結果

問題 No.1320 Two Type Min Cost Cycle
ユーザー umimel
提出日時 2024-08-15 21:15:36
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,312 ms / 2,000 ms
コード長 9,263 bytes
コンパイル時間 2,683 ms
コンパイル使用メモリ 197,104 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-08-15 21:15:56
合計ジャッジ時間 18,969 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 57
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In member function 'void dijkstra<T>::run(graph<T>&, int)':
main.cpp:135:18: warning: structured bindings only available with '-std=c++17' or '-std=gnu++17' [-Wc++17-extensions]
  135 |             auto [d, v] = que.top();
      |                  ^

ソースコード

diff # 

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
#define all(a) (a).begin(), (a).end()
#define pb push_back
#define fi first
#define se second
mt19937_64 rng(chrono::system_clock::now().time_since_epoch().count());
const ll MOD1000000007 = 1000000007;
const ll MOD998244353 = 998244353;
const ll MOD[3] = {999727999, 1070777777, 1000000007};
const ll LINF = 1LL << 60LL;
const int IINF = (1 << 30) - 2;


template<typename T> 
struct edge{
    int from;
    int to;
    T cost;
    int id;

    edge(){}
    edge(int to, T cost=1) : from(-1), to(to), cost(cost){}
    edge(int to, T cost, int id) : from(-1), to(to), cost(cost), id(id){}
    edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id){}

    void reverse(){swap(from, to);}
};

template<typename T>
struct edges : std::vector<edge<T>>{
    void sort(){
        std::sort(
            (*this).begin(),
            (*this).end(), 
            [](const edge<T>& a, const edge<T>& b){
                return a.cost < b.cost;
            }
        );
    }
};

template<typename T = bool>
struct graph : std::vector<edges<T>>{
private:
    int n = 0;
    int m = 0;
    edges<T> es;
    bool dir;

public:
    graph(int n, bool dir) : n(n), dir(dir){
        (*this).resize(n);
    }

    void add_edge(int from, int to, T cost=1){
        if(dir){
            es.push_back(edge<T>(from, to, cost, m));
            (*this)[from].push_back(edge<T>(from, to, cost, m++));
        }else{
            if(from > to) swap(from, to);
            es.push_back(edge<T>(from, to, cost, m));
            (*this)[from].push_back(edge<T>(from, to, cost, m));
            (*this)[to].push_back(edge<T>(to, from, cost, m++));
        }
    }

    int get_vnum(){
        return n;
    }

    int get_enum(){
        return m;
    }

    bool get_dir(){
        return dir;
    }

    edge<T> get_edge(int i){
        return es[i];
    }

    edges<T> get_edge_set(){
        return es;
    }
};

template<typename T>
struct redge{
    int from, to;
    T cap, cost;
    int rev;
    
    redge(int to, T cap, T cost=(T)(1)) : from(-1), to(to), cap(cap), cost(cost){}
    redge(int to, T cap, T cost, int rev) : from(-1), to(to), cap(cap), cost(cost), rev(rev){}
};

template<typename T> using Edges = vector<edge<T>>;
template<typename T> using weighted_graph = vector<Edges<T>>;
template<typename T> using tree = vector<Edges<T>>;
using unweighted_graph = vector<vector<int>>;
template<typename T> using residual_graph = vector<vector<redge<T>>>;


template<typename T>
struct dijkstra{
private:
    const T TINF = numeric_limits<T>::max()/2;
    int n, s;
    graph<T> G;
    vector<T> dist;
    vector<int> vpar;
    edges<T> epar;

public:
    dijkstra(graph<T> G, int s) : G(G), s(s){
        // initilization
        n = G.get_vnum();
        dist.resize(n, TINF);
        vpar.resize(n, -1);
        epar.resize(n);

        // running Dijkstra algorithm
        run(G, s);
    }

    void run(graph<T> &G, int s){
        dist[s] = 0;
        priority_queue<pair<T, int>, vector<pair<T, int>>, greater<>> que;
        que.push({0, s});
        while(!que.empty()){
            auto [d, v] = que.top();
            que.pop();
            if(dist[v] < d) continue;

            for(auto e : G[v]){
                if(dist[v] + e.cost < dist[e.to]){
                    dist[e.to] = dist[v] + e.cost;
                    vpar[e.to] = v;
                    epar[e.to] = e;
                    que.push({dist[e.to], e.to});
                }
            }
        }
    }

    T get_dist(int t){
        return dist[t];
    }

    vector<T> get_dist(){
        return dist;
    }

    vector<int> get_vpar(){
        return vpar;
    }

    int get_vpar(int v){
        return vpar[v];
    }

    edges<T> get_epar(){
        return epar;
    }

    edge<T> get_epar(int v){
        return epar[v];
    }

    vector<int> get_vpath(int t){
        vector<int> vpath;
        int cur = t;
        while(cur != -1){
            vpath.push_back(cur);
            cur = vpar[cur];
        }
        reverse(vpath.begin(), vpath.end());

        return vpath;
    }

    edges<T> get_epath(int t){
        edges<T> epath;
        int cur = t;
        while(cur != s){
            epath.push_back(epar[cur]);
            cur = vpar[cur];
        }
        reverse(epath.begin(), epath.end());

        return epath;
    }

    graph<T> get_shotest_path_tree(){
        graph<T> spt(n, false);
        for(int v=0; v<n; v++) if(v != s){
            int p = vpar[v];
            auto e = G.get_edge(epar[v]);
            spt[vpar[v]].add_edge(vpar[v], v, e.cost);
        }

        return spt;
    }
};


struct cycle{

    template<typename S>
    static edges<S> find_cycle(graph<S> &G){
        int n = G.get_vnum();
        vector<int> used(n, 0);
        edges<S> cyc;

        function<bool(int, int)> dfs = [&](int v, int e_id){
            for(auto e : G[v]) if(e.id != e_id){
                if(used[e.to]==1){
                    cyc.push_back(e);
                    return true;
                }else if(used[e.to]==0){
                    used[e.to] = used[v];
                    if(dfs(e.to, e.id)){
                        cyc.push_back(e);
                        return true;
                    }
                }
            }

            used[v] = 2;
            return false;
        };

        for(int v=0; v<n; v++) if(used[v]==0){
            used[v] = 1;
            if(dfs(v, -1)) break;
        }

        if(cyc.empty()) return cyc;
        while(cyc.back().from != cyc[0].to) cyc.pop_back();
        reverse(cyc.begin(), cyc.end());

        return cyc;
    }

    template<typename T>
    static edges<T> find_oddcycle(graph<T> &G, int s){

    }

    template<typename T>
    static edges<T> find_evencycle(graph<T> &G, int s){
        
    }

    template<typename S>
    static edges<S> find_mincostcycle(graph<S> &G, int s){
        int n = G.get_vnum();
        const S SINF = numeric_limits<S>::max()/2;
        bool dir = G.get_dir();
        dijkstra<S> dijk(G, s);
        auto dist = dijk.get_dist();
        edges<S> cyc;

        // find minimum cost cycle on directed graph
        if(dir){
            S cost = SINF;
            edge<S> emin; 
            for(int v=0; v<n; v++) for(auto e : G[v]) if(e.to == s){
                if(dist[v] + e.cost < cost){
                    cost = dist[v] + e.cost;
                    emin = e;
                }
            }

            if(cost == SINF) return {};
            cyc = dijk.get_epath(emin.from);
            cyc.push_back(emin);
        }

        // find minimum cost cycle on undirected graph
        if(!dir){
            vector<vector<int>> ch(n);
            for(int v=0; v<n; v++) if(v != s && dijk.get_vpar(v)!=-1){
                ch[dijk.get_vpar(v)].push_back(v);
            }
            
            vector<int> label(n, -1);
            label[s] = s;
            function<void(int, int)> labeling = [&](int v, int l){
                label[v] = l;
                for(int to : ch[v]) labeling(to, l);
            };
            for(int to : ch[s]) labeling(to, to);

            S cost = SINF;
            edge<S> emin;
            for(int v=0; v<n; v++) if(v != s) for(auto e : G[v]){
                if(e.id != dijk.get_epar(v).id && label[v] != label[e.to] && dist[v] + dist[e.to] + e.cost < cost){
                    cost = dist[v] + dist[e.to] + e.cost;
                    emin = e;
                }   
            }

            if(cost == SINF) return {};

            cyc = dijk.get_epath(emin.from);
            cyc.push_back(emin);
            auto epath = dijk.get_epath(emin.to);
            reverse(epath.begin(), epath.end());
            for(auto e : epath){
                e.reverse();
                cyc.push_back(e);
            }
        }

        return cyc;
    }

    template<typename S>
    static edges<S> find_mincostcycle(graph<S> &G){
        int n = G.get_vnum();
        const S SINF = numeric_limits<S>::max()/2;
        S cost = SINF;
        edges<S> min_cyc;
        
        for(int s=0; s<n; s++){
            auto cyc = find_mincostcycle(G, s);
            if(cyc.empty()) continue;
            S sum = 0;
            for(auto e : cyc) sum += e.cost;
            if(sum < cost){
                cost = sum;
                min_cyc = cyc;
            }
        }

        return min_cyc;
    }

    template<typename T>
    static edges<T> find_minmeancycle(graph<T> &G){

    }

    template<typename T>
    static edges<T> enumerate_3cycle(graph<T> &G){

    }

    template<typename T>
    static edges<T> enumerate_4cycle(graph<T> &G){

    }
};


void solve(){
    int dir; cin >> dir;
    int n, m; cin >> n >> m;
    graph<ll> G(n, dir);
    
    for(int i=0; i<m; i++){
        int u, v; cin >> u >> v;
        u--; v--;
        ll w; cin >> w;
        G.add_edge(u, v, w);
    }

    auto cycle = cycle::find_mincostcycle<ll>(G);
    if(cycle.empty()){
        cout << -1 << '\n';
        return;
    }
    ll ans = 0;
    for(auto e : cycle) ans += e.cost;
    cout << ans << '\n';
}

int main(){
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    
    int T=1;
    //cin >> T;
    while(T--) solve();
}
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