結果
問題 | No.1436 Rgaph |
ユーザー | nok0 |
提出日時 | 2020-12-27 13:39:09 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 36 ms / 2,000 ms |
コード長 | 18,406 bytes |
コンパイル時間 | 3,606 ms |
コンパイル使用メモリ | 259,720 KB |
実行使用メモリ | 6,820 KB |
最終ジャッジ日時 | 2024-11-21 07:25:36 |
合計ジャッジ時間 | 5,884 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge3 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
6,816 KB |
testcase_01 | AC | 2 ms
6,820 KB |
testcase_02 | AC | 2 ms
6,820 KB |
testcase_03 | AC | 2 ms
6,816 KB |
testcase_04 | AC | 2 ms
6,820 KB |
testcase_05 | AC | 2 ms
6,816 KB |
testcase_06 | AC | 16 ms
6,816 KB |
testcase_07 | AC | 2 ms
6,816 KB |
testcase_08 | AC | 2 ms
6,816 KB |
testcase_09 | AC | 2 ms
6,820 KB |
testcase_10 | AC | 18 ms
6,816 KB |
testcase_11 | AC | 3 ms
6,816 KB |
testcase_12 | AC | 3 ms
6,820 KB |
testcase_13 | AC | 2 ms
6,820 KB |
testcase_14 | AC | 3 ms
6,816 KB |
testcase_15 | AC | 2 ms
6,820 KB |
testcase_16 | AC | 2 ms
6,816 KB |
testcase_17 | AC | 3 ms
6,820 KB |
testcase_18 | AC | 3 ms
6,816 KB |
testcase_19 | AC | 3 ms
6,820 KB |
testcase_20 | AC | 6 ms
6,816 KB |
testcase_21 | AC | 5 ms
6,820 KB |
testcase_22 | AC | 19 ms
6,820 KB |
testcase_23 | AC | 13 ms
6,820 KB |
testcase_24 | AC | 22 ms
6,816 KB |
testcase_25 | AC | 34 ms
6,816 KB |
testcase_26 | AC | 36 ms
6,816 KB |
testcase_27 | AC | 36 ms
6,816 KB |
testcase_28 | AC | 2 ms
6,816 KB |
testcase_29 | AC | 17 ms
6,820 KB |
ソースコード
/** * author: nok0 * created: 2020.11.07 23:37:48 **/ #ifdef LOCAL #define _GLIBCXX_DEBUG #endif #include <bits/stdc++.h> using namespace std; #pragma region Macros #define FOR(i, l, r) for(int i = (l); i < (r); ++i) #define REP(i, n) FOR(i, 0, n) #define REPS(i, n) FOR(i, 1, n + 1) #define RFOR(i, l, r) for(int i = (l); i >= (r); --i) #define RREP(i, n) RFOR(i, n - 1, 0) #define RREPS(i, n) RFOR(i, n, 1) #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() template <class T = int> using V = vector<T>; template <class T = int> using VV = V<V<T>>; using ll = long long; using ld = long double; using pii = pair<int, int>; using pll = pair<ll, ll>; #define VEC(type, name, size) \ V<type> name(size); \ INPUT(name) #define VVEC(type, name, h, w) \ VV<type> name(h, V<type>(w)); \ INPUT(name) #define INT(...) \ int __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ INPUT(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ INPUT(__VA_ARGS__) #define DOUBLE(...) \ DOUBLE __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LD(...) \ LD __VA_ARGS__; \ INPUT(__VA_ARGS__) void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(long double &a) { cin >> a; } void scan(char a[]) { scanf("%s", a); } void scan(string &a) { cin >> a; } template <class T> void scan(V<T> &); template <class T, class L> void scan(pair<T, L> &); template <class T> void scan(V<T> &a) { for(auto &i : a) scan(i); } template <class T, class L> void scan(pair<T, L> &p) { scan(p.first); scan(p.second); } template <class T> void scan(T &a) { cin >> a; } void INPUT() {} template <class Head, class... Tail> void INPUT(Head &head, Tail &... tail) { scan(head); INPUT(tail...); } template <class T> inline void print(T x) { cout << x << '\n'; } template <class T> inline void dump(T x) { cout << x << '\n'; exit(0); } template <typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p) { is >> p.first >> p.second; return is; } template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p) { os << p.first << " " << p.second; return os; } template <typename T> istream &operator>>(istream &is, vector<T> &v) { for(T &in : v) is >> in; return is; } template <class T> ostream &operator<<(ostream &os, const V<T> &v) { REP(i, SZ(v)) { if(i) os << " "; os << v[i]; } return os; } //debug template <typename T> void view(const V<T> &v) { cerr << "{ "; for(const auto &e : v) { cerr << e << ", "; } cerr << "\b\b }"; } template <typename T> void view(const VV<T> &vv) { cerr << "{\n"; for(const auto &v : vv) { cerr << "\t"; view(v); cerr << "\n"; } cerr << "}"; } template <typename T, typename U> void view(const V<pair<T, U>> &v) { cerr << "{\n"; for(const auto &c : v) cerr << "\t(" << c.first << ", " << c.second << ")\n"; cerr << "}"; } template <typename T, typename U> void view(const map<T, U> &m) { cerr << "{\n"; for(auto &t : m) cerr << "\t[" << t.first << "] : " << t.second << "\n"; cerr << "}"; } template <typename T, typename U> void view(const pair<T, U> &p) { cerr << "(" << p.first << ", " << p.second << ")"; } template <typename T> void view(const set<T> &s) { cerr << "{ "; for(auto &t : s) { view(t); cerr << ", "; } cerr << "\b\b }"; } template <typename T> void view(T e) { cerr << e; } #ifdef LOCAL void debug_out() {} template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) { view(H); cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ cerr << "\b\b]\n"; \ } while(0) #else #define debug(...) (void(0)) #endif template <class T> V<T> press(V<T> &x) { V<T> res = x; sort(all(res)); res.erase(unique(all(res)), res.end()); REP(i, SZ(x)) { x[i] = lower_bound(all(res), x[i]) - res.begin(); } return res; } template <class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } template <class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return true; } return false; } inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; } inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; } inline void err(bool b = true) { if(b) { cout << -1 << '\n'; exit(0); } } template <class T> inline void fin(bool b = true, T e = 0) { if(b) { cout << e << '\n'; exit(0); } } template <class T> T divup(T x, T y) { return (x + (y - 1)) / y; } template <typename T> T pow(T a, long long n, T e = 1) { T ret = e; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } struct iofast { iofast() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } iofast_; const int inf = 1e9; const ll INF = 1e18; #pragma endregion struct Edge { int to; long long cost; Edge() = default; Edge(int to_, long long cost_) : to(to_), cost(cost_) {} bool operator<(const Edge &a) const { return cost < a.cost; } bool operator>(const Edge &a) const { return cost > a.cost; } friend std::ostream &operator<<(std::ostream &s, Edge &a) { s << "to:" << a.to << " cost:" << a.cost; return s; } }; struct Graph : private std::vector<std::vector<Edge>> { using std::vector<std::vector<Edge>>::vector; using std::vector<std::vector<Edge>>::operator[]; using std::vector<std::vector<Edge>>::operator=; using std::vector<std::vector<Edge>>::size; using std::vector<std::vector<Edge>>::resize; using std::vector<std::vector<Edge>>::clear; using std::vector<std::vector<Edge>>::push_back; using std::vector<std::vector<Edge>>::emplace_back; using std::vector<std::vector<Edge>>::begin; using std::vector<std::vector<Edge>>::end; private: const long long INF = 1e18; bool isweight = true, lcainit_done = false; std::vector<std::vector<int>> parent; std::vector<int> lcadist; template <class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return true; } return false; } template <class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } vector<pii> edges; public: void read(int e = -1, bool weight = 0, bool directed = false, int idx = 1) { if(e == -1) e = size() - 1; if(!weight) isweight = false; while(e--) { int u, v; long long cost = 1; std::cin >> u >> v; if(weight) std::cin >> cost; u -= idx, v -= idx; edges.eb(u, v); (*this)[u].emplace_back(v, cost); if(!directed) (*this)[v].emplace_back(u, cost); } } void add(int u, int v, int cost = -1, bool directed = false, int idx = 1) { if(cost != -1) isweight = true; else cost = 1; u -= idx, v -= idx; (*this)[u].emplace_back(v, cost); if(!directed) (*this)[v].emplace_back(u, cost); } std::vector<long long> Dijkstra(int s) { std::vector dist(size(), INF); if(isweight) { using pll = std::pair<long long, long long>; std::priority_queue<pll, std::vector<pll>, std::greater<pll>> que; dist[s] = 0; que.push(pll(0, s)); while(!que.empty()) { pll p = que.top(); que.pop(); int v = p.second; if(dist[v] < p.first) continue; for(int i = 0; i < int((*this)[v].size()); i++) { Edge e = (*this)[v][i]; if(dist[e.to] > dist[v] + e.cost) { dist[e.to] = dist[v] + e.cost; que.push(pll(dist[e.to], e.to)); } } } return dist; } else { std::vector dist(size(), INF); std::queue<int> que; dist[s] = 0; que.push(s); while(!que.empty()) { int v = que.front(); que.pop(); for(auto nv : (*this)[v]) { if(dist[nv.to] != INF) continue; dist[nv.to] = dist[v] + 1; que.push(nv.to); } } return dist; } } std::vector<long long> BellmanFord(int s) { int n = size(); std::vector res(n, INF); res[s] = 0; for(int loop = 0; loop < n - 1; loop++) { for(int v = 0; v < n; v++) { if(res[v] == INF) continue; for(auto &e : (*this)[v]) { res[e.to] = std::min(res[e.to], res[v] + e.cost); } } } std::queue<int> que; std::vector chk(n, 0); for(int v = 0; v < n; v++) { if(res[v] == INF) continue; for(auto &e : (*this)[v]) { if(res[e.to] > res[v] + e.cost) { res[e.to] = res[v] + e.cost; if(!chk[e.to]) { que.push(e.to); chk[e.to] = 1; } } } } while(!que.empty()) { int now = que.front(); que.pop(); for(auto &e : (*this)[now]) { if(!chk[e.to]) { chk[e.to] = 1; que.push(e.to); } } } for(int i = 0; i < n; i++) if(chk[i]) res[i] = -INF; return res; } std::vector<std::vector<long long>> WarshallFloyd() { int n = size(); std::vector dist(n, std::vector(n, INF)); for(int i = 0; i < n; i++) { dist[i][i] = 0; } for(int i = 0; i < n; i++) { for(auto e : (*this)[i]) { chmin(dist[i][e.to], e.cost); } } for(int k = 0; k < n; k++) for(int i = 0; i < n; i++) for(int j = 0; j < n; j++) chmin(dist[i][j], dist[i][k] + dist[k][j]); return dist; } int lca(int u, int v) { std::function<void(int, int, int)> dfs = [&](int now, int per, int d) { parent[0][now] = per; lcadist[now] = d; for(auto &e : (*this)[now]) if(e.to != per) dfs(e.to, now, d + 1); }; if(!lcainit_done) { lcainit_done = true; int n = size(); int k = 1; while((1 << k) < n) k++; parent.assign(k, std::vector(n, -1)); lcadist.assign(n, -1); dfs(0, -1, 0); for(int i = 0; i < k - 1; i++) for(int v = 0; v < n; v++) { if(parent[i][v] < 0) parent[i + 1][v] = -1; else parent[i + 1][v] = parent[i][parent[i][v]]; } } if(lcadist[u] < lcadist[v]) std::swap(u, v); int k = parent.size(); for(int i = 0; i < k; i++) if((lcadist[u] - lcadist[v]) >> i & 1) u = parent[i][u]; if(u == v) return u; for(int i = k - 1; i >= 0; i--) if(parent[i][u] != parent[i][v]) u = parent[i][u], v = parent[i][v]; return parent[0][u]; } int dist(int u, int v) { return lcadist[u] + lcadist[v] - 2 * lcadist[lca(u, v)]; } std::vector<int> tsort() { std::vector<int> res; int n = size(); std::vector<int> used(n, 0); bool notDAG = false; std::function<void(int)> dfs = [&](int k) { if(notDAG) return; if(used[k]) { if(used[k] == 1) notDAG = true; return; } used[k] = 1; for(auto &e : (*this)[k]) dfs(e.to); used[k] = 2; res.push_back(k); }; for(int i = 0; i < n; i++) dfs(i); if(notDAG) return std::vector<int>{}; std::reverse(res.begin(), res.end()); return res; } bool isDAG() { return tsort().size(); } std::vector<long long> height() { std::vector<long long> fir(size(), -1), sec(size(), -1); std::function<long long(int, int)> dfs = [&](int now, int par) { long long f = 0, s = 0; for(auto &e : (*this)[now]) { if(e.to == par) continue; s = std::max(s, dfs(e.to, now) + e.cost); if(f < s) std::swap(f, s); } sec[now] = s; return fir[now] = f; }; std::function<void(int, int, long long, long long, long long)> solve = [&](int now, int par, long long parf, long long pars, long long parcost) { if(fir[now] + parcost == parf) parf = pars; sec[now] = std::max(sec[now], parf + parcost); if(fir[now] < sec[now]) std::swap(fir[now], sec[now]); for(auto &e : (*this)[now]) { if(e.to == par) continue; solve(e.to, now, fir[now], sec[now], e.cost); } return; }; dfs(0, -1); solve(0, -1, -1, -1, -1); return fir; } //{二部グラフか、二部グラフのどちらに属するかを0か1で表した配列} std::pair<bool, std::vector<int>> isBiparate() { std::vector<int> colors(size()), ret(size()); std::function<bool(int, int)> dfs = [&](int now, int col) { colors[now] = col; if(col == 1) ret[now] = 1; for(auto &e : (*this)[now]) { if(col == colors[e.to]) return false; if(colors[e.to] == 0 and !dfs(e.to, -col)) return false; } return true; }; return std::pair(dfs(0, 1), ret); } //{{端点、端点},直径の大きさ} std::pair<std::pair<int, int>, long long> Diameter() { auto vec = Dijkstra(0); int v1 = -1, v2 = -1; long long dia = -1; for(int i = 0; i < int(size()); i++) if(chmax(dia, vec[i])) v1 = i; vec = Dijkstra(v1); dia = -1; for(int i = 0; i < int(size()); i++) if(chmax(dia, vec[i])) v2 = i; std::pair<std::pair<int, int>, long long> res = {{v1, v2}, dia}; return res; } //最小全域木 long long Prim() { long long res = 0; std::priority_queue<Edge, std::vector<Edge>, std::greater<Edge>> que; for(auto &e : (*this)[0]) que.push(e); std::vector chk(size(), 0); chk[0] = 1; while(!que.empty()) { auto e = que.top(); que.pop(); if(chk[e.to]) continue; res += e.cost; chk[e.to] = 1; for(auto &e : (*this)[e.to]) { que.push(e); } } return res; } //重心 std::vector<int> Centroid() { int n = size(); std::vector<int> centroid, sz(n); std::function<void(int, int)> dfs = [&](int now, int per) { sz[now] = 1; bool is_centroid = true; for(auto &e : (*this)[now]) if(e.to != per) { dfs(e.to, now); sz[now] += sz[e.to]; if(sz[e.to] > n / 2) is_centroid = false; } if(n - sz[now] > n / 2) is_centroid = false; if(is_centroid) centroid.push_back(now); }; return centroid; } //pair{橋(pairの配列),関節点(intの配列)} std::pair<std::vector<std::pair<int, int>>, std::vector<int>> lowlink() { int n = size(), k = 0; std::vector<int> used(n, 0), order(n, 0), low(n, 0), articulation; std::vector<std::pair<int, int>> bridge; std::function<int(int, int, int)> dfs = [&](int idx, int k, int par) { used[idx] = 1; order[idx] = k++; low[idx] = order[idx]; bool is_articulation = false, neko = false; int cnt = 0; for(auto &e : (*this)[idx]) { if(e.to == par and !std::exchange(neko, true)) { continue; } if(!used[e.to]) { ++cnt; k = dfs(e.to, k, idx); low[idx] = std::min(low[idx], low[e.to]); is_articulation |= par >= 0 and low[e.to] >= order[idx]; if(order[idx] < low[e.to]) { auto p = std::minmax(idx, e.to); bridge.emplace_back(p.first, p.second); } } else { low[idx] = std::min(low[idx], order[e.to]); } } is_articulation |= par == -1 and cnt > 1; if(is_articulation) articulation.push_back(idx); return k; }; for(int i = 0; i < n; i++) if(!used[i]) k = dfs(i, k, -1); return std::pair(bridge, articulation); } //根から葉への有向グラフ Graph RootToLeaf(int root = 0) { Graph res(size()); std::vector chk(size(), 0); chk[root] = 1; std::function<void(int)> dfs = [&](int now) { for(auto &e : (*this)[now]) { if(chk[e.to] == 1) continue; chk[e.to] = 1; res.add(now, e.to, e.cost, 1, 0); dfs(e.to); } }; dfs(root); return res; } //葉から根への有向グラフ Graph LeafToRoot(int root = 0) { Graph res(size()); std::vector chk(size(), 0); chk[root] = 1; std::function<void(int)> dfs = [&](int now) { for(auto &e : (*this)[now]) { if(chk[e.to] == 1) continue; chk[e.to] = 1; res.add(e.to, now, e.cost, 1, 0); dfs(e.to); } }; dfs(root); return res; } //辺(from,to)を返す(無向ならu->vとv->u共に入る) std::vector<std::pair<int, int>> getedges() { return edges; } //辺(from,to,cost)を返す(無向ならu->vとv->u共に入る) std::vector<std::tuple<int, int, long long>> getwedges() { std::vector<std::tuple<int, int, long long>> ret; for(int i = 0; i < size(); i++) { for(auto &e : (*this)[i]) ret.emplace_back(i, e.to, e.cost); } return ret; } }; //Strongly Connected Components(強成分連結分解)(Graph Templateと併用) struct SCC { const Graph &g; Graph ng, rg; V<int> compo, order, used; //g:元のグラフ, ret:強連結成分分解後のグラフ SCC(Graph &g, Graph &ret) : g(g), ng(SZ(g)), rg(SZ(g)), compo(SZ(g), -1), used(SZ(g)) { REP(i, SZ(g)) { for(auto &v : g[i]) { ng[i].eb(v.to, 1); rg[v.to].eb(i, 1); } } build(ret); } int operator[](int k) { return compo[k]; } void dfs(int now) { if(used[now]) return; used[now] = true; for(auto &e : ng[now]) dfs(e.to); order.eb(now); } void rdfs(int now, int count) { if(compo[now] != -1) return; compo[now] = count; for(auto &e : rg[now]) rdfs(e.to, count); } void build(Graph &ret) { REP(i, SZ(ng)) dfs(i); reverse(all(order)); int group = 0; for(auto i : order) if(compo[i] == -1) rdfs(i, group), group++; ret.resize(group); REP(i, SZ(g)) { for(auto &e : g[i]) { int s = compo[i], t = compo[e.to]; if(s != t) ret[s].eb(t, 1); } } } }; int main() { INT(n, m); vector res(m, 0); Graph G(n); G.read(m, 0, 1); Graph ret; SCC scc(G, ret); if(ret.size() > 1) dump(-1); if(G.isBiparate().first) dump(-1); V<> ver; int shortest = n + 1; REP(i, n) { vector dist(n, -1); vector prev(n, -1); queue<int> que; que.push(i); dist[i] = 0; while(SZ(que)) { int now = que.front(); que.pop(); for(auto &e : G[now]) { int to = e.to; if(dist[to] == -1) { dist[to] = dist[now] + 1; prev[to] = now; que.push(to); } } } REP(j, n) { if(j == i or dist[j] == -1) continue; for(auto &e : G[j]) { if(e.to == i) { vector tmp(1, i); int cur = j; while(cur != i) tmp.pb(cur), cur = prev[cur]; if(shortest > SZ(tmp)) { shortest = SZ(tmp); ver = tmp; } } } } } reverse(all(ver)); if(SZ(ver) == m) dump(-1); ver.pb(ver[0]); auto E = G.getedges(); map<pii, int> encode; REP(i, SZ(E)) { encode[E[i]] = i; } debug(ver); int tmp = (SZ(ver) - 1) / 2 + 1; debug(tmp); V<pii> chk; REP(i, SZ(ver) - 1) { chk.eb(encode[{ver[i], ver[i + 1]}], SZ(G[ver[i]])); } sort(all(chk), [](pii a, pii b) { return a.second > b.second; }); REP(i, tmp) { res[chk[i].first] = 1; } string ans = ""; REP(i, m) { ans += (res[i] ? 'G' : 'R'); } dump(ans); }