結果
問題 | No.1745 Selfish Spies 2 (à la Princess' Perfectionism) |
ユーザー |
![]() |
提出日時 | 2021-11-14 21:08:41 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 487 ms / 5,000 ms |
コード長 | 15,894 bytes |
コンパイル時間 | 2,947 ms |
コンパイル使用メモリ | 201,000 KB |
実行使用メモリ | 53,360 KB |
最終ジャッジ日時 | 2024-11-30 05:44:37 |
合計ジャッジ時間 | 9,912 ms |
ジャッジサーバーID (参考情報) |
judge2 / judge4 |
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ファイルパターン | 結果 |
---|---|
other | AC * 59 |
ソースコード
#include <algorithm>#include <array>#include <bitset>#include <cassert>#include <chrono>#include <cmath>#include <complex>#include <deque>#include <forward_list>#include <fstream>#include <functional>#include <iomanip>#include <ios>#include <iostream>#include <limits>#include <list>#include <map>#include <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <tuple>#include <type_traits>#include <unordered_map>#include <unordered_set>#include <utility>#include <vector>using namespace std;using lint = long long;using pint = pair<int, int>;using plint = pair<lint, lint>;struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;#define ALL(x) (x).begin(), (x).end()#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)#define REP(i, n) FOR(i,0,n)#define IREP(i, n) IFOR(i,0,n)template <typename T, typename V>void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); }template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); }template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end());return vec; }template <typename T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }template <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; }template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']';return os; }#if __cplusplus >= 201703Ltemplate <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); returnis; }template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }#endiftemplate <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os;}template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ',';os << '}'; return os; }template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os;}template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}';return os; }template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')';return os; }template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp)os << v.first << "=>" << v.second << ','; os << '}'; return os; }#ifdef HITONANODE_LOCALconst string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";#define dbg(x) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET <<endl#define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ <<COLOR_RESET << endl : cerr)#else#define dbg(x) (x)#define dbgif(cond, x) 0#endif// Bipartite matching of undirected bipartite graph (Hopcroft-Karp)// https://ei1333.github.io/luzhiled/snippets/graph/hopcroft-karp.html// Comprexity: O((V + E)sqrtV)// int solve(): enumerate maximum number of matching / return -1 (if graph is not bipartite)struct BipartiteMatching {int V;std::vector<std::vector<int>> to; // Adjacency liststd::vector<int> dist; // dist[i] = (Distance from i'th node)std::vector<int> match; // match[i] = (Partner of i'th node) or -1 (No parter)std::vector<int> used, vv;std::vector<int> color; // color of each node(checking bipartition): 0/1/-1(not determined)BipartiteMatching() = default;BipartiteMatching(int V_) : V(V_), to(V_), match(V_, -1), used(V_), color(V_, -1) {}void add_edge(int u, int v) {assert(u >= 0 and u < V and v >= 0 and v < V and u != v);to[u].push_back(v);to[v].push_back(u);}void _bfs() {dist.assign(V, -1);std::vector<int> q;int lq = 0;for (int i = 0; i < V; i++) {if (!color[i] and !used[i]) q.push_back(i), dist[i] = 0;}while (lq < int(q.size())) {int now = q[lq++];for (auto nxt : to[now]) {int c = match[nxt];if (c >= 0 and dist[c] == -1) q.push_back(c), dist[c] = dist[now] + 1;}}}bool _dfs(int now) {vv[now] = true;for (auto nxt : to[now]) {int c = match[nxt];if (c < 0 or (!vv[c] and dist[c] == dist[now] + 1 and _dfs(c))) {match[nxt] = now, match[now] = nxt;used[now] = true;return true;}}return false;}bool _color_bfs(int root) {color[root] = 0;std::vector<int> q{root};int lq = 0;while (lq < int(q.size())) {int now = q[lq++], c = color[now];for (auto nxt : to[now]) {if (color[nxt] == -1) {color[nxt] = !c, q.push_back(nxt);} else if (color[nxt] == c) {return false;}}}return true;}int solve() {for (int i = 0; i < V; i++) {if (color[i] == -1 and !_color_bfs(i)) return -1;}int ret = 0;while (true) {_bfs();vv.assign(V, false);int flow = 0;for (int i = 0; i < V; i++) {if (!color[i] and !used[i] and _dfs(i)) flow++;}if (!flow) break;ret += flow;}return ret;}template <class OStream> friend OStream &operator<<(OStream &os, const BipartiteMatching &bm) {os << "{N=" << bm.V << ':';for (int i = 0; i < bm.V; i++) {if (bm.match[i] > i) os << '(' << i << '-' << bm.match[i] << "),";}return os << '}';}};// Directed graph library to find strongly connected components (強連結成分分解)// 0-indexed directed graph// Complexity: O(V + E)struct DirectedGraphSCC {int V; // # of Verticesstd::vector<std::vector<int>> to, from;std::vector<int> used; // Only true/falsestd::vector<int> vs;std::vector<int> cmp;int scc_num = -1;DirectedGraphSCC(int V = 0) : V(V), to(V), from(V), cmp(V) {}void _dfs(int v) {used[v] = true;for (auto t : to[v])if (!used[t]) _dfs(t);vs.push_back(v);}void _rdfs(int v, int k) {used[v] = true;cmp[v] = k;for (auto t : from[v])if (!used[t]) _rdfs(t, k);}void add_edge(int from_, int to_) {assert(from_ >= 0 and from_ < V and to_ >= 0 and to_ < V);to[from_].push_back(to_);from[to_].push_back(from_);}// Detect strongly connected components and return # of them.// Also, assign each vertex `v` the scc id `cmp[v]` (0-indexed)int FindStronglyConnectedComponents() {used.assign(V, false);vs.clear();for (int v = 0; v < V; v++)if (!used[v]) _dfs(v);used.assign(V, false);scc_num = 0;for (int i = (int)vs.size() - 1; i >= 0; i--)if (!used[vs[i]]) _rdfs(vs[i], scc_num++);return scc_num;}// Find and output the vertices that form a closed cycle.// output: {v_1, ..., v_C}, where C is the length of cycle,// {} if there's NO cycle (graph is DAG)int _c, _init;std::vector<int> _ret_cycle;bool _dfs_detectcycle(int now, bool b0) {if (now == _init and b0) return true;for (auto nxt : to[now])if (cmp[nxt] == _c and !used[nxt]) {_ret_cycle.emplace_back(nxt), used[nxt] = 1;if (_dfs_detectcycle(nxt, true)) return true;_ret_cycle.pop_back();}return false;}std::vector<int> DetectCycle() {int ns = FindStronglyConnectedComponents();if (ns == V) return {};std::vector<int> cnt(ns);for (auto x : cmp) cnt[x]++;_c = std::find_if(cnt.begin(), cnt.end(), [](int x) { return x > 1; }) - cnt.begin();_init = std::find(cmp.begin(), cmp.end(), _c) - cmp.begin();used.assign(V, false);_ret_cycle.clear();_dfs_detectcycle(_init, false);return _ret_cycle;}// After calling `FindStronglyConnectedComponents()`, generate a new graph by uniting all vertices// belonging to the same component(The resultant graph is DAG).DirectedGraphSCC GenerateTopologicalGraph() {DirectedGraphSCC newgraph(scc_num);for (int s = 0; s < V; s++)for (auto t : to[s]) {if (cmp[s] != cmp[t]) newgraph.add_edge(cmp[s], cmp[t]);}return newgraph;}};// 2-SAT solver: Find a solution for `(Ai v Aj) ^ (Ak v Al) ^ ... = true`// - `nb_sat_vars`: Number of variables// - Considering a graph with `2 * nb_sat_vars` vertices// - Vertices [0, nb_sat_vars) means `Ai`// - vertices [nb_sat_vars, 2 * nb_sat_vars) means `not Ai`struct SATSolver : DirectedGraphSCC {int nb_sat_vars;std::vector<int> solution;SATSolver(int nb_variables = 0) : DirectedGraphSCC(nb_variables * 2), nb_sat_vars(nb_variables), solution(nb_sat_vars) {}void add_x_or_y_constraint(bool is_x_true, int x, bool is_y_true, int y) {assert(x >= 0 and x < nb_sat_vars);assert(y >= 0 and y < nb_sat_vars);if (!is_x_true) x += nb_sat_vars;if (!is_y_true) y += nb_sat_vars;add_edge((x + nb_sat_vars) % (nb_sat_vars * 2), y);add_edge((y + nb_sat_vars) % (nb_sat_vars * 2), x);}// Solve the 2-SAT problem. If no solution exists, return `false`.// Otherwise, dump one solution to `solution` and return `true`.bool run() {FindStronglyConnectedComponents();for (int i = 0; i < nb_sat_vars; i++) {if (cmp[i] == cmp[i + nb_sat_vars]) return false;solution[i] = cmp[i] > cmp[i + nb_sat_vars];}return true;}};// Dulmage–Mendelsohn (DM) decomposition (DM 分解)// return: [(W+0, W-0), (W+1,W-1),...,(W+(k+1), W-(k+1))]// : sequence of pair (left vetrices, right vertices)// - |W+0| < |W-0| or both empty// - |W+i| = |W-i| (i = 1, ..., k)// - |W+(k+1)| > |W-(k+1)| or both empty// - W is topologically sorted// Example:// (2, 2, [(0,0), (0,1), (1,0)]) => [([],[]),([0,],[1,]),([1,],[0,]),([],[]),]// Complexity: O(N + (N + M) sqrt(N))// Verified: https://yukicoder.me/problems/no/1615std::vector<std::pair<std::vector<int>, std::vector<int>>>dulmage_mendelsohn(int L, int R, const std::vector<std::pair<int, int>> &edges) {for (auto p : edges) {assert(0 <= p.first and p.first < L);assert(0 <= p.second and p.second < R);}BipartiteMatching bm(L + R);for (auto p : edges) bm.add_edge(p.first, L + p.second);bm.solve();DirectedGraphSCC scc(L + R);for (auto p : edges) scc.add_edge(p.first, L + p.second);for (int l = 0; l < L; ++l) {if (bm.match[l] >= L) scc.add_edge(bm.match[l], l);}int nscc = scc.FindStronglyConnectedComponents();std::vector<int> cmp_map(nscc, -2);std::vector<int> vis(L + R);std::vector<int> st;for (int c = 0; c < 2; ++c) {std::vector<std::vector<int>> to(L + R);auto color = [&L](int x) { return x >= L; };for (auto p : edges) {int u = p.first, v = L + p.second;if (color(u) != c) std::swap(u, v);to[u].push_back(v);if (bm.match[u] == v) to[v].push_back(u);}for (int i = 0; i < L + R; ++i) {if (bm.match[i] >= 0 or color(i) != c or vis[i]) continue;vis[i] = 1, st = {i};while (!st.empty()) {int now = st.back();cmp_map[scc.cmp[now]] = c - 1;st.pop_back();for (int nxt : to[now]) {if (!vis[nxt]) vis[nxt] = 1, st.push_back(nxt);}}}}int nset = 1;for (int n = 0; n < nscc; ++n) {if (cmp_map[n] == -2) cmp_map[n] = nset++;}for (auto &x : cmp_map) {if (x == -1) x = nset;}nset++;std::vector<std::pair<std::vector<int>, std::vector<int>>> groups(nset);for (int l = 0; l < L; ++l) {if (bm.match[l] < 0) continue;int c = cmp_map[scc.cmp[l]];groups[c].first.push_back(l);groups[c].second.push_back(bm.match[l] - L);}for (int l = 0; l < L; ++l) {if (bm.match[l] >= 0) continue;int c = cmp_map[scc.cmp[l]];groups[c].first.push_back(l);}for (int r = 0; r < R; ++r) {if (bm.match[L + r] >= 0) continue;int c = cmp_map[scc.cmp[L + r]];groups[c].second.push_back(r);}return groups;}int main() {int N, M, L;cin >> N >> M >> L;vector<pint> edges(L);for (auto &[s, t] : edges) {cin >> s >> t;s--, t--;}dbg(edges);auto dm = dulmage_mendelsohn(N, M, edges);dbg(dm);vector<int> grp1(N, -1), grp2(M, -1);REP(g, dm.size()) {for (auto i : dm[g].first) grp1[i] = g;for (auto i : dm[g].second) grp2[i] = g;}dbg(grp1);dbg(grp2);for (auto [s, t] : edges) {if (grp1[s] == grp2[t]) puts("Yes");else puts("No");}}