#722365 (C++17) No.1777 万華鏡美術館

• 問題: No.1777 万華鏡美術館
• ユーザー: NyaanNyaan
• 提出日時: 2021-12-06 15:02:39
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 36 ms / 3,153 ms
• コード長: 20,401 bytes
• コンパイル時間: 4,886 ms
• コンパイル使用メモリ: 295,360 KB
• 実行使用メモリ: 6,516 KB
• 最終ジャッジ日時: 2023-09-22 03:35:18
• 合計ジャッジ時間: 5,288 ms
• ジャッジサーバーID （参考情報）: judge12 / judge14

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	2 ms; 4,380 KB
testcase_01	AC	2 ms; 4,380 KB
testcase_02	AC	2 ms; 4,376 KB
testcase_03	AC	2 ms; 4,380 KB
testcase_04	AC	36 ms; 4,692 KB
testcase_05	AC	6 ms; 4,380 KB
testcase_06	AC	8 ms; 4,856 KB
testcase_07	AC	10 ms; 5,248 KB
testcase_08	AC	28 ms; 5,260 KB
testcase_09	AC	18 ms; 5,108 KB
testcase_10	AC	2 ms; 4,380 KB
testcase_11	AC	19 ms; 6,516 KB
testcase_12	AC	2 ms; 4,376 KB

ソースコード

/**
 *  date : 2021-12-06 15:02:34
 */

#define NDEBUG
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  T &x() { return first; }
  const T &x() const { return first; }
  U &y() { return second; }
  const U &y() const { return second; }

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }

  P operator*(const P &r) const { return P(*this) *= r; }

  P operator*(int r) const { return {first * r, second * r}; }

  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

}  // namespace Nyaan

// bit operation
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan

// inout
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &... u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &... u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

void outr() {}
template <typename T, class... U, char sep = ' '>
void outr(const T &t, const U &... u) {
  cout << t;
  outr(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan

// debug
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

// macro
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }

//

struct UnionFind {
  vector<int> data;
  UnionFind(int N) : data(N, -1) {}

  int find(int k) { return data[k] < 0 ? k : data[k] = find(data[k]); }

  int unite(int x, int y) {
    if ((x = find(x)) == (y = find(y))) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  // f ... merge function
  template<typename F>
  int unite(int x, int y,const F &f) {
    if ((x = find(x)) == (y = find(y))) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    f(x, y);
    return true;
  }

  int size(int k) { return -data[find(k)]; }

  int same(int x, int y) { return find(x) == find(y); }
};

/**
 * @brief Union Find(Disjoint Set Union)
 * @docs docs/data-structure/union-find.md
 */


template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}
using namespace Nyaan;

// https://github.com/not522/CompetitiveProgramming/blob/master/include/math/sat.hpp
class SatSolver {
 private:
  vector<vector<pair<int, bool>>> cl;
  map<pair<int, bool>, vector<int>> w;
  vector<int> reason, level, que, activity;
  int n, qi;

  void enqueue(int v, bool a, int r = -1) {
    assigns[v] = a;
    reason[v] = r;
    level[v] = (que.empty() ? 1 : level[que.back()]);
    que.emplace_back(v);
  }

  void add(const vector<pair<int, bool>> &clause) {
    for (auto l : clause) {
      w[l].emplace_back(cl.size());
    }
    cl.emplace_back(clause);
  }

  void analyze(int confl) {
    int i = que.size(), lv = 1;
    unordered_set<int> used;
    vector<pair<int, bool>> learnt;
    for (int cnt = 0; cnt || used.empty(); --cnt) {
      for (auto q : cl[confl]) {
        if (!used.emplace(q.first).second) {
          continue;
        }
        activity[q.first] += 1e5;
        if (level[q.first] == level[que.back()]) {
          ++cnt;
        } else {
          learnt.emplace_back(q);
          lv = max(lv, level[q.first]);
        }
      }
      while (!used.count(que[--i])) {
        ;
      }
      confl = reason[que[i]];
    }
    learnt.emplace_back(que[i], !assigns[que[i]]);
    for (; !que.empty() && level[que.back()] > lv; que.pop_back()) {
      level[que.back()] = 0;
    }
    qi = que.size();
    enqueue(learnt.back().first, learnt.back().second, cl.size());
    add(learnt);
  }

  int propagate() {
    for (; qi < int(que.size()); ++qi) {
      for (int cr : w[make_pair(que[qi], !assigns[que[qi]])]) {
        int cnt = 0;
        for (auto &lit : cl[cr]) {
          if (level[lit.first] == 0) {
            activity[lit.first] += 1e3;
            swap(lit, cl[cr][0]);
            ++cnt;
          } else if (assigns[lit.first] == lit.second) {
            swap(lit, cl[cr][0]);
            cnt = -1;
            break;
          }
        }
        if (cnt == 0) {
          return cr;
        }
        if (cnt == 1) {
          enqueue(cl[cr][0].first, cl[cr][0].second, cr);
        }
      }
    }
    return -1;
  }

 public:
  vector<bool> assigns;

  SatSolver(int _n, const vector<vector<pair<int, bool>>> &clauses)
      : reason(_n), level(_n), activity(_n), n(_n), qi(0), assigns(_n) {
    for (const auto &clause : clauses) {
      add(clause);
    }
  }

  bool solve() {
    while (true) {
      int confl = propagate();
      if (confl != -1) {
        if (level[que.back()] == 1u) {
          return false;
        }
        for (auto &a : activity) {
          a /= 1.05;
        }
        analyze(confl);
      } else {
        int k = -1;
        for (int i = 0; i < n; ++i) {
          if (level[i] == 0 && (k == -1 || activity[k] < activity[i])) {
            k = i;
          }
        }
        if (k == -1) {
          return true;
        }
        enqueue(k, assigns[k]);
        ++level[k];
      }
    }
  }
};

struct Plane {
  vector<int> nodes;
  int index;
  static int all_index;

  Plane() : index(-1) {}
  bool in(int u) const { return find(all(nodes), u) != end(nodes); }
  bool in(int u, int v) const { return in(u) and in(v); }
  bool edge_in(int u, int v) const {
    if (u > v) swap(u, v);
    auto itu = find(all(nodes), u);
    auto itv = find(all(nodes), v);
    if (itu == end(nodes) or itv == end(nodes)) return false;
    if (itu + 1 == itv) return true;
    if (itv + 1 == end(nodes) and itu == begin(nodes)) return true;
    return false;
  }
  // 破壊的
  Plane split(int u, int v) {
    assert(in(u, v) and !edge_in(u, v));
    Plane chd;
    chd.set_index();
    if (u > v) swap(u, v);
    auto itl = find(all(nodes), u);
    auto itr = find(all(nodes), v);
    chd.nodes = {itl, itr + 1};
    nodes.erase(itl + 1, itr);
    return chd;
  }
  void set_index() { index = all_index++; }

  friend ostream &operator<<(ostream &os, const Plane &p) {
    os << endl;
    os << "index : " << p.index << endl;
    os << "nodes : " << p.nodes << endl;
    os << endl;
    return os;
  }
};
int Plane::all_index = 0;

void Nyaan::solve() {
  inl(N, M);
  auto g = graph(N, M);

  // 外周
  Plane soto;
  soto.set_index();
  Plane naka;
  naka.set_index();

  {
    vi init(N);
    iota(all(init), 0);
    soto.nodes = naka.nodes = init;
  }

  vector<Plane> ps;
  ps.push_back(naka);

  rep(i, N) each(j, g[i]) {
    if (i > j) continue;
    each(p, ps) {
      if (p.in(i, j)) {
        auto ch = p.split(i, j);
        ps.push_back(ch);
        break;
      }
    }
  }

  vp pg_es;
  auto es_push = [&](int i, int j) {
    if (i > j) swap(i, j);
    pg_es.emplace_back(i, j);
  };

  rep(i, N) {
    int j = (i + 1) % N;
    each(p, ps) {
      if (p.edge_in(i, j)) {
        es_push(0, p.index);
        break;
      }
    }
  }

  rep(i, N) each(j, g[i]) {
    int p1 = -1, p2 = -1;
    rep(k, sz(ps)) {
      if (ps[k].edge_in(i, j)) {
        p1 = k;
        break;
      }
    }
    reg(k, p1 + 1, sz(ps)) {
      if (ps[k].edge_in(i, j)) {
        p2 = k;
        break;
      }
    }
    if (p1 != -1 and p2 != -1) es_push(ps[p1].index, ps[p2].index);
  }
  pg_es = mkuni(pg_es);
  ps.insert(begin(ps), soto);
  trc(pg_es);

  // SAT を書けばよい

  // SatSolver sat((N + M) * 4, {});

  M = sz(ps);

  using Clause = vector<pair<int, bool>>;
  V<Clause> clauses;

  rep(i, N + M) {
    Clause c;
    rep(j, 4) c.emplace_back(i * 4 + j, true);
    clauses.push_back(c);
    /*
    rep(j, 4) rep(k, j) {
      Clause c2;
      c2.emplace_back(i * 4 + j, false);
      c2.emplace_back(i * 4 + k, false);
      clauses.push_back(c2);
    }
    */
  }

  // a と b は異なる色
  auto add = [&](int a, int b) {
    trc(a, b);
    rep(j, 4) {
      // a が j 色 -> b は not j
      Clause c;
      c.emplace_back(a * 4 + j, false);
      c.emplace_back(b * 4 + j, false);
      clauses.push_back(c);
    }
  };

  // 頂点同士
  rep(i, N) {
    each(j, g[i]) add(i, j);
    add(i, (i + 1) % N);
  }
  // 面同士
  each2(i, j, pg_es) add(i + N, j + N);
  // 面と頂点
  each(p, ps) {
    int i = p.index + N;
    each(j, p.nodes) add(i, j);
  }
  SatSolver sat((N + M) * 4, clauses);
  auto sol = sat.solve();
  trc(sol);
  out(sol ? 4 : 5);

  /*

  // すべて 偶数か？

  bool all_even = true;

  each(p, ps) {
    if (sz(p.nodes) % 2 != 0) all_even = false;
  }

  if (all_even) {
    // 二部グラフか？
    int NN = sz(ps);
    UnionFind uf(2 * NN);
    each2(u, v, pg_es) {
      uf.unite(u, v + NN);
      uf.unite(v, u + NN);
    }
    bool bip = true;
    rep(i, NN) {
      if (uf.same(i, i + NN)) bip = false;
    }
    die(bip ? 4 : 5);
  }

  // 奇数同士が面で接しているか？
  // 接してたらダメ(無証明)
  bool sparse = 1;
  each2(u, v, pg_es) {
    if (sz(ps[u].nodes) % 2 == 0) continue;
    if (sz(ps[v].nodes) % 2 == 0) continue;
    sparse = 0;
  }
  if (!sparse) die(5);

  // わかっていること
  // 周上に奇数頂点ある平面 -> (奇数) のように表す

  // - 答えは 4 か 5 (無証明)
  // - (奇数) はすべて辺で接していない

  // (奇数) を全て同色で塗れれば 4 が達成できる
  // -> 頂点・(偶数) を三色で塗り分けられるか？

  // (奇数) 同士は隣り合っていない
  // -> すべての頂点は(偶数)に属している


  */
}