#621088 (C++17) No.583 鉄道同好会

• 問題: No.583 鉄道同好会
• ユーザー: tokusakurai
• 提出日時: 2021-02-22 10:14:56
• 言語: C++17 (gcc 15.2.0 + boost 1.89.0)
• 結果: AC
• 実行時間: 34 ms / 2,000 ms
• コード長: 4,194 bytes
• コンパイル時間: 2,775 ms
• コンパイル使用メモリ: 218,036 KB
• 最終ジャッジ日時: 2025-01-19 03:21:36
• ジャッジサーバーID （参考情報）: judge1 / judge2

ファイルパターン	結果
sample	AC * 3
other	AC * 16

ソースコード

//オイラー路(グラフの全ての辺をちょうど1回ずつ通るパス)の検出
//計算量 O(E+V)

//verified with
//https://codeforces.com/contest/1361/problem/C
//https://yukicoder.me/submissions/591125

#include <bits/stdc++.h>
using namespace std;

struct io_setup{
    io_setup(){
        ios_base::sync_with_stdio(false);
        cin.tie(NULL);
        cout << fixed << setprecision(15);
    }
} io_setup;

struct Union_Find_Tree{
    vector<int> data;
    const int n;
    
    Union_Find_Tree(int n) : data(n, -1), n(n) {}
    
    int root(int x){
        if(data[x] < 0) return x;
        return data[x] = root(data[x]);
    }

    int operator [] (int i) {return root(i);}
    
    bool unite(int x, int y){
        x = root(x), y = root(y);
        if(x == y) return false;
        if(data[x] > data[y]) swap(x, y);
        data[x] += data[y], data[y] = x;
        return true;
    }
    
    int size(int x) {return -data[root(x)];}
    
    bool same(int x, int y) {return root(x) == root(y);}
    
    void clear() {fill(begin(data), end(data), -1);}
};

template<bool directed = false>
struct Eulerian_Trail{
    struct edge{
        int to, id;
        edge(int to, int id) : to(to), id(id) {}
    };

    vector<vector<edge>> es;
    vector<pair<int, int>> list;
    vector<bool> used_e, used_v;
    vector<int> deg;
    const int n;
    int m;

    Eulerian_Trail(int n) : es(n), used_v(n), deg(n), n(n), m(0) {}

    void add_edge(int from, int to){
        list.emplace_back(from, to), es[from].emplace_back(to, m);
        if(directed) deg[from]++, deg[to]--;
        else es[to].emplace_back(from, m), deg[from]++, deg[to]++;
        m++;
    }

    pair<int, int> get_edge(int id) {return list[id];}

    vector<int> trace(int s){
        stack<edge> st;
        vector<int> ret;
        st.emplace(s, -1);
        while(!st.empty()){
            int now = st.top().to;
            used_v[now] = true;
            if(es[now].empty()){
                ret.push_back(st.top().id);
                st.pop();
            }
            else{
                auto e = es[now].back();
                es[now].pop_back();
                if(used_e[e.id]) continue;
                used_e[e.id] = true, st.push(e);
            }
        }
        ret.pop_back();
        reverse(begin(ret), end(ret));
        return ret;
    }

    vector<vector<int>> eulerian_trail(){
        vector<vector<int>> ret;
        fill(begin(used_v), end(used_v), false);
        if(directed){
            for(auto &e: deg) if(e != 0) return {};
        }
        else{
            for(auto &e: deg) if(e&1) return {};
        }
        used_e.assign(m, false);
        for(int i = 0; i < n; i++){
            if(es[i].empty() || used_v[i]) continue;
            ret.push_back(trace(i));
        }
        return ret;
    }

    vector<vector<int>> semi_eulerian_trail(){
        Union_Find_Tree uf(n);
        for(auto &e: list) uf.unite(e.first, e.second);
        vector<vector<int>> group(n);
        for(int i = 0; i < n; i++){
            group[uf[i]].emplace_back(i);
        }
        vector<vector<int>> ret;
        used_e.assign(m, false);
        for(auto &vs: group){
            if(vs.empty()) continue;
            int s = -1, t = -1;
            if(directed){
                for(auto &u: vs){
                    if(abs(deg[u]) > 1) return {};
                    else if(deg[u] == 1){
                        if(s != -1) return {};
                        s = u;
                    }
                }
            }
            else{
                for(auto &u: vs){
                    if(deg[u]&1){
                        if(s == -1) s = u;
                        else if(t == -1) t = u;
                        else return {};
                    }
                }
            }
            ret.push_back(trace(s == -1? vs.front() : s));
            if(ret.back().empty()) ret.pop_back();
        }
        return ret;
    }
};

int main(){
    int V, E; cin >> V >> E;

    Eulerian_Trail<false> G(V);
    while(E--){
        int u, v; cin >> u >> v;
        G.add_edge(u, v);
    }

    cout << (G.semi_eulerian_trail().size() == 1? "YES" : "NO") << '\n';
}