Procon

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:heavy_check_mark: verify/LC-StronglyConnectedComponents.test.cpp

Depends on

Code

#define PROBLEM "https://judge.yosupo.jp/problem/scc"

#include "../Library/Template.hpp"
#include "../Library/Graph/StronglyConnectedComponents.hpp"

int main(){
    cin.tie(0)->sync_with_stdio(false);
    int N, M; cin >> N >> M;
    auto G = InputGraph(N, M, 0, false, true);
    
    StronglyConnectedComponents scc(G);
    cout << scc.ComponentCount() << '\n';
    for(const auto &vs : scc.Components()){
        cout << vs.size();
        for(const auto &v : vs){
            cout << ' ' << v;
        }
        cout << '\n';
    }
}
#line 1 "verify/LC-StronglyConnectedComponents.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/scc"

#line 2 "Library/Template.hpp"

#line 2 "Library/Common.hpp"

/**
 * @file Common.hpp
 */

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cstdint>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
using namespace std;

using ll = int64_t;
using ull = uint64_t;

constexpr const ll INF = (1LL << 62) - (3LL << 30) - 1;
#line 4 "Library/Template.hpp"

inline bool YnPrint(bool flag){cout << (flag ? "Yes" : "No") << '\n'; return flag;}
inline bool YNPrint(bool flag){cout << (flag ? "YES" : "NO") << '\n'; return flag;}
template<typename Container>
inline void Sort(Container &container){sort(container.begin(), container.end());}
template<typename Container>
inline void ReverseSort(Container &container){sort(container.rbegin(), container.rend());}
template<typename Container>
inline void Reverse(Container &container){reverse(container.begin(), container.end());}
template<typename Value>
inline int PopCount(const Value &value){return __builtin_popcount(value);}
template<typename Value>
inline Value Floor(Value numerator, Value denominator){if(denominator < 0) numerator *= -1, denominator *= -1; return numerator < 0 ? (numerator + 1) / denominator - 1 : numerator / denominator;}
template<typename Value>
inline Value Ceil(Value numerator, Value denominator){if(denominator < 0) numerator *= -1, denominator *= -1; return numerator > 0 ? (numerator - 1) / denominator + 1 : numerator / denominator;}
template<typename Value>
inline int LowerBoundIndex(const vector<Value> &container, const Value &value){return distance(container.begin(), lower_bound(container.begin(), container.end(), value));}
template<typename Value>
inline int UpperBoundIndex(const vector<Value> &container, const Value &value){return distance(container.begin(), upper_bound(container.begin(), container.end(), value));}
template<typename Value>
inline bool Between(const Value &lower, const Value &x, const Value &higher){return lower <= x && x <= higher;}
template<typename Value>
inline bool InGrid(const Value &y, const Value &x, const Value &ymax, const Value &xmax){return Between(0, y, ymax - 1) && Between(0, x, xmax - 1);}
template<typename Value>
inline Value Median(const Value &a, const Value &b, const Value &c){return Between(b, a, c) || Between(c, a, b) ? a : (Between(a, b, c) || Between(c, b, a) ? b : c);}
template<typename Value>
inline Value Except(Value &src, Value &cond, Value &excp){return (src == cond ? excp : src);}

template<class Value>
bool chmin(Value &src, const Value &cmp){if(src > cmp){src = cmp; return true;} return false;}
template<class Value>
bool chmax(Value &src, const Value &cmp){if(src < cmp){src = cmp; return true;} return false;}
template<typename Value>
inline Value min(vector<Value> &v){return *min_element((v).begin(), (v).end());}
template<typename Value>
inline Value max(vector<Value> &v){return *max_element((v).begin(), (v).end());}

const int dx4[4] = {1, 0, -1, 0};
const int dy4[4] = {0, -1, 0, 1};
const int dx8[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const int dy8[8] = {0, -1, -1, -1, 0, 1, 1, 1};

vector<pair<int, int>> adjacent(int current_y, int current_x, int max_y, int max_x, bool dir_8 = false){
    vector<pair<int, int>> ret;
    for(int d = 0; d < 4 * (1 + dir_8); ++d){
        int next_y = current_y + (dir_8 ? dy8[d] : dy4[d]);
        int next_x = current_x + (dir_8 ? dx8[d] : dx4[d]);
        if(InGrid(next_y, next_x, max_y, max_x)){
            ret.emplace_back(next_y, next_x);
        }
    }
    return ret;
}

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p){
    os << p.first << " " << p.second;
    return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p){
    is >> p.first >> p.second;
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, vector<T> &v){
    for (int i = 0; i < v.size(); ++i){
        os << v[i] << (i + 1 != v.size() ? " " : "");
    }
    return os;
}

template <typename T>
ostream &operator<<(ostream &os, vector<vector<T>> &v){
    for (int i = 0; i < v.size(); ++i){
        os << v[i] << (i + 1 != v.size() ? "\n" : "");
    }
    return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v){
    for (int i = 0; i < v.size(); ++i) is >> v[i];
    return is;
}

template <typename T>
ostream &operator<<(ostream &os, set<T> &v){
    for (auto &u : v){
        os << u << " ";
    }
    return os;
}

template<typename T1, typename T2>
vector<pair<T1, T2>> AssembleVectorPair(vector<T1> &v1, vector<T2> &v2){
    assert(v1.size() == v2.size());
    vector<pair<T1, T2>> v;
    for(int i = 0; i < v1.size(); ++i) v.push_back({v1[i], v2[i]});
    return v;
}

template<typename T1, typename T2>
pair<vector<T1>, vector<T2>> DisassembleVectorPair(vector<pair<T1, T2>> &v){
    vector<T1> v1;
    vector<T2> v2;
    transform(v.begin(), v.end(), back_inserter(v1), [](auto p){return p.first;});
    transform(v.begin(), v.end(), back_inserter(v2), [](auto p){return p.second;});
    return {v1, v2};
}

template<typename T1, typename T2, typename T3>
tuple<vector<T1>, vector<T2>, vector<T3>> DisassembleVectorTuple(vector<tuple<T1, T2, T3>> &v){
    vector<T1> v1;
    vector<T2> v2;
    vector<T3> v3;
    transform(v.begin(), v.end(), back_inserter(v1), [](auto p){return get<0>(p);});
    transform(v.begin(), v.end(), back_inserter(v2), [](auto p){return get<1>(p);});
    transform(v.begin(), v.end(), back_inserter(v3), [](auto p){return get<2>(p);});
    return {v1, v2, v3};
}

template<typename T1 = int, typename T2 = T1>
pair<vector<T1>, vector<T2>> InputVectorPair(int size){
    vector<pair<T1, T2>> v(size);
    for(auto &[p, q] : v) cin >> p >> q;
    return DisassembleVectorPair(v);
}

template<typename T1 = int, typename T2 = T1, typename T3 = T1>
tuple<vector<T1>, vector<T2>, vector<T3>> InputVectorTuple(int size){
    vector<tuple<T1, T2, T3>> v(size);
    for(auto &[p, q, r] : v) cin >> p >> q >> r;
    return DisassembleVectorTuple(v);
}
#line 2 "Library/Graph/Graph.hpp"

#line 4 "Library/Graph/Graph.hpp"

using Vertex = int;

template<typename WeightType = int32_t>
struct Edge{
    public:
    Edge() = default;

    Edge(Vertex from_, Vertex to_, WeightType weight_ = 1, int idx_ = -1) :
        from(from_), to(to_), cost(weight_), idx(idx_){}
    
    bool operator<(const Edge<WeightType> &e) const {return cost < e.cost;}

    operator int() const {return to;}

    Vertex from, to;
    WeightType cost;
    int idx;
};

template<typename WeightType = int32_t>
class Graph{
    public:
    Graph() = default;

    Graph(int V) : edge_size_(0), adjacent_list_(V){}
    
    inline void AddUndirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
        adjacent_list_[v].push_back(Edge<WeightType>(v, u, w, idx));
    }
    
    inline void AddDirectedEdge(Vertex u, Vertex v, WeightType w = 1){
        int idx = edge_size_++;
        adjacent_list_[u].push_back(Edge<WeightType>(u, v, w, idx));
    }

    inline size_t VertexSize() const {
        return adjacent_list_.size();
    }

    inline size_t EdgeSize() const {
        return edge_size_;
    }

    inline vector<Edge<WeightType>> &operator[](const Vertex v){
        return adjacent_list_[v];
    }

    inline const vector<Edge<WeightType>> &operator[](const Vertex v) const {
        return adjacent_list_[v];
    }
    
    private:
    size_t edge_size_;
    vector<vector<Edge<WeightType>>> adjacent_list_;
};

template<typename WeightType = int32_t>
Graph<WeightType> InputGraph(int N, int M, int padding = -1, bool weighted = false, bool directed = false){
    Graph<WeightType> G(N);
    for(int i = 0; i < M; ++i){
        Vertex u, v; WeightType w = 1;
        cin >> u >> v, u += padding, v += padding;
        if(weighted) cin >> w;
        if(directed) G.AddDirectedEdge(u, v, w);
        else G.AddUndirectedEdge(u, v, w);
    }
    return G;
}
#line 2 "Library/Graph/GraphMisc.hpp"

#line 4 "Library/Graph/GraphMisc.hpp"

template<typename WeightType>
vector<Edge<WeightType>> ConvertEdgeSet(const Graph<WeightType> &G){
    vector<Edge<WeightType>> ret;
    vector<bool> check(G.EdgeSize(), false);
    int n = G.VertexSize();
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            if(check[e.idx]) continue;
            check[e.idx] = true;
            ret.push_back(e);
        }
    }
    return ret;
}

template<typename WeightType>
vector<vector<WeightType>> ConvertDistanceMatrix(const Graph<WeightType> &G){
    int n = G.VertexSize();
    vector<vector<WeightType>> ret(n, vector<WeightType>(n, WeightType(INF)));
    for(int u = 0; u < n; ++u){
        ret[u][u] = WeightType(0);
        for(const Edge<WeightType> &e : G[u]){
            ret[u][e.to] = e.cost;
        }
    }
    return ret;
}

template<typename WeightType>
Graph<WeightType> ReverseGraph(const Graph<WeightType> &G){
    int n = G.VertexSize();
    Graph<WeightType> ret(n);
    for(int u = 0; u < n; ++u){
        for(const Edge<WeightType> &e : G[u]){
            ret.AddDirectedEdge(e.to, e.from, e.cost);
        }
    }
    return ret;
}
#line 3 "Library/Graph/StronglyConnectedComponents.hpp"

template<typename WeightType>
struct StronglyConnectedComponents{
    public:
    StronglyConnectedComponents(Graph<WeightType> &graph) :
        G(graph), RG(ReverseGraph(graph)), V(G.VertexSize()), belong_(V, -1){
        vector<int> label(V, -1);
        vector<bool> state(V, false);
        int nex = 0;
        vector<Vertex> vs(V);
        iota(vs.begin(), vs.end(), 0);
        for(auto v : vs){
            if(!state[v]) dfs1(v, label, nex, state);
        }
        sort(vs.begin(), vs.end(), [&](Vertex u, Vertex v){
            return label[u] > label[v];
        });
        for(auto v : vs){
            if(state[v]){
                int c = components_.size();
                components_.push_back(vector<Vertex>{});
                dfs2(v, label, c, state);
            }
        }
    }

    inline vector<vector<Vertex>> &Components(){
        return components_;
    }

    inline int ComponentCount() const {
        return (int)components_.size();
    }

    inline int BelongComponent(const Vertex &v) const {
        return belong_[v];
    }

    vector<Vertex> TopologicalSort() const {
        vector<Vertex> ret;
        for(const auto &vs : components_){
            for(const auto &v : vs){
                ret.emplace_back(v);
            }
        }
        return ret;
    }
    
    Graph<WeightType> ContractedGraph() const {
        int nn = ComponentCount();
        Graph<WeightType> ret(nn);
        for(int u = 0; u < V; ++u){
            int nu = BelongComponent(u);
            for(const Edge<WeightType> &e : G[u]){
                int nv = BelongComponent(e.to);
                if(nu == nv) continue;
                ret.AddDirectedEdge(nu, nv, e.cost);
            }
        }
        return ret;
    }

    inline int operator[](const Vertex &v){
        return BelongComponent(v);
    }

    inline const int operator[](const Vertex &v) const {
        return BelongComponent(v);
    }

    private:
    Graph<WeightType> &G;
    Graph<WeightType> RG;
    int V;
    vector<vector<Vertex>> components_;
    vector<int> belong_;

    void dfs1(Vertex v, vector<int> &label, int &nex, vector<bool> &state){
        state[v] = true;
        for(const Edge<WeightType> &e : G[v]){
            if(state[e.to]) continue;
            dfs1(e.to, label, nex, state);
        }
        label[v] = nex++;
        return;
    }

    void dfs2(Vertex v, vector<int> &label, int component, vector<bool> &state){
        components_[component].push_back(v);
        belong_[v] = component;
        state[v] = false;
        for(const Edge<WeightType> &e : RG[v]){
            if(!state[e.to]) continue;
            dfs2(e.to, label, component, state);
        }
        return;
    }
};
#line 5 "verify/LC-StronglyConnectedComponents.test.cpp"

int main(){
    cin.tie(0)->sync_with_stdio(false);
    int N, M; cin >> N >> M;
    auto G = InputGraph(N, M, 0, false, true);
    
    StronglyConnectedComponents scc(G);
    cout << scc.ComponentCount() << '\n';
    for(const auto &vs : scc.Components()){
        cout << vs.size();
        for(const auto &v : vs){
            cout << ' ' << v;
        }
        cout << '\n';
    }
}
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