test/yukicoder/1848.zalgo.test.cpp

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• Last update: 2024-10-01 17:03:34+09:00
• Problem: https://yukicoder.me/problems/no/1848

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)
• Z-Algorithm (src/String/z_algorithm.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1848
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <algorithm>
#include "src/String/z_algorithm.hpp"
#include "src/Math/ModInt.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<int(1e9) + 7>;
 int N;
 cin >> N;
 vector<int> A(N);
 for (int i= 0; i < N; ++i) cin >> A[i];
 string S;
 cin >> S;
 vector<long long> sum(N + 1);
 for (int i= 0; i < N; ++i) sum[i + 1]= sum[i] + A[i];
 vector<pair<char, int>> B(N - 1);
 for (int i= 1; i < N; ++i) B[i - 1]= {S[i], A[i]};
 auto Z= z_algorithm(B);
 Mint ans= 0;
 for (int i= 0; i < N; ++i) {
  if (S[i] != S[0]) continue;
  long long a= A[0], b= A[i], k= min(a, b);
  ans+= k * (k + 1) / 2 + a * (b - k);
  if (A[i] < A[0]) continue;
  if (i == N - 1) break;
  int z= Z[i];
  long long s= sum[z + 1];
  if (i + z + 1 < N && S[1 + z] == S[1 + z + i]) s+= min(A[1 + z], A[1 + z + i]);
  ans+= s - a;
 }
 cout << ans << '\n';
 return 0;
}

#line 1 "test/yukicoder/1848.zalgo.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/1848
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <algorithm>
#line 2 "src/String/z_algorithm.hpp"
#include <vector>
#line 4 "src/String/z_algorithm.hpp"
#include <string>
#include <tuple>
template <class String> std::vector<int> z_algorithm(const String &s) {
 const int n= s.size();
 if (n == 0) return {};
 std::vector<int> z(n);
 for (int i= 1, j= 0; i < n; ++i) {
  int &k= z[i];
  for (k= (j + z[j] <= i) ? 0 : std::min(j + z[j] - i, z[i - j]); i + k < n && s[k] == s[i + k];) ++k;
  if (j + z[j] < i + z[i]) j= i;
 }
 return z[0]= n, z;
}
std::vector<int> z_to_kmp(const std::vector<int> &z) {
 const int n= z.size();
 std::vector<int> kmp(n + 1);
 kmp[0]= -1;
 for (int i= n; --i;) kmp[i + z[i]]= std::max(kmp[i + z[i]], z[i]);
 for (int i= n; i--;) kmp[i]= std::max(kmp[i], kmp[i + 1] - 1);
 return kmp;
}
namespace string_internal {
template <class String> auto run_enumerate_(const String &s, typename String::value_type a= 0) {
 using Run= std::tuple<int, int, int>;
 std::vector<Run> glb;
 auto rec= [&](auto rec, int l, int r) -> std::vector<Run> {
  if (r - l <= 1) return {};
  const int m= (l + r) / 2, lsz= m - l, rsz= r - m;
  std::vector<Run> run_l= lsz > 1 ? rec(rec, l, m) : std::vector<Run>(), run_r= rsz > 1 ? rec(rec, m, r) : std::vector<Run>();
  std::vector<typename String::value_type> rl(r - l + 1, a);
  std::copy(s.begin() + m, s.begin() + r, rl.begin()), std::copy(s.begin() + l, s.begin() + m, rl.begin() + rsz + 1);
  std::vector<int> zrl= z_algorithm(rl);
  std::reverse(rl.begin(), rl.end());
  std::vector<int> zrl_r= z_algorithm(rl);
  const int sz= rl.size();
  std::vector<Run> ret;
  auto push= [&](int b, int e, int p) { (b == l || e == r ? ret : glb).emplace_back(b, e, p); };
  std::vector<Run> run_m(rsz / 2 + 1);
  for (auto [b, e, p]: run_r) {
   if (b != m) ret.emplace_back(b, e, p);
   else run_m[p]= Run{b, e, p};
  }
  for (auto [b, e, p]: run_l)
   if (e != m) ret.emplace_back(b, e, p);
   else if (zrl[sz - p] == p) {
    if (std::get<2>(run_m[p])) push(b, std::get<1>(run_m[p]), p), run_m[p]= Run{};
    else push(b, m + p + zrl[p], p);
   } else push(b, m + zrl[sz - p], p);
  for (auto [b, e, p]: run_m)
   if (p) {
    if (zrl[sz - p] != p) push(m - zrl_r[sz - p], e, p);
    else if (2 * p > lsz || zrl[sz - 2 * p] < p) push(m - p - zrl_r[p], e, p);
   }
  for (int p= 1; p <= lsz; ++p)
   if (bool skpr= 2 * p <= rsz && zrl[p] >= p, skpl= 2 * p <= lsz && zrl[sz - 2 * p] >= p; zrl[sz - p] == p) {
    if (!skpl && !skpr) push(m - p - zrl_r[p], m + p + zrl[p], p);
   } else {
    if (!skpr)
     if (int b= m - zrl_r[sz - p], e= m + p + zrl[p]; e - b >= 2 * p) push(b, e, p);
    if (!skpl)
     if (int b= m - p - zrl_r[p], e= m + zrl[sz - p]; e - b >= 2 * p) push(b, e, p);
   }
  return ret;
 };
 std::vector<std::tuple<int, int, int>> runs= rec(rec, 0, s.size());
 std::copy(glb.begin(), glb.end(), std::back_inserter(runs)), std::sort(runs.begin(), runs.end()), runs.erase(std::unique(runs.begin(), runs.end(), [](auto &r1, auto &r2) { return std::get<0>(r1) == std::get<0>(r2) && std::get<1>(r1) == std::get<1>(r2); }), runs.end());
 int rn= runs.size(), n= s.size();
 glb.resize(rn);
 std::vector<int> pt(n);
 for (auto [l, r, p]: runs) ++pt[p];
 for (int i= 1; i < n; ++i) pt[i]+= pt[i - 1];
 for (int i= rn; i--;) glb[--pt[std::get<2>(runs[i])]]= {std::get<2>(runs[i]), std::get<0>(runs[i]), std::get<1>(runs[i])};
 return glb;
}
template <class Int, typename= std::enable_if_t<std::is_integral_v<Int>>> auto run_enumerate(const std::vector<Int> &s) { return run_enumerate_(s, *std::max_element(s.begin(), s.end()) + 1); }
template <class String> auto run_enumerate(const String &s) {
 auto v= s;
 std::sort(v.begin(), v.end()), v.erase(std::unique(v.begin(), v.end()), v.end());
 std::vector<int> t(s.size());
 for (int i= s.size(); i--;) t[i]= std::lower_bound(v.begin(), v.end(), s[i]) - v.begin();
 return run_enumerate_(t, v.size() + 1);
}
auto run_enumerate(const std::string &s) { return run_enumerate_(s); }
}
using string_internal::run_enumerate;
#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 8 "test/yukicoder/1848.zalgo.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 using Mint= ModInt<int(1e9) + 7>;
 int N;
 cin >> N;
 vector<int> A(N);
 for (int i= 0; i < N; ++i) cin >> A[i];
 string S;
 cin >> S;
 vector<long long> sum(N + 1);
 for (int i= 0; i < N; ++i) sum[i + 1]= sum[i] + A[i];
 vector<pair<char, int>> B(N - 1);
 for (int i= 1; i < N; ++i) B[i - 1]= {S[i], A[i]};
 auto Z= z_algorithm(B);
 Mint ans= 0;
 for (int i= 0; i < N; ++i) {
  if (S[i] != S[0]) continue;
  long long a= A[0], b= A[i], k= min(a, b);
  ans+= k * (k + 1) / 2 + a * (b - k);
  if (A[i] < A[0]) continue;
  if (i == N - 1) break;
  int z= Z[i];
  long long s= sum[z + 1];
  if (i + z + 1 < N && S[1 + z] == S[1 + z + i]) s+= min(A[1 + z], A[1 + z + i]);
  ans+= s - a;
 }
 cout << ans << '\n';
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	in00.txt	AC	24 ms	9 MB
g++-13	in01.txt	AC	18 ms	9 MB
g++-13	in02.txt	AC	20 ms	9 MB
g++-13	in03.txt	AC	21 ms	9 MB
g++-13	in04.txt	AC	17 ms	9 MB
g++-13	in05.txt	AC	22 ms	9 MB
g++-13	in06.txt	AC	20 ms	9 MB
g++-13	in07.txt	AC	17 ms	9 MB
g++-13	in08.txt	AC	19 ms	9 MB
g++-13	in09.txt	AC	20 ms	9 MB
g++-13	in10.txt	AC	18 ms	9 MB
g++-13	in11.txt	AC	21 ms	9 MB
g++-13	in12.txt	AC	20 ms	9 MB
g++-13	in13.txt	AC	16 ms	9 MB
g++-13	in14.txt	AC	21 ms	9 MB
g++-13	in15.txt	AC	6 ms	4 MB
g++-13	in16.txt	AC	5 ms	4 MB
g++-13	in17.txt	AC	6 ms	4 MB
g++-13	in18.txt	AC	5 ms	4 MB
g++-13	in19.txt	AC	5 ms	4 MB
g++-13	in20.txt	AC	5 ms	4 MB
g++-13	in21.txt	AC	5 ms	4 MB
g++-13	in22.txt	AC	5 ms	4 MB
g++-13	in23.txt	AC	5 ms	4 MB
g++-13	in24.txt	AC	5 ms	4 MB
g++-13	in25.txt	AC	5 ms	4 MB
g++-13	in26.txt	AC	5 ms	4 MB
g++-13	in27.txt	AC	5 ms	4 MB
g++-13	in28.txt	AC	5 ms	4 MB
g++-13	in29.txt	AC	5 ms	4 MB
g++-13	in30.txt	AC	5 ms	4 MB
g++-13	in31.txt	AC	5 ms	4 MB
g++-13	in32.txt	AC	5 ms	4 MB
g++-13	in33.txt	AC	11 ms	6 MB
g++-13	in34.txt	AC	15 ms	8 MB
g++-13	in35.txt	AC	9 ms	4 MB
g++-13	in36.txt	AC	11 ms	5 MB
g++-13	in37.txt	AC	13 ms	7 MB
g++-13	in38.txt	AC	14 ms	6 MB
g++-13	in39.txt	AC	11 ms	6 MB
clang++-18	in00.txt	AC	23 ms	9 MB
clang++-18	in01.txt	AC	17 ms	9 MB
clang++-18	in02.txt	AC	20 ms	9 MB
clang++-18	in03.txt	AC	20 ms	9 MB
clang++-18	in04.txt	AC	17 ms	9 MB
clang++-18	in05.txt	AC	21 ms	9 MB
clang++-18	in06.txt	AC	19 ms	9 MB
clang++-18	in07.txt	AC	16 ms	9 MB
clang++-18	in08.txt	AC	19 ms	9 MB
clang++-18	in09.txt	AC	19 ms	9 MB
clang++-18	in10.txt	AC	18 ms	9 MB
clang++-18	in11.txt	AC	21 ms	9 MB
clang++-18	in12.txt	AC	19 ms	9 MB
clang++-18	in13.txt	AC	15 ms	9 MB
clang++-18	in14.txt	AC	20 ms	9 MB
clang++-18	in15.txt	AC	6 ms	4 MB
clang++-18	in16.txt	AC	5 ms	4 MB
clang++-18	in17.txt	AC	6 ms	4 MB
clang++-18	in18.txt	AC	5 ms	4 MB
clang++-18	in19.txt	AC	6 ms	4 MB
clang++-18	in20.txt	AC	5 ms	4 MB
clang++-18	in21.txt	AC	5 ms	4 MB
clang++-18	in22.txt	AC	5 ms	4 MB
clang++-18	in23.txt	AC	5 ms	4 MB
clang++-18	in24.txt	AC	5 ms	4 MB
clang++-18	in25.txt	AC	5 ms	4 MB
clang++-18	in26.txt	AC	5 ms	4 MB
clang++-18	in27.txt	AC	5 ms	4 MB
clang++-18	in28.txt	AC	5 ms	4 MB
clang++-18	in29.txt	AC	5 ms	4 MB
clang++-18	in30.txt	AC	5 ms	4 MB
clang++-18	in31.txt	AC	5 ms	4 MB
clang++-18	in32.txt	AC	5 ms	4 MB
clang++-18	in33.txt	AC	11 ms	6 MB
clang++-18	in34.txt	AC	15 ms	8 MB
clang++-18	in35.txt	AC	8 ms	5 MB
clang++-18	in36.txt	AC	11 ms	5 MB
clang++-18	in37.txt	AC	13 ms	7 MB
clang++-18	in38.txt	AC	13 ms	6 MB
clang++-18	in39.txt	AC	11 ms	6 MB

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