結果

問題 No.1436 Rgaph
コンテスト
ユーザー tokusakurai
提出日時 2021-03-20 15:05:19
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 5 ms / 2,000 ms
コード長 6,330 bytes
コンパイル時間 3,866 ms
コンパイル使用メモリ 215,208 KB
最終ジャッジ日時 2025-01-19 20:15:39
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample AC * 2
other AC * 28
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i = 0; i < n; i++)
#define rep2(i, x, n) for(int i = x; i <= n; i++)
#define rep3(i, x, n) for(int i = x; i >= n; i--)
#define each(e, v) for(auto &e: v)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
const int MOD = 1000000007;
//const int MOD = 998244353;
const int inf = (1<<30)-1;
const ll INF = (1LL<<60)-1;
template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;};
template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;};

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

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

    vector<vector<edge>> es;
    const int n;
    int m;

    Graph(int n) : es(n), n(n), m(0) {}

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

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

    vector<vector<edge>> es, rs;
    vector<int> vs, comp;
    vector<bool> used;
    const int n;
    int m;

    Strongly_Connected_Components(int n) : es(n), rs(n), vs(n), comp(n), used(n), n(n), m(0) {}

    void add_edge(int from, int to){
        es[from].emplace_back(to, m), rs[to].emplace_back(from, m);
        if(!directed) es[to].emplace_back(from, m), rs[from].emplace_back(to, m);
        m++;
    }

    void _dfs(int now){
        used[now] = true;
        for(auto &e: es[now]){
            if(!used[e.to]) _dfs(e.to);
        }
        vs.push_back(now);
    }

    void _rdfs(int now, int cnt){
        used[now] = true, comp[now] = cnt;
        for(auto &e: rs[now]){
            if(!used[e.to]) _rdfs(e.to, cnt);
        }
    }

    Graph<true> decompose(){
        fill(begin(used), end(used), false);
        for(int i = 0; i < n; i++){
            if(!used[i]) _dfs(i);
        }
        fill(begin(used), end(used), false), reverse(begin(vs), end(vs));
        int cnt = 0;
        for(auto &e: vs){
            if(!used[e]) _rdfs(e, cnt++);
        }
        Graph<true> G(cnt);
        for(int i = 0; i < n; i++){
            for(auto &e: es[i]){
                int u = comp[i], v = comp[e.to];
                if(u != v) G.add_edge(u, v);
            }
        }
        return G;
    }

    int operator [] (int k) const {return comp[k];}

    vector<int> ret_path;

    bool detect_path(int now, int t, bool use_id = false){
        used[now] = true;
        if(now == t){
            if(!use_id) ret_path.push_back(now);
            return true;
        }
        for(auto &e : es[now]){
            if(used[e.to]) continue;
            if(detect_path(e.to, t, use_id)){
                ret_path.push_back(use_id? e.id : now);
                return true;
            }
        }
        return false;
    }

    vector<int> find_path(int s, int t, bool use_id = false){
        ret_path.clear(), fill(begin(used), end(used), false);
        detect_path(s, t, use_id);
        reverse(begin(ret_path), end(ret_path));
        return ret_path;
    }

    vector<int> bfs(int s = 0){
        vector<int> pre_v(n, -1), pre_e(n, -1), col(n, -1);
        queue<int> que;
        que.emplace(s), col[s] = 0;

        vector<int> ret;

        while(!que.empty()){
            int i = que.front(); que.pop();
            each(e, es[i]){
                if(col[e.to] == (col[i]^1)) continue;
                if(col[e.to] == -1){
                    col[e.to] = col[i]^1, pre_v[e.to] = i, pre_e[e.to] = e.id;
                    que.emplace(e.to);
                }
                else if(ret.empty()){
                    vector<int> path = find_path(e.to, s, true);
                    int k = sz(path)&1;

                    if(k == col[e.to]){
                        ret.eb(e.id);
                        int ptr = i;
                        while(ptr != s){
                            ret.eb(pre_e[ptr]), ptr = pre_v[ptr];
                        }
                        reverse(all(ret));
                        each(e, path) ret.eb(e);
                    }
                    else{
                        int ptr = e.to;
                        while(ptr != s){
                            ret.eb(pre_e[ptr]), ptr = pre_v[ptr];
                        }
                        reverse(all(ret));
                        each(e, path) ret.eb(e);
                    }
                }
            }
        }

        return ret;
    }
};

int main(){
    int N, M; cin >> N >> M;

    Strongly_Connected_Components<true> G(N);

    vector<int> u(M), v(M), deg(N, 0);

    rep(i, M){
        cin >> u[i] >> v[i]; u[i]--, v[i]--;
        G.add_edge(u[i], v[i]);
        deg[u[i]]++;
    }

    if(G.decompose().n > 1) {cout << "-1\n"; return 0;}

    vector<int> cycle = G.bfs();
    int n = sz(cycle);
    if(n == 0) {cout << "-1\n"; return 0;}

    //each(e, cycle) cout << e << ' '; cout << '\n';

    vector<int> vs;
    rep(i, n){
        if(i == 0) vs.eb(u[cycle[i]]);
        vs.eb(v[cycle[i]]);
    }

    vector<int> nxt(n+1), pre(N, inf);

    rep3(i, n, 0){
        nxt[i] = pre[vs[i]];
        pre[vs[i]] = i;
    }

    int l = 0, r = n, d = n;

    rep(i, n+1){
        if(chmin(d, nxt[i]-i)) l = i, r = nxt[i];
    }

    vector<int> odd_cycle;

    while(l < r){
        if(nxt[l] < r) l = nxt[l];
        else odd_cycle.eb(cycle[l++]);
    }

    //each(e, odd_cycle) cout << e << ' '; cout << '\n';

    int K = sz(odd_cycle);
    string ans(M, 'G');

    bool flag = false;

    rep(i, K){
        int U = u[odd_cycle[i]];
        if(deg[U] >= 2){
            flag = true;
            rep(j, (K+1)/2){
                ans[odd_cycle[(i+j)%K]] = 'R';
            }
            break;
        }
    }

    if(!flag) {cout << "-1\n";}
    else cout << ans << '\n';
}
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