제출 #791292

#제출 시각아이디문제언어결과실행 시간메모리
791292skittles1412Split the Attractions (IOI19_split)C++17
100 / 100
100 ms27680 KiB
#include "bits/extc++.h" using namespace std; template <typename T, typename... U> void dbgh(const T& t, const U&... u) { cerr << t; ((cerr << " | " << u), ...); cerr << endl; } #ifdef DEBUG #define dbg(...) \ cerr << "L" << __LINE__ << " [" << #__VA_ARGS__ << "]: "; \ dbgh(__VA_ARGS__) #else #define dbg(...) #define cerr \ if (false) \ cerr #endif #define endl "\n" #define long int64_t #define sz(x) int(std::size(x)) struct DSU { vector<int> p; DSU(int n) : p(n, -1) {} int find(int u) { return p[u] < 0 ? u : (p[u] = find(p[u])); } bool merge(int u, int v) { u = find(u); v = find(v); if (u == v) { return false; } if (p[u] < p[v]) { swap(u, v); } p[v] += p[u]; p[u] = v; return true; } }; vector<pair<int, int>> spanning_tree(int n, const vector<pair<int, int>>& edges) { DSU dsu(n); vector<pair<int, int>> ans; for (auto& [u, v] : edges) { if (dsu.merge(u, v)) { ans.emplace_back(u, v); } } return ans; } struct Centroid { int n, cu; vector<int> siz; vector<vector<int>> graph, comps; Centroid(int n, const vector<pair<int, int>>& edges) : n(n), siz(n), graph(n) { for (auto& [u, v] : edges) { graph[u].push_back(v); graph[v].push_back(u); } pdfs(0, -1); cu = 0; while (true) { pair<int, int> opt {-1, -1}; for (auto& v : graph[cu]) { opt = max(opt, {siz[v], v}); } if (opt.first <= n / 2) { break; } int nu = opt.second; siz[cu] -= siz[nu]; siz[nu] += siz[cu]; cu = nu; } for (auto& v : graph[cu]) { comps.emplace_back(); dfs(v, cu, comps.back()); dbg(v, siz[v], sz(comps.back())); } } void pdfs(int u, int p) { siz[u] = 1; for (auto& v : graph[u]) { if (v == p) { continue; } pdfs(v, u); siz[u] += siz[v]; } } void dfs(int u, int p, vector<int>& out) { out.push_back(u); for (auto& v : graph[u]) { if (v == p) { continue; } dfs(v, u, out); } } }; struct Solver1 { bool found = false; int n, kv, csum; vector<char> vis; vector<int> arr, st; vector<vector<int>> graph; Solver1(int n, int kv, const vector<int>& arr, const vector<pair<int, int>>& edges) : n(n), kv(kv), vis(n), arr(arr), graph(n) { assert(*max_element(begin(arr), end(arr)) < kv); for (auto& [u, v] : edges) { graph[u].push_back(v); graph[v].push_back(u); } for (int i = 0; i < n && !found; i++) { if (vis[i]) { continue; } st.clear(); csum = 0; dfs(i); found |= csum >= kv; } } void dfs(int u) { if (found || vis[u]) { return; } else if (csum >= kv) { assert(csum <= 2 * kv - 2); found = true; return; } vis[u] = true; st.push_back(u); csum += arr[u]; for (auto& v : graph[u]) { dfs(v); } } }; struct Solver2 { int n, kv; vector<char> vis; vector<int> st; vector<vector<int>> graph; Solver2(int n, int kv, const vector<int>& nodes, const vector<pair<int, int>>& edges) : n(n), kv(kv), vis(n), graph(n) { bool inode[n] {}; for (auto& a : nodes) { inode[a] = true; } assert(kv <= n); for (auto& [u, v] : edges) { if (!inode[u] || !inode[v]) { continue; } graph[u].push_back(v); graph[v].push_back(u); } dfs(nodes[0]); assert(sz(st) == kv); } void dfs(int u) { if (vis[u] || sz(st) == kv) { return; } vis[u] = true; st.push_back(u); for (auto& v : graph[u]) { dfs(v); } } }; vector<int> find_split(int n, int kv1, int kv2, int kv3, vector<int> edges_u, vector<int> edges_v) { int m = sz(edges_u); vector<pair<int, int>> edges(m); for (int i = 0; i < m; i++) { edges[i] = {edges_u[i], edges_v[i]}; } array<int, 3> ikv {kv1, kv2, kv3}; { array<int, 3> ckv {kv1, kv2, kv3}; sort(begin(ckv), end(ckv)); kv1 = ckv[0]; kv2 = ckv[1]; kv3 = ckv[2]; } auto repermute = [&](vector<int> arr) -> vector<int> { int cnt[3] {}; for (auto& a : arr) { cnt[a - 1]++; } int perm[3]; iota(begin(perm), end(perm), 0); do { bool ok = true; for (int i = 0; i < 3; i++) { ok &= ikv[perm[i]] == cnt[i]; } if (!ok) { continue; } for (auto& a : arr) { a = perm[a - 1] + 1; } return arr; } while (next_permutation(begin(perm), end(perm))); assert(false); }; dbg(kv1, kv2, kv3); Centroid centroid(n, spanning_tree(n, edges)); auto& comps = centroid.comps; int i_comp[n]; i_comp[centroid.cu] = -1; for (int i = 0; i < sz(comps); i++) { for (auto& a : comps[i]) { i_comp[a] = i; } } auto not_nodes = [&](const vector<int>& arr) -> vector<int> { bool vis[n] {}; for (auto& a : arr) { vis[a] = true; } vector<int> ans; for (int i = 0; i < n; i++) { if (!vis[i]) { ans.push_back(i); } } return ans; }; auto answer = [&](const vector<int>& arra, const vector<int>& arrb) -> vector<int> { dbg(sz(arra), sz(arrb)); assert(kv1 <= sz(arra) && kv2 <= sz(arrb)); vector<int> ans(n, 3); auto go = [&](const vector<int>& nodes, int kv, int val) -> void { auto c_comp = Solver2(n, kv, nodes, edges).st; for (auto& a : c_comp) { ans[a] = val; } }; go(arra, kv1, 1); go(arrb, kv2, 2); return repermute(ans); }; for (int i = 0; i < sz(comps); i++) { if (sz(comps[i]) < kv1) { continue; } auto arra = comps[i]; dbg("centroid quick"); return answer(arra, not_nodes(arra)); } vector<int> c_sizes; for (auto& a : comps) { c_sizes.push_back(sz(a)); } vector<pair<int, int>> c_edges; for (auto& [u, v] : edges) { if (u == centroid.cu || v == centroid.cu) { continue; } dbg(i_comp[u], i_comp[v]); c_edges.emplace_back(i_comp[u], i_comp[v]); } Solver1 s1(sz(comps), kv1, c_sizes, c_edges); if (!s1.found) { // assert(false); return vector<int>(n); } vector<int> arra; for (auto& a : s1.st) { arra.insert(arra.end(), begin(comps[a]), end(comps[a])); } return answer(arra, not_nodes(arra)); }
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