結果

問題 No.1436 Rgaph
ユーザー SHIJOU
提出日時 2021-03-26 00:33:09
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 38 ms / 2,000 ms
コード長 5,312 bytes
コンパイル時間 3,855 ms
コンパイル使用メモリ 213,156 KB
最終ジャッジ日時 2025-01-19 21:46:26
ジャッジサーバーID
（参考情報） 		judge2 / judge3
このコードへのチャレンジ
（要ログイン）
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 # 

//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for(int i=0; i<n; ++i)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using ll = int64_t;
using ull = uint64_t;
using ld = long double;
using P = pair<int, int>;
using vs = vector<string>;
using vi = vector<int>;
using vvi = vector<vi>;
template<class T> using PQ = priority_queue<T>;
template<class T> using PQG = priority_queue<T, vector<T>, greater<T>>;
const int INF = 0xccccccc;
const ll LINF = 0xcccccccccccccccLL;
template<typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {return a < b && (a = b, true);}
template<typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {return a > b && (a = b, true);}
template<typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) { return is >> p.first >> p.second;}
template<typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) { return os << p.first << ' ' << p.second;}

struct SCC {
  struct csr {
    vector<int> start, elist;
    csr(int n, const vector<pair<int, int>> &edges)
      : start(n+1), elist(edges.size()) {
        for(pair<int, int> e:edges) {
          start[e.first+1]++;
        }
        for(int i = 1; i <= n; i++) {
          start[i] += start[i-1];
        }
        vector<int> counter = start;
        for(pair<int, int> e:edges) {
          elist[counter[e.first]++] = e.second;
        }
    }
  };
  int n;
  vector<pair<int, int>> edges;
  SCC(int n_) : n(n_) {}
  void add(int from, int to) {edges.emplace_back(from, to);}
  pair<int, vector<int>> scc_ids() {
    csr g(n, edges);
    int now_ord = 0, group_num = 0;
    vector<int> used, low(n), ord(n, -1), ids(n);
    used.reserve(n);
    auto dfs = [&](auto self, int v)->void {
      low[v] = ord[v] = now_ord++;
      used.push_back(v);
      for(int i = g.start[v]; i < g.start[v+1]; i++) {
        int to = g.elist[i];
        if(ord[to] == -1) {
          self(self, to);
          low[v] = min(low[v], low[to]);
        }
        else {
          low[v] = min(low[v], ord[to]);
        }
      }
      if(low[v] == ord[v]) {
        while(true) {
          int u = used.back();
          used.pop_back();
          ord[u] = n;
          ids[u] = group_num;
          if(u == v) break;
        }
        group_num++;
      }
    };
    for(int i = 0; i < n; i++) {
      if(ord[i] == -1) dfs(dfs, i);
    }
    for(int &x:ids) {
      x = group_num - 1 - x;
    }
    return {group_num, ids};
  }
  vector<vector<int>> scc() {
    pair<int, vector<int>> ids = scc_ids();
    int group_num = ids.first;
    vector<int> counts(group_num);
    for(int x:ids.second) counts[x]++;
    vector<vector<int>> groups(group_num);
    for(int i = 0; i < group_num; i++) {
      groups[i].reserve(counts[i]);
    }
    for(int i = 0; i < n; i++) {
      groups[ids.second[i]].push_back(i);
    }
    return groups;
  }
};

//head



int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  if(m <= n) {
    puts("-1");
    return 0;
  }
  SCC scc(n);
  vector<vector<P>> G(n);
  rep(i, m) {
    int a, b;
    cin >> a >> b;
    a--; b--;
    scc.add(a, b);
    G[a].emplace_back(b, i);
  }
  if(scc.scc_ids().first != 1) {
    puts("-1");
    return 0;
  }
  vi check(n, -1);
  vvi r(n);
  auto dfs = [&](auto self, int i) -> vi {
    vi res;
    for(auto [ne, id]:G[i]) {
      vi u;
      if(check[ne] == -1) {
        check[ne] = check[i]^1;
        r[ne] = r[i];
        r[ne].emplace_back(id);
        u = self(self, ne);
        if(not u.empty()) u.emplace_back(id);
      }
      else if(check[ne] == check[i]) {
        u.emplace_back(id);
      }
      if(not u.empty()) res = u;
    }
    return res;
  };
  auto __s = [&](int root) {
    fill(all(check), -1);
    check[root] = 0;
    rep(i, n) r[i].clear();
    return dfs(dfs, root);
  };
  vi x = __s(0);
  if(x.empty()) {
    puts("-1");
    return 0;
  }
  int to = scc.edges[x[0]].second;
  vi y = r[to];
  __s(to);
  vi z = r[0];
  if((int(z.size())^int(x.size()))&1) {
    while(not x.empty()) {
      z.emplace_back(x.back());
      x.pop_back();
    }
  }
  else {
    z.reserve(int(z.size())+int(y.size()));
    copy(all(y), back_inserter(z));
  }
  vector<P> pa(n, {-1, -1});
  pa[to] = {0, 0};
  vi re;
  rep(i, int(z.size())) {
    auto [f, t] = scc.edges[z[i]];
    if(pa[t].first == -1) {
      pa[t] = {pa[f].first^1, i+1};
    }
    else {
      if(pa[t].first == pa[f].first) {
        vi zz;
        for(int j = pa[t].second; j <= i; j++) {
          zz.emplace_back(z[j]);
        }
        rep(k, pa[t].second) re.emplace_back(z[k]);
        for(int k = i+1; k < int(z.size()); k++) re.emplace_back(z[k]);
        z.swap(zz);
        break;
      }
      else {
        pa[t].second = i+1;
      }
    }
  }
  string ans(m, '_');
  for(auto x:re) ans[x] = 'R';
  if(re.empty()) {
    int u = -1;
    vi ch(m);
    for(auto x:z) ch[x] = 1;
    rep(i, m) if(not ch[i]) {
      chmax(u, pa[scc.edges[i].second].second);
    }
    ans[z[u]] = 'R';
  }
  rep(i, int(z.size())) if(ans[z[i]] == 'R') {
    rotate(z.begin(), z.begin()+i+1, z.end());
  }
  ans[z[0]] = 'G';
  for(int i = 1; i < int(z.size()); i++) ans[z[i]] = (i&1?'G':'R');
  rep(i, m) if(ans[i] == '_') ans[i] = 'R';
  cout << ans << endl;
}
0