結果
| 問題 | No.3031 曲面の向き付け |
| ユーザー |
 iilj
|
| 提出日時 | 2025-02-21 23:26:13 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 918 ms / 2,000 ms |
| コード長 | 15,949 bytes |
| コンパイル時間 | 3,017 ms |
| コンパイル使用メモリ | 198,832 KB |
| 実行使用メモリ | 87,580 KB |
| 最終ジャッジ日時 | 2025-02-21 23:26:35 |
| 合計ジャッジ時間 | 14,448 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 |
|---|---|
| sample | AC * 4 |
| other | AC * 29 |
ソースコード
/* #region Head */// #include <bits/stdc++.h>#include <algorithm>#include <array>#include <bitset>#include <cassert> // assert.h#include <cmath> // math.h#include <cstring>#include <ctime>#include <deque>#include <fstream>#include <functional>#include <iomanip>#include <iostream>#include <list>#include <map>#include <memory>#include <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <unordered_map>#include <unordered_set>#include <vector>using namespace std;using ll = long long;using ull = unsigned long long;using ld = long double;using pll = pair<ll, ll>;template <class T> using vc = vector<T>;template <class T> using vvc = vc<vc<T>>;using vll = vc<ll>;using vvll = vvc<ll>;using vld = vc<ld>;using vvld = vvc<ld>;using vs = vc<string>;using vvs = vvc<string>;template <class T, class U> using um = unordered_map<T, U>;template <class T> using pq = priority_queue<T>;template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;template <class T> using us = unordered_set<T>;#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)#define ALL(x) begin(x), end(x)#define SIZE(x) ((ll)(x).size())#define ISIZE(x) ((int)(x).size())#define PERM(c) \sort(ALL(c)); \for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))#define UNIQ(v) v.erase(unique(ALL(v)), v.end());#define CEIL(a, b) (((a) + (b)-1) / (b))#define endl '\n'constexpr ll INF = 1'010'000'000'000'000'017LL;constexpr int IINF = 1'000'000'007LL;constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7// constexpr ll MOD = 998244353;constexpr ld EPS = 1e-12;constexpr ld PI = 3.14159265358979323846;// 前方宣言template <typename T> istream &operator>>(istream &is, vc<T> &vec);template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec);template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec);template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr);template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr);template <typename T, size_t _Nm> ostream &operator>>(ostream &os, const array<T, _Nm> &arr);template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var);template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var);template <class T> ostream &out_iter(ostream &os, const T &map_var);template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var);template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var);template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var);template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var);template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var);template <typename T> ostream &operator<<(ostream &os, const queue<T> &queue_var);template <typename T> ostream &operator<<(ostream &os, const stack<T> &stk_var);template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力for (T &x : vec)is >> x;return is;}template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)os << "{";REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");os << "}";return os;}template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");return os;}template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力REP(i, 0, SIZE(arr)) is >> arr[i];return is;}template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)os << "{";REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");os << "}";return os;}template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力is >> pair_var.first >> pair_var.second;return is;}template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力os << "(" << pair_var.first << ", " << pair_var.second << ")";return os;}// map, um, set, us 出力template <class T> ostream &out_iter(ostream &os, const T &map_var) {os << "{";REPI(itr, map_var) {os << *itr;auto itrcp = itr;if (++itrcp != map_var.end()) os << ", ";}return os << "}";}template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {return out_iter(os, map_var);}template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {os << "{";REPI(itr, map_var) {auto [key, value] = *itr;os << "(" << key << ", " << value << ")";auto itrcp = itr;if (++itrcp != map_var.end()) os << ", ";}os << "}";return os;}template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {pq<T> pq_cp(pq_var);os << "{";if (!pq_cp.empty()) {os << pq_cp.top(), pq_cp.pop();while (!pq_cp.empty())os << ", " << pq_cp.top(), pq_cp.pop();}return os << "}";}// tuple 出力template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {if constexpr (N < std::tuple_size_v<tuple<Args...>>) {os << get<N>(a);if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {os << ' ';} else if constexpr (end_line) {os << '\n';}return operator<< <N + 1, end_line>(os, a);}return os;}template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<< <0, true>(std::cout, a); }void pprint() { std::cout << endl; }template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {std::cout << head;if (sizeof...(Tail) > 0) std::cout << ' ';pprint(move(tail)...);}// dump#define DUMPOUT cerrvoid dump_func() { DUMPOUT << endl; }template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {DUMPOUT << head;if (sizeof...(Tail) > 0) DUMPOUT << ", ";dump_func(move(tail)...);}// chmax (更新「される」かもしれない値が前)template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {if (comp(xmax, x)) {xmax = x;return true;}return false;}// chmin (更新「される」かもしれない値が前)template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {if (comp(x, xmin)) {xmin = x;return true;}return false;}// ローカル用#ifndef ONLINE_JUDGE#define DEBUG_#endif#ifndef MYLOCAL#undef DEBUG_#endif#ifdef DEBUG_#define DEB#define dump(...) \DUMPOUT << " " << string(#__VA_ARGS__) << ": " \<< "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \<< " ", \dump_func(__VA_ARGS__)#else#define DEB if (false)#define dump(...)#endif#define VAR(type, ...) \type __VA_ARGS__; \assert((std::cin >> __VA_ARGS__));template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }struct AtCoderInitialize {static constexpr int IOS_PREC = 15;static constexpr bool AUTOFLUSH = false;AtCoderInitialize() {ios_base::sync_with_stdio(false), std::cin.tie(nullptr), std::cout.tie(nullptr);std::cout << fixed << setprecision(IOS_PREC);if (AUTOFLUSH) std::cout << unitbuf;}} ATCODER_INITIALIZE;void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; }void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; }template <typename T> constexpr void operator--(vc<T> &v, int) noexcept {for (int i = 0; i < ISIZE(v); ++i)v[i]--;}template <typename T> constexpr void operator++(vc<T> &v, int) noexcept {for (int i = 0; i < ISIZE(v); ++i)v[i]++;}/* #endregion */// #include <atcoder/all>// using namespace atcoder;/* #region Graph */// エッジ（本来エッジは双方向だが，ここでは単方向で管理）template <class weight_t = int, class flow_t = int> struct Edge {int src; // エッジ始点となる頂点int dst; // エッジ終点となる頂点weight_t weight; // 重みflow_t cap;Edge() : src(0), dst(0), weight(0) {}Edge(int src, int dst, weight_t weight) : src(src), dst(dst), weight(weight) {}Edge(int src, int dst, weight_t weight, flow_t cap) : src(src), dst(dst), weight(weight), cap(cap) {}// Edge 標準出力friend ostream &operator<<(ostream &os, Edge &edge) {os << "(" << edge.src << " -> " << edge.dst << ", " << edge.weight << ")";return os;}};// 同じ頂点を始点とするエッジ集合template <class weight_t = int, class flow_t = int> class Node : public vc<Edge<weight_t, flow_t>> {public:int idx;Node() : vc<Edge<weight_t, flow_t>>() {}// void add(int a, int b, weight_t w, flow_t cap) { this->emplace_back(a, b, w, cap); };};// graph[i] := 頂点 i を始点とするエッジ集合template <class weight_t = int, class flow_t = int> class Graph : public vc<Node<weight_t, flow_t>> {public:Graph() : vc<Node<weight_t, flow_t>>() {}Graph(int n) : vc<Node<weight_t, flow_t>>(n) { REP(i, 0, n)(*this)[i].idx = i; }/** 単方向 */void add_arc(int a, int b, weight_t w = 1, flow_t cap = 1) { (*this)[a].emplace_back(a, b, w, cap); }/** 双方向 */void add_edge(int a, int b, weight_t w = 1, flow_t cap = 1) { add_arc(a, b, w, cap), add_arc(b, a, w, cap); }/** ノード追加 */int add_node() {int idx = (int)this->size();this->emplace_back();Node<weight_t, flow_t> &node = this->back();node.idx = idx;return idx;}};// using Array = vc<Weight>;// using Matrix = vc<Array>;/* #endregion *//* #region scc */// 強連結成分分解template <class weight_t, class flow_t> vll scc(const Graph<weight_t, flow_t> &g) {ll n = SIZE(g); // ノード数Graph<weight_t, flow_t> rg(n); // 逆向きのグラフfor (const Node<weight_t, flow_t> &es : g)for (Edge<weight_t, flow_t> e : es) {swap(e.src, e.dst);rg[e.src].emplace_back(e);}vll order;order.reserve(n);{ // dfs 1回目vc<bool> visited(n), added(n);REP(i, 0, n) {if (visited[i]) continue;stack<ll> stk;stk.push(i);while (!stk.empty()) {ll cur = stk.top();visited[cur] = true;bool pushed = false;for (const Edge<weight_t, flow_t> &e : g[cur])if (!visited[e.dst]) stk.push(e.dst), pushed = true;if (!pushed) { // カレントノードからは未訪問ノードへ到達できないll t = stk.top();stk.pop(); // 未訪問ノードへ到達できないノードは除いていくif (!added[t]) added[t] = true, order.push_back(t);}}}reverse(ALL(order));}vll ret(n, -1);{ // dfs 2回目ll groupnum = 0;for (ll &v : order) {if (ret[v] != -1) continue;stack<ll> stk;stk.push(v);while (!stk.empty()) {ll cur = stk.top();stk.pop(), ret[cur] = groupnum;for (Edge<weight_t, flow_t> &e : rg[cur])if (ret[e.dst] == -1) stk.push(e.dst);}++groupnum;}}return ret;}/* #endregion *//* #region TwoSat */// 2-SATstruct TwoSat {using G = Graph<int, int>;int _var_cnt; // 命題論理式に含まれる変数の個数int _sz; // グラフのサイズG graph; // graph[i] <-> not(graph[i+_var_cnt])vc<int> result; // 結果格納用，外からアクセスする前提// var_cnt: 変数の個数，P と ¬P あわせて1個．TwoSat(int var_cnt) : _var_cnt(var_cnt), _sz(var_cnt * 2), graph(_sz), result(var_cnt) {}// (x ∨ y) の形の節を追加する．¬x は x+_var_cnt に変えておく．void add_arcs(int x, int y) {graph.add_arc((x + _var_cnt) % _sz, y); // ¬x -> ygraph.add_arc((y + _var_cnt) % _sz, x); // ¬y -> x}// 充足可能性を判定する．不能なら false. 可能なら result に変数の T/F を入れる．bool sat() {vll groups = scc(graph);// dump(groups);REP(i, 0, _var_cnt) if (groups[i] == groups[i + _var_cnt]) return false;REP(i, 0, _var_cnt) result[i] = groups[i] > groups[i + _var_cnt];return true;}};/* #endregion */// Problemvoid solve() {VAR(int, m);vc<int> a(m), b(m), c(m);REP(i, 0, m) cin >> a[i], b[i], c[i];const auto inv = [&m](int p) { return (m + p) % (2 * m); };map<pair<int, int>, vc<int>> mp;REP(i, 0, m) {mp[{a[i], b[i]}].push_back(i);mp[{b[i], c[i]}].push_back(i);mp[{c[i], a[i]}].push_back(i);const int inv_i = inv(i);mp[{a[i], c[i]}].push_back(inv_i);mp[{c[i], b[i]}].push_back(inv_i);mp[{b[i], a[i]}].push_back(inv_i);}TwoSat ts(m);for (const auto &[k, v] : mp) {if (SIZE(v) <= 1) continue;if (SIZE(v) > 2) {YN(false);return;}ts.add_arcs(v[0], v[1]);}YN(ts.sat());}// entry pointint main() {solve();return 0;}