Luzhiled's Library

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

概要

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.

使い方

計算量

$O(E + V)$

Depends on

Required by

Verified with

Code

#pragma once

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

/**
 * @brief Topological Sort(トポロジカルソート)
 * @docs docs/topological-sort.md
 */
template< typename T >
vector< int > topological_sort(const Graph< T > &g) {
  const int N = (int) g.size();
  vector< int > deg(N);
  for(int i = 0; i < N; i++) {
    for(auto &to : g[i]) ++deg[to];
  }
  stack< int > st;
  for(int i = 0; i < N; i++) {
    if(deg[i] == 0) st.emplace(i);
  }
  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"

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

/**
 * @brief Graph Template(グラフテンプレート)
 */
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 {
  vector< vector< Edge< T > > > g;
  int es;

  Graph() = default;

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

  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;
      cin >> a >> b;
      a += padding;
      b += padding;
      T c = T(1);
      if(weighted) cin >> c;
      if(directed) add_directed_edge(a, b, c);
      else add_edge(a, b, c);
    }
  }

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

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

template< typename T = int >
using Edges = vector< Edge< T > >;
#line 4 "graph/others/topological-sort.hpp"

/**
 * @brief Topological Sort(トポロジカルソート)
 * @docs docs/topological-sort.md
 */
template< typename T >
vector< int > topological_sort(const Graph< T > &g) {
  const int N = (int) g.size();
  vector< int > deg(N);
  for(int i = 0; i < N; i++) {
    for(auto &to : g[i]) ++deg[to];
  }
  stack< int > st;
  for(int i = 0; i < N; i++) {
    if(deg[i] == 0) st.emplace(i);
  }
  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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