Editorial for Hai Bộ Bài
Remember to use this editorial only when stuck, and not to copy-paste code from it. Please be respectful to the problem author and editorialist.
Submitting an official solution before solving the problem yourself is a bannable offence.
Submitting an official solution before solving the problem yourself is a bannable offence.
#include <bits/stdc++.h> #include <algorithm> #include <cassert> #include <limits> #include <queue> #include <vector> #include <vector> namespace atcoder { namespace internal { template <class T> struct simple_queue { std::vector<T> payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder namespace atcoder { template <class Cap> struct mf_graph { public: mf_graph() : _n(0) {} explicit mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector<edge> edges() { int m = int(pos.size()); std::vector<edge> result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits<Cap>::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector<int> level(_n), iter(_n); internal::simple_queue<int> que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) return res; } level[v] = _n; return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector<bool> min_cut(int s) { std::vector<bool> visited(_n); internal::simple_queue<int> que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector<std::pair<int, int>> pos; std::vector<std::vector<_edge>> g; }; } // namespace atcoder using namespace std; using namespace atcoder; struct dsu { vector<int> par, fre; dsu(int n) : par(n, -1), fre(n, 1) {} int trace(int u) { return par[u] < 0 ? u : par[u] = trace(par[u]); } int connect(int u, int v) { if ((u = trace(u)) == (v = trace(v))) { return u; } if (par[u] > par[v]) { swap(par[u], par[v]); } par[u] += par[v]; par[v] = u; fre[u] += fre[v]; return u; } int& operator[](int u) { return fre[u]; } }; int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int t; cin >> t; while (t--) { int n, m; cin >> n >> m; vector<pair<int, int>> a(n), b(m); for (int i = 0; i < n; i++) { cin >> a[i].first >> a[i].second; a[i].first--; a[i].second--; } for (int i = 0; i < m; i++) { cin >> b[i].first >> b[i].second; b[i].first--; b[i].second--; } int value_set = 2 * (n + m); auto gen_con_components = [&](vector<pair<int, int>>& a, vector<int>& com) { dsu dsu(value_set); for (auto [u, v] : a) { int p = dsu.connect(u, v); dsu[p]--; } for (int i = 0; i < value_set; i++) { int p = dsu.trace(i); if (dsu[p] < 0) { return false; } else if (dsu[p] > 0) { com[i] = p; } } return true; }; vector<int> com_a(value_set, -1), com_b(value_set, -1); if (!gen_con_components(a, com_a) || !gen_con_components(b, com_b)) { cout << "-1\n"; continue; } mf_graph<int> remove_values(2 * value_set + 2); vector<int> rep_edg(value_set, -1); auto left_side = [&](int u) { return u + 2; }; auto right_side = [&](int u) { return u + value_set + 2; }; int src = 0, snk = 1; for (int i = 0; i < value_set; i++) { remove_values.add_edge(src, left_side(i), 1); remove_values.add_edge(right_side(i), snk, 1); if (com_a[i] != -1 && com_b[i] != -1) { rep_edg[i] = remove_values.add_edge(left_side(com_a[i]), right_side(com_b[i]), 1); } } cout << value_set - remove_values.flow(src, snk) << '\n'; vector<bool> ok(value_set, true); for (int v = 0; v < value_set; v++) { if (rep_edg[v] != -1 && remove_values.get_edge(rep_edg[v]).flow == 1) { ok[v] = false; } } auto construct = [&](vector<pair<int, int>>& a) { int n = a.size(); vector<pair<int, int>> choice(n); mf_graph<int> mf(n + value_set + 2); int src = 0, snk = 1; auto card = [&](int i) { return 2 + i; }; auto value = [&](int v) { return 2 + n + v; }; for (int i = 0; i < n; i++) { auto [l, r] = a[i]; mf.add_edge(src, card(i), 1); int el = mf.add_edge(card(i), value(l), 1); int er = mf.add_edge(card(i), value(r), 1); choice[i] = {el, er}; } for (int v = 0; v < value_set; v++) { if (ok[v]) { mf.add_edge(value(v), snk, 1); } } assert(mf.flow(src, snk) == n); for (int i = 0; i < n; i++) { auto [l, r] = a[i]; auto [el, er] = choice[i]; int val = mf.get_edge(el).flow == 1 ? l : r; cout << val + 1 << " \n"[i + 1 == n]; } }; construct(a); construct(b); } }
Comments