test/yukicoder/911.test.cpp

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• Last update: 2024-10-11 11:57:14+09:00
• Problem: https://yukicoder.me/problems/no/911

Depends on

• オートマトン上のDP (src/Misc/Automaton.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/911
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 128
#include <iostream>
#include <vector>
#include <algorithm>
#include "src/Misc/Automaton.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 int64_t L, R;
 cin >> L >> R;
 vector<int64_t> A(N);
 for (int i= 0; i < N; ++i) cin >> A[i];
 vector alp= {0, 1};
 auto tr_l= [&](int s, int c) {
  if (s <= -1) return s;
  int d= (L >> s) & 1;
  if (c < d) return -2;
  if (c > d) return -1;
  return s - 1;
 };
 auto tr_r= [&](int s, int c) {
  if (s <= -1) return s;
  int d= (R >> s) & 1;
  if (c < d) return -1;
  if (c > d) return -2;
  return s - 1;
 };
 auto ac0= [&](int) { return true; };
 Automaton dfa_l(alp, 60, tr_l, ac0, -2), dfa_r(alp, 60, tr_r, ac0, -2);
 using state_t= pair<vector<int>, int>;
 state_t rej= make_pair(vector<int>(), -1);
 state_t init= make_pair(vector<int>{0, N}, 60);
 auto tr_x= [&](const state_t &s, int c) -> state_t {
  const auto &[sep, i]= s;
  if (i <= -1) return s;
  const int n= sep.size();
  vector<int> nsep{0};
  for (int j= 0; j + 1 < n; ++j) {
   int bg= sep[j], ed= sep[j + 1];
   for (int k= bg; k + 1 < ed; ++k) {
    int l= ((A[k] >> i) & 1) ^ c, r= ((A[k + 1] >> i) & 1) ^ c;
    if (l > r) return rej;
    if (l < r) nsep.push_back(k + 1);
   }
   nsep.push_back(ed);
  }
  return {nsep, i - 1};
 };
 auto ac_x= [&](const state_t &s) {
  const auto &[sep, i]= s;
  return sep.size() == N + 1;
 };
 Automaton dfa_x(alp, init, tr_x, ac_x, rej);
 auto dfa= dfa_l & dfa_r & dfa_x;
 cout << dfa.num<int64_t>(61) << '\n';
 return 0;
}

#line 1 "test/yukicoder/911.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/911
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 128
#include <iostream>
#include <vector>
#include <algorithm>
#line 2 "src/Misc/Automaton.hpp"
#include <type_traits>
#include <set>
#include <map>
#include <unordered_map>
#line 8 "src/Misc/Automaton.hpp"
#include <queue>
#include <cstdlib>
#include <cassert>
template <class symbol_t> class Automaton {
 std::vector<int> table;
 std::vector<int8_t> info;
 std::vector<symbol_t> alph;
 const int m;
 template <class Map, class state_t, class F, class G, class H> void build(const state_t &initial_state, const F &transition, const G &is_accept, const H &abs_reject) {
  static_assert(std::is_same_v<bool, std::invoke_result_t<G, state_t>>);
  static_assert(std::is_same_v<bool, std::invoke_result_t<H, state_t>>);
  Map encode;
  std::vector<state_t> decode;
  int ts= 0;
  decode.push_back(initial_state), encode.emplace(initial_state, ts++);
  for (int i= 0, k= 0; i < ts; ++i) {
   auto s= decode[i];
   table.resize(table.size() + m);
   for (int j= 0; j < m; ++j) {
    if (auto t= transition(s, j); abs_reject(t)) table[k++]= -1;
    else if (auto it= encode.find(t); it != encode.end()) table[k++]= it->second;
    else table[k++]= ts, decode.push_back(t), encode.emplace(t, ts++);
   }
  }
  info.resize(ts);
  for (int i= ts; i--;) info[i]= is_accept(decode[i]);
 }
 Automaton(const std::vector<symbol_t> &alphabet): alph(alphabet), m(alph.size()) {}
public:
 template <class state_t, class F, class G, std::enable_if_t<std::is_invocable_r_v<state_t, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept): alph(alphabet), m(alph.size()) {
  std::sort(alph.begin(), alph.end());
  auto tr= [&](const state_t &s, int i) { return transition(s, alph[i]); };
  auto rej= [](const state_t &) { return false; };
  if constexpr (std::is_integral_v<state_t>) build<std::unordered_map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
  else build<std::map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
 }
 template <class state_t, class F, class G, std::enable_if_t<std::is_invocable_r_v<state_t, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept, const state_t &abs_rej_state): alph(alphabet), m(alph.size()) {
  std::sort(alph.begin(), alph.end());
  auto tr= [&](const state_t &s, int i) { return transition(s, alph[i]); };
  auto rej= [abs_rej_state](const state_t &s) { return s == abs_rej_state; };
  if constexpr (std::is_integral_v<state_t>) build<std::unordered_map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
  else build<std::map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
 }
 template <class state_t, class F, class G, std::enable_if_t<std::is_invocable_r_v<std::set<state_t>, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept): alph(alphabet), m(alph.size()) {
  static_assert(std::is_same_v<bool, std::invoke_result_t<G, state_t>>);
  std::sort(alph.begin(), alph.end());
  auto tr= [&](const std::set<state_t> &s, int i) {
   std::set<state_t> ret;
   for (const auto &x: s) {
    auto ys= transition(x, alph[i]);
    ret.insert(ys.begin(), ys.end());
   }
   return ret;
  };
  auto ac= [&](const std::set<state_t> &s) { return std::any_of(s.begin(), s.end(), is_accept); };
  auto rej= [](const std::set<state_t> &s) { return s == std::set<state_t>(); };
  build<std::map<std::set<state_t>, int>, std::set<state_t>>(std::set<state_t>({initial_state}), tr, ac, rej);
 }
 template <class state_t, class F, class G, class H, std::enable_if_t<std::is_invocable_r_v<std::set<state_t>, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept, const H &eps_trans): alph(alphabet), m(alph.size()) {
  static_assert(std::is_same_v<bool, std::invoke_result_t<G, state_t>>);
  static_assert(std::is_same_v<std::set<state_t>, std::invoke_result_t<H, state_t>>);
  std::sort(alph.begin(), alph.end());
  auto eps_closure= [&](std::set<state_t> s) {
   for (std::set<state_t> t; s != t;) {
    t= s;
    for (const auto &x: t) {
     auto ys= eps_trans(x);
     s.insert(ys.begin(), ys.end());
    }
   }
   return s;
  };
  auto tr= [&](const std::set<state_t> &s, int i) {
   std::set<state_t> ret;
   for (const auto &x: s) {
    auto ys= transition(x, alph[i]);
    ret.insert(ys.begin(), ys.end());
   }
   return eps_closure(ret);
  };
  auto ac= [&](const std::set<state_t> &s) { return std::any_of(s.begin(), s.end(), is_accept); };
  auto rej= [](const std::set<state_t> &s) { return s == std::set<state_t>(); };
  build<std::map<std::set<state_t>, int>, std::set<state_t>>(eps_closure({initial_state}), tr, ac, rej);
 }
 Automaton operator&(const Automaton &r) const {
  assert(alph == r.alph);
  const int S= info.size();
  auto tr= [&](int s, int q) {
   auto [s1, s0]= std::div(s, S);
   int t1= r.table[s1 * m + q], t0= table[s0 * m + q];
   return t0 == -1 || t1 == -1 ? -1 : t1 * S + t0;
  };
  auto ac= [&](int s) {
   auto [s1, s0]= std::div(s, S);
   return info[s0] == 1 && r.info[s1] == 1;
  };
  auto rej= [](int s) { return s == -1; };
  Automaton ret(alph);
  return ret.build<std::unordered_map<int, int>, int>(0, tr, ac, rej), ret;
 }
 template <class T, class A, class F> T dp_run(int n, const A &op, const T &ti, const F &f, const T &init) const {
  static_assert(std::is_same_v<T, std::invoke_result_t<A, T, T>>);
  static_assert(std::is_same_v<T, std::invoke_result_t<F, T, symbol_t, int>>);
  const size_t S= info.size();
  std::queue<std::pair<int, int>> que;
  T dp[2][S], ret= ti;
  bool in[2][S];
  for (std::fill_n(dp[0], S, ti), std::fill_n(dp[1], S, ti), std::fill_n(in[0], S, 0), std::fill_n(in[1], S, 0), dp[0][0]= init, que.emplace(0, 0), in[0][0]= 1; que.size();) {
   auto [s, i]= que.front();
   bool b= i & 1;
   T tmp= dp[b][s];
   if (que.pop(), in[b][s]= 0, dp[b][s]= ti; i == n) {
    if (info[s] == 1) ret= op(ret, tmp);
    continue;
   }
   auto l= table.cbegin() + s * m;
   for (int j= m; j--;)
    if (int t= l[j]; t != -1)
     if (dp[!b][t]= op(dp[!b][t], f(tmp, alph[j], i)); !in[!b][t]) que.emplace(t, i + 1), in[!b][t]= 1;
  }
  return ret;
 }
 template <class T> T num(int n) const {
  return dp_run(n, [](const T &l, const T &r) { return l + r; }, T(), [](const T &x, const auto &, auto) { return x; }, T(1));
 }
};
#line 8 "test/yukicoder/911.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 int N;
 cin >> N;
 int64_t L, R;
 cin >> L >> R;
 vector<int64_t> A(N);
 for (int i= 0; i < N; ++i) cin >> A[i];
 vector alp= {0, 1};
 auto tr_l= [&](int s, int c) {
  if (s <= -1) return s;
  int d= (L >> s) & 1;
  if (c < d) return -2;
  if (c > d) return -1;
  return s - 1;
 };
 auto tr_r= [&](int s, int c) {
  if (s <= -1) return s;
  int d= (R >> s) & 1;
  if (c < d) return -1;
  if (c > d) return -2;
  return s - 1;
 };
 auto ac0= [&](int) { return true; };
 Automaton dfa_l(alp, 60, tr_l, ac0, -2), dfa_r(alp, 60, tr_r, ac0, -2);
 using state_t= pair<vector<int>, int>;
 state_t rej= make_pair(vector<int>(), -1);
 state_t init= make_pair(vector<int>{0, N}, 60);
 auto tr_x= [&](const state_t &s, int c) -> state_t {
  const auto &[sep, i]= s;
  if (i <= -1) return s;
  const int n= sep.size();
  vector<int> nsep{0};
  for (int j= 0; j + 1 < n; ++j) {
   int bg= sep[j], ed= sep[j + 1];
   for (int k= bg; k + 1 < ed; ++k) {
    int l= ((A[k] >> i) & 1) ^ c, r= ((A[k + 1] >> i) & 1) ^ c;
    if (l > r) return rej;
    if (l < r) nsep.push_back(k + 1);
   }
   nsep.push_back(ed);
  }
  return {nsep, i - 1};
 };
 auto ac_x= [&](const state_t &s) {
  const auto &[sep, i]= s;
  return sep.size() == N + 1;
 };
 Automaton dfa_x(alp, init, tr_x, ac_x, rej);
 auto dfa= dfa_l & dfa_r & dfa_x;
 cout << dfa.num<int64_t>(61) << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	01_sample_01	AC	6 ms	4 MB
g++-13	01_sample_02	AC	5 ms	4 MB
g++-13	01_sample_03	AC	5 ms	4 MB
g++-13	02_small_01	AC	5 ms	4 MB
g++-13	02_small_02	AC	5 ms	4 MB
g++-13	02_small_03	AC	5 ms	4 MB
g++-13	02_small_04	AC	5 ms	4 MB
g++-13	02_small_05	AC	5 ms	4 MB
g++-13	02_small_06	AC	5 ms	4 MB
g++-13	02_small_07	AC	5 ms	4 MB
g++-13	02_small_08	AC	5 ms	4 MB
g++-13	02_small_09	AC	5 ms	4 MB
g++-13	02_small_10	AC	5 ms	4 MB
g++-13	03_large_01	AC	101 ms	84 MB
g++-13	03_large_02	AC	100 ms	83 MB
g++-13	03_large_03	AC	102 ms	80 MB
g++-13	03_large_04	AC	106 ms	78 MB
g++-13	03_large_05	AC	115 ms	81 MB
g++-13	03_large_06	AC	120 ms	78 MB
g++-13	03_large_07	AC	127 ms	74 MB
g++-13	03_large_08	AC	123 ms	71 MB
g++-13	03_large_09	AC	112 ms	61 MB
g++-13	03_large_10	AC	106 ms	51 MB
g++-13	03_large_11	AC	116 ms	49 MB
g++-13	03_large_12	AC	107 ms	43 MB
g++-13	03_large_13	AC	65 ms	23 MB
g++-13	03_large_14	AC	70 ms	21 MB
g++-13	03_large_15	AC	29 ms	9 MB
g++-13	03_large_16	AC	17 ms	6 MB
g++-13	03_large_17	AC	11 ms	5 MB
g++-13	03_large_18	AC	6 ms	4 MB
g++-13	03_large_19	AC	5 ms	4 MB
g++-13	03_large_20	AC	5 ms	4 MB
g++-13	04_corner_01	AC	5 ms	4 MB
g++-13	04_corner_02	AC	5 ms	4 MB
g++-13	04_corner_03	AC	5 ms	4 MB
g++-13	04_corner_04	AC	5 ms	4 MB
g++-13	04_corner_05	AC	5 ms	4 MB
g++-13	05_corner_01	AC	103 ms	81 MB
g++-13	05_corner_02	AC	111 ms	52 MB
g++-13	05_corner_03	AC	11 ms	4 MB
g++-13	05_corner_04	AC	125 ms	71 MB
g++-13	05_corner_05	AC	105 ms	33 MB
g++-13	05_corner_06	AC	106 ms	82 MB
g++-13	06_large_01	AC	23 ms	5 MB
g++-13	06_large_02	AC	23 ms	5 MB
g++-13	06_large_03	AC	23 ms	5 MB
g++-13	06_large_04	AC	22 ms	5 MB
g++-13	06_large_05	AC	21 ms	5 MB
clang++-18	01_sample_01	AC	6 ms	4 MB
clang++-18	01_sample_02	AC	5 ms	4 MB
clang++-18	01_sample_03	AC	5 ms	4 MB
clang++-18	02_small_01	AC	5 ms	4 MB
clang++-18	02_small_02	AC	5 ms	4 MB
clang++-18	02_small_03	AC	5 ms	4 MB
clang++-18	02_small_04	AC	5 ms	4 MB
clang++-18	02_small_05	AC	5 ms	4 MB
clang++-18	02_small_06	AC	5 ms	4 MB
clang++-18	02_small_07	AC	5 ms	4 MB
clang++-18	02_small_08	AC	5 ms	4 MB
clang++-18	02_small_09	AC	5 ms	4 MB
clang++-18	02_small_10	AC	5 ms	4 MB
clang++-18	03_large_01	AC	99 ms	84 MB
clang++-18	03_large_02	AC	98 ms	83 MB
clang++-18	03_large_03	AC	100 ms	79 MB
clang++-18	03_large_04	AC	105 ms	78 MB
clang++-18	03_large_05	AC	112 ms	81 MB
clang++-18	03_large_06	AC	117 ms	78 MB
clang++-18	03_large_07	AC	123 ms	74 MB
clang++-18	03_large_08	AC	120 ms	71 MB
clang++-18	03_large_09	AC	109 ms	61 MB
clang++-18	03_large_10	AC	104 ms	51 MB
clang++-18	03_large_11	AC	112 ms	49 MB
clang++-18	03_large_12	AC	106 ms	43 MB
clang++-18	03_large_13	AC	63 ms	22 MB
clang++-18	03_large_14	AC	69 ms	21 MB
clang++-18	03_large_15	AC	29 ms	9 MB
clang++-18	03_large_16	AC	17 ms	6 MB
clang++-18	03_large_17	AC	11 ms	4 MB
clang++-18	03_large_18	AC	6 ms	4 MB
clang++-18	03_large_19	AC	5 ms	4 MB
clang++-18	03_large_20	AC	5 ms	4 MB
clang++-18	04_corner_01	AC	5 ms	4 MB
clang++-18	04_corner_02	AC	5 ms	4 MB
clang++-18	04_corner_03	AC	5 ms	4 MB
clang++-18	04_corner_04	AC	5 ms	4 MB
clang++-18	04_corner_05	AC	5 ms	4 MB
clang++-18	05_corner_01	AC	100 ms	81 MB
clang++-18	05_corner_02	AC	110 ms	52 MB
clang++-18	05_corner_03	AC	11 ms	4 MB
clang++-18	05_corner_04	AC	121 ms	71 MB
clang++-18	05_corner_05	AC	101 ms	33 MB
clang++-18	05_corner_06	AC	103 ms	82 MB
clang++-18	06_large_01	AC	23 ms	5 MB
clang++-18	06_large_02	AC	23 ms	5 MB
clang++-18	06_large_03	AC	23 ms	5 MB
clang++-18	06_large_04	AC	23 ms	5 MB
clang++-18	06_large_05	AC	23 ms	5 MB

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