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#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(g)
g
$O(E + V)$
#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; }