test/atcoder/arc127_a.test.cpp

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• Last update: 2025-08-08 18:52:16+09:00
• Problem: https://atcoder.jp/contests/arc127/tasks/arc127_a

Depends on

• オートマトン上のDP (src/Misc/Automaton.hpp)

Code

// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/arc127/tasks/arc127_a
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#include "src/Misc/Automaton.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 int64_t N;
 cin >> N;
 vector alp= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
 auto tr= [](int64_t s, int c) { return (s - c + 10) / 10 - 1; };
 auto ac= [](int64_t) { return true; };
 Automaton dfa(alp, N, tr, ac, int64_t(-1));
 using T= array<int64_t, 2>;
 auto op= [](const T& l, const T& r) { return T{l[0] + r[0], l[1] + r[1]}; };
 auto f= [](T x, int c, int) {
  if (c == 1) x[1]+= x[0];
  else x[1]= 0;
  return x;
 };
 int64_t ans= 0;
 for (int i= 1; i <= 60; ++i) ans+= dfa.dp_run(i, op, T{0, 0}, f, T{1, 0})[1];
 cout << ans << '\n';
 return 0;
}

#line 1 "test/atcoder/arc127_a.test.cpp"
// competitive-verifier: IGNORE
// competitive-verifier: PROBLEM https://atcoder.jp/contests/arc127/tasks/arc127_a
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#line 2 "src/Misc/Automaton.hpp"
#include <type_traits>
#include <set>
#include <map>
#include <unordered_map>
#line 7 "src/Misc/Automaton.hpp"
#include <algorithm>
#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 9 "test/atcoder/arc127_a.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 int64_t N;
 cin >> N;
 vector alp= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
 auto tr= [](int64_t s, int c) { return (s - c + 10) / 10 - 1; };
 auto ac= [](int64_t) { return true; };
 Automaton dfa(alp, N, tr, ac, int64_t(-1));
 using T= array<int64_t, 2>;
 auto op= [](const T& l, const T& r) { return T{l[0] + r[0], l[1] + r[1]}; };
 auto f= [](T x, int c, int) {
  if (c == 1) x[1]+= x[0];
  else x[1]= 0;
  return x;
 };
 int64_t ans= 0;
 for (int i= 1; i <= 60; ++i) ans+= dfa.dp_run(i, op, T{0, 0}, f, T{1, 0})[1];
 cout << ans << '\n';
 return 0;
}

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