg[to];
  }
  std::stack<int> st;
  for (int i = 0; i < N; i++) {
    if (deg[i] == 0) st.emplace(i);
  }
  std::vector<int> ord;
  while (!st.empty()) {
    auto p = st.top();
    st.pop();
    ord.emplace_back(p);
    for (auto& to : g[p]) {
      if (--deg[to] == 0) st.emplace(to);
    }
  }
  return ord;
}

#line 2 "graph/others/topological-sort.hpp"

#include <stack>
#include <vector>

#line 2 "graph/graph-template.hpp"

#include <cstddef>
#include <iostream>
#line 6 "graph/graph-template.hpp"

template <typename T = int>
struct Edge {
  int from, to;
  T cost;
  int idx;

  Edge() = default;

  Edge(int from, int to, T cost = 1, int idx = -1)
      : from(from), to(to), cost(cost), idx(idx) {}

  operator int() const { return to; }
};

template <typename T = int>
struct Graph {
  std::vector<std::vector<Edge<T> > > g;
  int es;

  Graph() = default;

  explicit Graph(int n) : g(n), es(0) {}

  std::size_t size() const { return g.size(); }

  void add_directed_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es++);
  }

  void add_edge(int from, int to, T cost = 1) {
    g[from].emplace_back(from, to, cost, es);
    g[to].emplace_back(to, from, cost, es++);
  }

  void read(int M, int padding = -1, bool weighted = false,
            bool directed = false) {
    for (int i = 0; i < M; i++) {
      int a, b;
      std::cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if (weighted) std::cin >> c;
      if (directed)
        add_directed_edge(a, b, c);
      else
        add_edge(a, b, c);
    }
  }

  inline std::vector<Edge<T> >& operator[](const int& k) { return g[k]; }

  inline const std::vector<Edge<T> >& operator[](const int& k) const {
    return g[k];
  }
};

template <typename T = int>
using Edges = std::vector<Edge<T> >;
#line 7 "graph/others/topological-sort.hpp"

/**
 * @brief Topological Sort(トポロジカルソート)
 *
 */
template <typename T>
std::vector<int> topological_sort(const Graph<T>& g) {
  const int N = (int)g.size();
  std::vector<int> deg(N);
  for (int i = 0; i < N; i++) {
    for (auto& to : g[i]) ++deg[to];
  }
  std::stack<int> st;
  for (int i = 0; i < N; i++) {
    if (deg[i] == 0) st.emplace(i);
  }
  std::vector<int> ord;
  while (!st.empty()) {
    auto p = st.top();
    st.pop();
    ord.emplace_back(p);
    for (auto& to : g[p]) {
      if (--deg[to] == 0) st.emplace(to);
    }
  }
  return ord;
}

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