Hashiryo's Library

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:heavy_check_mark: test/yukicoder/1269.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1269
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <algorithm>
#include "src/Math/ModInt.hpp"
#include "src/String/AhoCorasick.hpp"
using namespace std;
int main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 using Mint= ModInt<int(1e9 + 7)>;
 long long N, L, R;
 cin >> N >> L >> R;
 vector<vector<int>> Fs;
 long long fp= 1, fpp= 1;
 if (L <= 1 && 1 <= R) Fs.push_back({1}), Fs.push_back({1});
 while (fp <= R) {
  long long tmp= fpp;
  fpp= fp;
  fp+= tmp;
  if (L <= fp && fp <= R) {
   vector<int> F;
   for (tmp= fp; tmp; tmp/= 10) F.push_back(tmp % 10);
   reverse(F.begin(), F.end());
   Fs.push_back(F);
  }
 }
 AhoCorasick ac(Fs);
 int M= ac.state_size();
 vector<Mint> dp(M);
 dp[0]= 1;
 for (int i= 0; i < N; i++) {
  vector<Mint> next(M);
  for (int s= 0; s < M; s++) {
   for (int k= 0; k < 10; k++) {
    int t= ac.transition(s, k);
    if (ac.is_accept(t)) continue;
    next[t]+= dp[s];
   }
  }
  dp.swap(next);
 }
 cout << accumulate(dp.begin(), dp.end(), Mint(0)) - 1 << '\n';
 return 0;
}
#line 1 "test/yukicoder/1269.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1269
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <algorithm>
#line 2 "src/Math/mod_inv.hpp"
#include <utility>
#include <type_traits>
#include <cassert>
template <class Uint> constexpr inline Uint mod_inv(Uint a, Uint mod) {
 std::make_signed_t<Uint> x= 1, y= 0, z= 0;
 for (Uint q= 0, b= mod, c= 0; b;) z= x, x= y, y= z - y * (q= a / b), c= a, a= b, b= c - b * q;
 return assert(a == 1), x < 0 ? mod - (-x) % mod : x % mod;
}
#line 2 "src/Internal/Remainder.hpp"
namespace math_internal {
using namespace std;
using u8= unsigned char;
using u32= unsigned;
using i64= long long;
using u64= unsigned long long;
using u128= __uint128_t;
struct MP_Na {  // mod < 2^32
 u32 mod;
 constexpr MP_Na(): mod(0) {}
 constexpr MP_Na(u32 m): mod(m) {}
 constexpr inline u32 mul(u32 l, u32 r) const { return u64(l) * r % mod; }
 constexpr inline u32 set(u32 n) const { return n; }
 constexpr inline u32 get(u32 n) const { return n; }
 constexpr inline u32 norm(u32 n) const { return n; }
 constexpr inline u32 plus(u64 l, u32 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u32 diff(u64 l, u32 r) const { return l-= r, l >> 63 ? l + mod : l; }
};
template <class u_t, class du_t, u8 B> struct MP_Mo {  // mod < 2^32, mod < 2^62
 u_t mod;
 constexpr MP_Mo(): mod(0), iv(0), r2(0) {}
 constexpr MP_Mo(u_t m): mod(m), iv(inv(m)), r2(-du_t(mod) % mod) {}
 constexpr inline u_t mul(u_t l, u_t r) const { return reduce(du_t(l) * r); }
 constexpr inline u_t set(u_t n) const { return mul(n, r2); }
 constexpr inline u_t get(u_t n) const { return n= reduce(n), n >= mod ? n - mod : n; }
 constexpr inline u_t norm(u_t n) const { return n >= mod ? n - mod : n; }
 constexpr inline u_t plus(u_t l, u_t r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u_t diff(u_t l, u_t r) const { return l-= r, l >> (B - 1) ? l + (mod << 1) : l; }
private:
 u_t iv, r2;
 static constexpr u_t inv(u_t n, int e= 6, u_t x= 1) { return e ? inv(n, e - 1, x * (2 - x * n)) : x; }
 constexpr inline u_t reduce(const du_t &w) const { return u_t(w >> B) + mod - ((du_t(u_t(w) * iv) * mod) >> B); }
};
using MP_Mo32= MP_Mo<u32, u64, 32>;
using MP_Mo64= MP_Mo<u64, u128, 64>;
struct MP_Br {  // 2^20 < mod <= 2^41
 u64 mod;
 constexpr MP_Br(): mod(0), x(0) {}
 constexpr MP_Br(u64 m): mod(m), x((u128(1) << 84) / m) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem(u128(l) * r); }
 static constexpr inline u64 set(u64 n) { return n; }
 constexpr inline u64 get(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 norm(u64 n) const { return n >= mod ? n - mod : n; }
 constexpr inline u64 plus(u64 l, u64 r) const { return l+= r, l < (mod << 1) ? l : l - (mod << 1); }
 constexpr inline u64 diff(u64 l, u64 r) const { return l-= r, l >> 63 ? l + (mod << 1) : l; }
private:
 u64 x;
 constexpr inline u128 quo(const u128 &n) const { return (n * x) >> 84; }
 constexpr inline u64 rem(const u128 &n) const { return n - quo(n) * mod; }
};
template <class du_t, u8 B> struct MP_D2B1 {  // mod < 2^63, mod < 2^64
 u64 mod;
 constexpr MP_D2B1(): mod(0), s(0), d(0), v(0) {}
 constexpr MP_D2B1(u64 m): mod(m), s(__builtin_clzll(m)), d(m << s), v(u128(-1) / d) {}
 constexpr inline u64 mul(u64 l, u64 r) const { return rem((u128(l) * r) << s) >> s; }
 constexpr inline u64 set(u64 n) const { return n; }
 constexpr inline u64 get(u64 n) const { return n; }
 constexpr inline u64 norm(u64 n) const { return n; }
 constexpr inline u64 plus(du_t l, u64 r) const { return l+= r, l < mod ? l : l - mod; }
 constexpr inline u64 diff(du_t l, u64 r) const { return l-= r, l >> B ? l + mod : l; }
private:
 u8 s;
 u64 d, v;
 constexpr inline u64 rem(const u128 &u) const {
  u128 q= (u >> 64) * v + u;
  u64 r= u64(u) - (q >> 64) * d - d;
  if (r > u64(q)) r+= d;
  if (r >= d) r-= d;
  return r;
 }
};
using MP_D2B1_1= MP_D2B1<u64, 63>;
using MP_D2B1_2= MP_D2B1<u128, 127>;
template <class u_t, class MP> constexpr u_t pow(u_t x, u64 k, const MP &md) {
 for (u_t ret= md.set(1);; x= md.mul(x, x))
  if (k & 1 ? ret= md.mul(ret, x) : 0; !(k>>= 1)) return ret;
}
}
#line 3 "src/Internal/modint_traits.hpp"
namespace math_internal {
struct m_b {};
struct s_b: m_b {};
}
template <class mod_t> constexpr bool is_modint_v= std::is_base_of_v<math_internal::m_b, mod_t>;
template <class mod_t> constexpr bool is_staticmodint_v= std::is_base_of_v<math_internal::s_b, mod_t>;
#line 6 "src/Math/ModInt.hpp"
namespace math_internal {
template <class MP, u64 MOD> struct SB: s_b {
protected:
 static constexpr MP md= MP(MOD);
};
template <class U, class B> struct MInt: public B {
 using Uint= U;
 static constexpr inline auto mod() { return B::md.mod; }
 constexpr MInt(): x(0) {}
 template <class T, typename= enable_if_t<is_modint_v<T> && !is_same_v<T, MInt>>> constexpr MInt(T v): x(B::md.set(v.val() % B::md.mod)) {}
 constexpr MInt(__int128_t n): x(B::md.set((n < 0 ? ((n= (-n) % B::md.mod) ? B::md.mod - n : n) : n % B::md.mod))) {}
 constexpr MInt operator-() const { return MInt() - *this; }
#define FUNC(name, op) \
 constexpr MInt name const { \
  MInt ret; \
  return ret.x= op, ret; \
 }
 FUNC(operator+(const MInt & r), B::md.plus(x, r.x))
 FUNC(operator-(const MInt & r), B::md.diff(x, r.x))
 FUNC(operator*(const MInt & r), B::md.mul(x, r.x))
 FUNC(pow(u64 k), math_internal::pow(x, k, B::md))
#undef FUNC
 constexpr MInt operator/(const MInt &r) const { return *this * r.inv(); }
 constexpr MInt &operator+=(const MInt &r) { return *this= *this + r; }
 constexpr MInt &operator-=(const MInt &r) { return *this= *this - r; }
 constexpr MInt &operator*=(const MInt &r) { return *this= *this * r; }
 constexpr MInt &operator/=(const MInt &r) { return *this= *this / r; }
 constexpr bool operator==(const MInt &r) const { return B::md.norm(x) == B::md.norm(r.x); }
 constexpr bool operator!=(const MInt &r) const { return !(*this == r); }
 constexpr bool operator<(const MInt &r) const { return B::md.norm(x) < B::md.norm(r.x); }
 constexpr inline MInt inv() const { return mod_inv<U>(val(), B::md.mod); }
 constexpr inline Uint val() const { return B::md.get(x); }
 friend ostream &operator<<(ostream &os, const MInt &r) { return os << r.val(); }
 friend istream &operator>>(istream &is, MInt &r) {
  i64 v;
  return is >> v, r= MInt(v), is;
 }
private:
 Uint x;
};
template <u64 MOD> using MP_B= conditional_t < (MOD < (1 << 30)) & MOD, MP_Mo32, conditional_t < MOD < (1ull << 32), MP_Na, conditional_t<(MOD < (1ull << 62)) & MOD, MP_Mo64, conditional_t<MOD<(1ull << 41), MP_Br, conditional_t<MOD<(1ull << 63), MP_D2B1_1, MP_D2B1_2>>>>>;
template <u64 MOD> using ModInt= MInt < conditional_t<MOD<(1 << 30), u32, u64>, SB<MP_B<MOD>, MOD>>;
}
using math_internal::ModInt;
#line 4 "src/String/AhoCorasick.hpp"
#include <numeric>
template <class String> struct AhoCorasick {
 using symbol_t= typename String::value_type;
 AhoCorasick(const std::vector<String> &ps) {
  const size_t n= ps.size();
  std::vector<int> ord(n), rows;
  std::iota(ord.begin(), ord.end(), 0), std::sort(ord.begin(), ord.end(), [&](int l, int r) { return ps[l] < ps[r]; });
  std::vector<size_t> lcp(n, 0), prev(n, 0), cur(n);
  for (size_t i= 1, j, ed; i < n; lcp[i++]= j)
   for (j= 0, ed= std::min(ps[ord[i - 1]].size(), ps[ord[i]].size()); j < ed; j++)
    if (ps[ord[i - 1]][j] != ps[ord[i]][j]) break;
  size_t nodes= 1;
  for (size_t i= 0; i < n; i++) nodes+= ps[ord[i]].size() - lcp[i];
  bg.reserve(nodes + 1), es.reserve(nodes), match.reserve(nodes), rows.reserve(n + 1);
  for (size_t row= 0; row < n; row++)
   if (!ps[ord[row]].empty()) rows.push_back(row);
  rows.push_back(-1), bg.push_back(0), match.push_back({});
  for (size_t i= 0; i < n && ps[ord[i]].empty(); ++i) match[0].push_back(ord[i]);
  for (size_t col= 0; rows[0] != -1; col++) {
   int size= 0;
   for (int &r: rows) {
    if (r == -1) break;
    size_t row= r;
    if (size++; lcp[row] <= col) {
     if (size_t par= prev[row]; bg[par] == -1) bg[par]= es.size();
     es.push_back(ps[ord[row]][col]), bg.push_back(-1);
     if (match.push_back({}); col + 1 == ps[ord[row]].size())
      for (size_t i= row; i < n && ps[ord[i]] == ps[ord[row]]; ++i) match.back().push_back(ord[i]);
    }
    if (cur[row]= bg.size() - 1; col + 1 == ps[ord[row]].size()) r= -1;
   }
   *std::remove(rows.begin(), rows.begin() + size, -1)= -1, prev.swap(cur);
  }
  bg.push_back(es.size());
  for (size_t i= bg.size() - 1; --i;)
   if (bg[i] == -1) bg[i]= bg[i + 1];
  fail.assign(match.size(), -1);
  for (int u= 0, ed= match.size(); u < ed; u++)
   for (auto i= bg[u], v= i + 1; i < bg[u + 1]; i++, v++) {
    int r= fail[v]= transition(fail[u], es[i]);
    match[v].insert(match[v].end(), match[r].begin(), match[r].end());
   }
 }
 inline int initial_state() const { return 0; }
 inline std::vector<int> matched_patterns(int s) const { return match[s]; }
 inline bool is_accept(int s) const { return !match[s].empty(); }
 inline int transition(int s, symbol_t c) const {
  for (; s >= 0; s= fail[s])
   if (int v= next(s, c); v != -1) return v;
  return 0;
 }
 inline int state_size() const { return match.size(); }
private:
 std::vector<int> bg, fail;
 std::vector<symbol_t> es;
 std::vector<std::vector<int>> match;
 inline int next(int s, symbol_t c) const {
  int index= std::lower_bound(es.begin() + bg[s], es.begin() + bg[s + 1], c) - es.begin();
  if (index != bg[s + 1] && c == es[index]) return index + 1;
  return -1;
 }
};
#line 9 "test/yukicoder/1269.test.cpp"
using namespace std;
int main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 using Mint= ModInt<int(1e9 + 7)>;
 long long N, L, R;
 cin >> N >> L >> R;
 vector<vector<int>> Fs;
 long long fp= 1, fpp= 1;
 if (L <= 1 && 1 <= R) Fs.push_back({1}), Fs.push_back({1});
 while (fp <= R) {
  long long tmp= fpp;
  fpp= fp;
  fp+= tmp;
  if (L <= fp && fp <= R) {
   vector<int> F;
   for (tmp= fp; tmp; tmp/= 10) F.push_back(tmp % 10);
   reverse(F.begin(), F.end());
   Fs.push_back(F);
  }
 }
 AhoCorasick ac(Fs);
 int M= ac.state_size();
 vector<Mint> dp(M);
 dp[0]= 1;
 for (int i= 0; i < N; i++) {
  vector<Mint> next(M);
  for (int s= 0; s < M; s++) {
   for (int k= 0; k < 10; k++) {
    int t= ac.transition(s, k);
    if (ac.is_accept(t)) continue;
    next[t]+= dp[s];
   }
  }
  dp.swap(next);
 }
 cout << accumulate(dp.begin(), dp.end(), Mint(0)) - 1 << '\n';
 return 0;
}

Test cases

Env Name Status Elapsed Memory
g++-13 00_sample01.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 00_sample02.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 00_sample03.txt :heavy_check_mark: AC 10 ms 4 MB
g++-13 01_small01.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small02.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small03.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small04.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small05.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small06.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small07.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small08.txt :heavy_check_mark: AC 6 ms 3 MB
g++-13 01_small09.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 01_small10.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 02_random01.txt :heavy_check_mark: AC 129 ms 4 MB
g++-13 02_random02.txt :heavy_check_mark: AC 161 ms 3 MB
g++-13 02_random03.txt :heavy_check_mark: AC 19 ms 4 MB
g++-13 02_random04.txt :heavy_check_mark: AC 126 ms 4 MB
g++-13 02_random05.txt :heavy_check_mark: AC 8 ms 4 MB
g++-13 02_random06.txt :heavy_check_mark: AC 133 ms 4 MB
g++-13 02_random07.txt :heavy_check_mark: AC 86 ms 4 MB
g++-13 02_random08.txt :heavy_check_mark: AC 26 ms 4 MB
g++-13 02_random09.txt :heavy_check_mark: AC 81 ms 4 MB
g++-13 02_random10.txt :heavy_check_mark: AC 67 ms 4 MB
g++-13 02_random11.txt :heavy_check_mark: AC 78 ms 4 MB
g++-13 02_random12.txt :heavy_check_mark: AC 39 ms 4 MB
g++-13 02_random13.txt :heavy_check_mark: AC 47 ms 4 MB
g++-13 02_random14.txt :heavy_check_mark: AC 9 ms 4 MB
g++-13 02_random15.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 02_random16.txt :heavy_check_mark: AC 24 ms 4 MB
g++-13 02_random17.txt :heavy_check_mark: AC 39 ms 4 MB
g++-13 02_random18.txt :heavy_check_mark: AC 19 ms 4 MB
g++-13 02_random19.txt :heavy_check_mark: AC 208 ms 4 MB
g++-13 02_random20.txt :heavy_check_mark: AC 51 ms 4 MB
g++-13 03_large01.txt :heavy_check_mark: AC 484 ms 4 MB
g++-13 03_large02.txt :heavy_check_mark: AC 7 ms 4 MB
g++-13 03_large03.txt :heavy_check_mark: AC 12 ms 4 MB
g++-13 04_hand01.txt :heavy_check_mark: AC 6 ms 4 MB
g++-13 04_hand02.txt :heavy_check_mark: AC 6 ms 3 MB
g++-13 04_hand03.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 00_sample01.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 00_sample02.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 00_sample03.txt :heavy_check_mark: AC 9 ms 4 MB
clang++-18 01_small01.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 01_small02.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 01_small03.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 01_small04.txt :heavy_check_mark: AC 5 ms 4 MB
clang++-18 01_small05.txt :heavy_check_mark: AC 5 ms 4 MB
clang++-18 01_small06.txt :heavy_check_mark: AC 5 ms 4 MB
clang++-18 01_small07.txt :heavy_check_mark: AC 5 ms 4 MB
clang++-18 01_small08.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 01_small09.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 01_small10.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 02_random01.txt :heavy_check_mark: AC 100 ms 4 MB
clang++-18 02_random02.txt :heavy_check_mark: AC 127 ms 4 MB
clang++-18 02_random03.txt :heavy_check_mark: AC 16 ms 4 MB
clang++-18 02_random04.txt :heavy_check_mark: AC 100 ms 4 MB
clang++-18 02_random05.txt :heavy_check_mark: AC 8 ms 4 MB
clang++-18 02_random06.txt :heavy_check_mark: AC 107 ms 4 MB
clang++-18 02_random07.txt :heavy_check_mark: AC 68 ms 4 MB
clang++-18 02_random08.txt :heavy_check_mark: AC 22 ms 4 MB
clang++-18 02_random09.txt :heavy_check_mark: AC 65 ms 4 MB
clang++-18 02_random10.txt :heavy_check_mark: AC 54 ms 4 MB
clang++-18 02_random11.txt :heavy_check_mark: AC 63 ms 4 MB
clang++-18 02_random12.txt :heavy_check_mark: AC 32 ms 4 MB
clang++-18 02_random13.txt :heavy_check_mark: AC 38 ms 4 MB
clang++-18 02_random14.txt :heavy_check_mark: AC 9 ms 4 MB
clang++-18 02_random15.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 02_random16.txt :heavy_check_mark: AC 20 ms 4 MB
clang++-18 02_random17.txt :heavy_check_mark: AC 32 ms 4 MB
clang++-18 02_random18.txt :heavy_check_mark: AC 15 ms 4 MB
clang++-18 02_random19.txt :heavy_check_mark: AC 163 ms 4 MB
clang++-18 02_random20.txt :heavy_check_mark: AC 41 ms 4 MB
clang++-18 03_large01.txt :heavy_check_mark: AC 381 ms 4 MB
clang++-18 03_large02.txt :heavy_check_mark: AC 7 ms 4 MB
clang++-18 03_large03.txt :heavy_check_mark: AC 11 ms 4 MB
clang++-18 04_hand01.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 04_hand02.txt :heavy_check_mark: AC 6 ms 4 MB
clang++-18 04_hand03.txt :heavy_check_mark: AC 6 ms 4 MB
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