結果
| 問題 | No.1370 置換門松列 |
| ユーザー |
 hitonanode
|
| 提出日時 | 2021-01-29 21:48:54 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 36 ms / 2,000 ms |
| コード長 | 9,225 bytes |
| コンパイル時間 | 1,966 ms |
| コンパイル使用メモリ | 205,696 KB |
| 最終ジャッジ日時 | 2025-01-18 09:08:30 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 5 |
| other | AC * 25 |
ソースコード
#include <bits/stdc++.h>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) { if (m < q) {m = q; return true;} else return false; }template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return 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> 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) { 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#else#define dbg(x) (x)#endif// 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;}};template <typename T> bool kado(T a, T b, T c) {if (a == b or b == c or a == c) return false;if (a < b and b > c) return true;if (a > b and b < c) return true;return false;}int main() {int N, M;cin >> N >> M;vector<int> A(N);cin >> A;for (auto &a : A) a--;DirectedGraphSCC graph(M);REP(i, N - 1) {if (i % 2 == 0) graph.add_edge(A[i], A[i + 1]);else graph.add_edge(A[i + 1], A[i]);}int s = graph.FindStronglyConnectedComponents();if (s < M) {puts("No");return 0;}dbg(A);dbg(graph.cmp);FOR(i, 1, N - 1) if (!kado(graph.cmp[A[i - 1]], graph.cmp[A[i]], graph.cmp[A[i + 1]])) {puts("No");return 0;}cout << "Yes\n";for (auto x : graph.cmp) cout << x + 1 << '\n';}