test/aoj/2863.test.cpp

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• Last update: 2024-10-01 21:03:13+09:00
• Problem: https://onlinejudge.u-aizu.ac.jp/problems/2863

Depends on

• modintを扱うテンプレート (src/Internal/modint_traits.hpp)
• 剰余の高速化 (src/Internal/Remainder.hpp)
• 逆元 ($\mathbb{Z}/m\mathbb{Z}$) (src/Math/mod_inv.hpp)
• ModInt (src/Math/ModInt.hpp)
• Aho-Corasick (src/String/AhoCorasick.hpp)

Code

// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2863
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <algorithm>
#include <string>
#include "src/String/AhoCorasick.hpp"
#include "src/Math/ModInt.hpp"
using namespace std;
int main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 using Mint= ModInt<int(1e9 + 7)>;
 int N;
 cin >> N;
 vector<string> S(N);
 for (int i= 0; i < N; i++) cin >> S[i];
 AhoCorasick ac(S);
 string t;
 cin >> t;
 int M= t.length();
 Mint dp[M + 1];
 fill_n(dp, M + 1, 0);
 dp[0]= 1;
 for (int i= 0, s= ac.initial_state();;) {
  auto ps= ac.matched_patterns(s);
  for (int j: ps) {
   int k= i - S[j].length();
   if (i < 0) continue;
   dp[i]+= dp[k];
  }
  if (i == M) break;
  s= ac.transition(s, t[i++]);
 }
 cout << dp[M] << '\n';
 return 0;
}

#line 1 "test/aoj/2863.test.cpp"
// competitive-verifier: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2863
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <algorithm>
#include <string>
#line 2 "src/String/AhoCorasick.hpp"
#include <vector>
#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 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 9 "test/aoj/2863.test.cpp"
using namespace std;
int main() {
 cin.tie(0);
 ios::sync_with_stdio(false);
 using Mint= ModInt<int(1e9 + 7)>;
 int N;
 cin >> N;
 vector<string> S(N);
 for (int i= 0; i < N; i++) cin >> S[i];
 AhoCorasick ac(S);
 string t;
 cin >> t;
 int M= t.length();
 Mint dp[M + 1];
 fill_n(dp, M + 1, 0);
 dp[0]= 1;
 for (int i= 0, s= ac.initial_state();;) {
  auto ps= ac.matched_patterns(s);
  for (int j: ps) {
   int k= i - S[j].length();
   if (i < 0) continue;
   dp[i]+= dp[k];
  }
  if (i == M) break;
  s= ac.transition(s, t[i++]);
 }
 cout << dp[M] << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	00_sample_00	AC	7 ms	3 MB
g++-13	00_sample_01	AC	6 ms	4 MB
g++-13	00_sample_02	AC	6 ms	4 MB
g++-13	00_sample_03	AC	6 ms	4 MB
g++-13	10_rand_00	AC	22 ms	9 MB
g++-13	10_rand_01	AC	17 ms	9 MB
g++-13	10_rand_02	AC	25 ms	10 MB
g++-13	10_rand_03	AC	21 ms	10 MB
g++-13	10_rand_04	AC	15 ms	7 MB
g++-13	11_rand_00	AC	22 ms	11 MB
g++-13	11_rand_01	AC	24 ms	11 MB
g++-13	11_rand_02	AC	22 ms	11 MB
g++-13	11_rand_03	AC	26 ms	11 MB
g++-13	11_rand_04	AC	26 ms	11 MB
g++-13	20_fixed_length_00	AC	28 ms	10 MB
g++-13	20_fixed_length_01	AC	28 ms	10 MB
g++-13	20_fixed_length_02	AC	28 ms	10 MB
g++-13	21_fixed_length_00	AC	17 ms	11 MB
g++-13	21_fixed_length_01	AC	16 ms	11 MB
g++-13	21_fixed_length_02	AC	16 ms	11 MB
g++-13	22_fixed_length_00	AC	23 ms	11 MB
g++-13	22_fixed_length_01	AC	23 ms	11 MB
g++-13	22_fixed_length_02	AC	24 ms	11 MB
g++-13	23_fixed_length_00	AC	22 ms	11 MB
g++-13	23_fixed_length_01	AC	21 ms	11 MB
g++-13	23_fixed_length_02	AC	21 ms	11 MB
g++-13	24_fixed_length_00	AC	19 ms	11 MB
g++-13	24_fixed_length_01	AC	19 ms	11 MB
g++-13	24_fixed_length_02	AC	18 ms	11 MB
g++-13	30_mixed_length_00	AC	18 ms	11 MB
g++-13	30_mixed_length_01	AC	17 ms	11 MB
g++-13	30_mixed_length_02	AC	17 ms	11 MB
g++-13	30_mixed_length_03	AC	17 ms	11 MB
g++-13	30_mixed_length_04	AC	17 ms	11 MB
g++-13	90_challenge_00	AC	12 ms	4 MB
g++-13	90_challenge_01	AC	96 ms	5 MB
g++-13	90_challenge_02	AC	13 ms	4 MB
g++-13	90_challenge_03	AC	53 ms	5 MB
g++-13	90_challenge_04	AC	21 ms	6 MB
g++-13	90_challenge_05	AC	6 ms	4 MB
clang++-18	00_sample_00	AC	7 ms	4 MB
clang++-18	00_sample_01	AC	6 ms	4 MB
clang++-18	00_sample_02	AC	6 ms	4 MB
clang++-18	00_sample_03	AC	6 ms	4 MB
clang++-18	10_rand_00	AC	22 ms	9 MB
clang++-18	10_rand_01	AC	18 ms	9 MB
clang++-18	10_rand_02	AC	26 ms	10 MB
clang++-18	10_rand_03	AC	20 ms	10 MB
clang++-18	10_rand_04	AC	14 ms	7 MB
clang++-18	11_rand_00	AC	21 ms	11 MB
clang++-18	11_rand_01	AC	23 ms	11 MB
clang++-18	11_rand_02	AC	21 ms	11 MB
clang++-18	11_rand_03	AC	24 ms	11 MB
clang++-18	11_rand_04	AC	26 ms	11 MB
clang++-18	20_fixed_length_00	AC	27 ms	10 MB
clang++-18	20_fixed_length_01	AC	27 ms	10 MB
clang++-18	20_fixed_length_02	AC	27 ms	10 MB
clang++-18	21_fixed_length_00	AC	16 ms	11 MB
clang++-18	21_fixed_length_01	AC	17 ms	11 MB
clang++-18	21_fixed_length_02	AC	16 ms	11 MB
clang++-18	22_fixed_length_00	AC	23 ms	11 MB
clang++-18	22_fixed_length_01	AC	23 ms	11 MB
clang++-18	22_fixed_length_02	AC	23 ms	11 MB
clang++-18	23_fixed_length_00	AC	20 ms	11 MB
clang++-18	23_fixed_length_01	AC	20 ms	11 MB
clang++-18	23_fixed_length_02	AC	20 ms	11 MB
clang++-18	24_fixed_length_00	AC	18 ms	11 MB
clang++-18	24_fixed_length_01	AC	18 ms	11 MB
clang++-18	24_fixed_length_02	AC	18 ms	11 MB
clang++-18	30_mixed_length_00	AC	17 ms	11 MB
clang++-18	30_mixed_length_01	AC	16 ms	11 MB
clang++-18	30_mixed_length_02	AC	17 ms	11 MB
clang++-18	30_mixed_length_03	AC	17 ms	11 MB
clang++-18	30_mixed_length_04	AC	18 ms	11 MB
clang++-18	90_challenge_00	AC	12 ms	5 MB
clang++-18	90_challenge_01	AC	103 ms	5 MB
clang++-18	90_challenge_02	AC	11 ms	5 MB
clang++-18	90_challenge_03	AC	59 ms	5 MB
clang++-18	90_challenge_04	AC	20 ms	6 MB
clang++-18	90_challenge_05	AC	7 ms	4 MB

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