結果

問題 No.3370 AB → BA
コンテスト
ユーザー risujiroh
提出日時 2025-11-17 23:04:33
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 739 ms / 2,000 ms
コード長 11,555 bytes
コンパイル時間 6,391 ms
コンパイル使用メモリ 339,360 KB
実行使用メモリ 25,652 KB
最終ジャッジ日時 2025-11-17 23:04:46
合計ジャッジ時間 12,657 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 1
other AC * 20
権限があれば一括ダウンロードができます

ソースコード

diff # 

#if __INCLUDE_LEVEL__ == 0

#include __BASE_FILE__

using Mint = atcoder::modint998244353;

void Solve() {
  string s;
  IN(s);
  int n = Sz(s);

  vector<int> pos;
  pos.reserve(ranges::count(s, 'A'));
  for (int i : Rep(0, n)) {
    if (s[i] == 'A') {
      pos.push_back(i);
    }
  }

  int N = Sz(pos);
  if (N == 0) {
    OUT(1);
    return;
  }

  vector<int> A(N);
  vector<int> B(N);
  for (int i : Rep(0, N)) {
    B[i] = pos[i] - i + 1;
  }
  OUT(po167::main(N, n, A, B));
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  Solve();
}

#elif __INCLUDE_LEVEL__ == 1

#include <bits/stdc++.h>

#include <atcoder/convolution>

// https://judge.yosupo.jp/submission/319327
namespace po167 {
template <class T>
struct Binomial {
  std::vector<T> fact_vec, fact_inv_vec;
  void extend(int m = -1) {
    int n = fact_vec.size();
    if (m == -1) m = n * 2;
    if (n >= m) return;
    fact_vec.resize(m);
    fact_inv_vec.resize(m);
    for (int i = n; i < m; i++) {
      fact_vec[i] = fact_vec[i - 1] * T(i);
    }
    fact_inv_vec[m - 1] = T(1) / fact_vec[m - 1];
    for (int i = m - 1; i > n; i--) {
      fact_inv_vec[i - 1] = fact_inv_vec[i] * T(i);
    }
  }
  Binomial(int MAX = 0) {
    fact_vec.resize(1, T(1));
    fact_inv_vec.resize(1, T(1));
    extend(MAX + 1);
  }

  T fact(int i) {
    if (i < 0) return 0;
    while (int(fact_vec.size()) <= i) extend();
    return fact_vec[i];
  }
  T invfact(int i) {
    if (i < 0) return 0;
    while (int(fact_inv_vec.size()) <= i) extend();
    return fact_inv_vec[i];
  }
  T C(int a, int b) {
    if (a < b || b < 0) return 0;
    return fact(a) * invfact(b) * invfact(a - b);
  }
  T invC(int a, int b) {
    if (a < b || b < 0) return 0;
    return fact(b) * fact(a - b) * invfact(a);
  }
  T P(int a, int b) {
    if (a < b || b < 0) return 0;
    return fact(a) * invfact(a - b);
  }
  T inv(int a) {
    if (a < 0) return inv(-a) * T(-1);
    if (a == 0) return 1;
    return fact(a - 1) * invfact(a);
  }
  T Catalan(int n) {
    if (n < 0) return 0;
    return fact(2 * n) * invfact(n + 1) * invfact(n);
  }
  T narayana(int n, int k) {
    if (n <= 0 || n < k || k < 1) return 0;
    return C(n, k) * C(n, k - 1) * inv(n);
  }
  T Catalan_pow(int n, int d) {
    if (n < 0 || d < 0) return 0;
    if (d == 0) {
      if (n == 0) return 1;
      return 0;
    }
    return T(d) * inv(d + n) * C(2 * n + d - 1, n);
  }
  T ruiseki(int a, int b) {
    if (a < 0 || b < 0) return 0;
    if (a == 0) {
      return 1;
    }
    return C(a + b - 1, b - 1);
  }
  T mirror(int a, int b, int c, int d, int e = 0) {
    if (a + e < b || c + e < d) return 0;
    if (a > c || b > d) return 0;
    a += e;
    c += e;
    return C(c + d - a - b, c - a) - C(c + d - a - b, c - b + 1);
  }
  T gird_sum(int a, int b) {
    if (a < 0 || b < 0) return 0;
    return C(a + b + 2, a + 1) - 1;
  }
  T gird_sum_2(int a, int b, int c, int d) {
    if (a >= b || c >= d) return 0;
    a--, b--, c--, d--;
    return gird_sum(a, c) - gird_sum(a, d) - gird_sum(b, c) + gird_sum(b, d);
  }

  T diagonal(int n, int k) {
    if (n <= 2 || n - 3 < k || k < 0) return 0;
    return C(n - 3, k) * C(n + k - 1, k) * inv(k + 1);
  }
};
}  // namespace po167

namespace po167 {
template <class T>
std::vector<T> FPS_cyclic_convolution(std::vector<T> f, std::vector<T> g) {
  atcoder::internal::butterfly(f);
  atcoder::internal::butterfly(g);
  for (int i = 0; i < (int)f.size(); i++) f[i] *= g[i];
  atcoder::internal::butterfly_inv(f);
  T iz = (T)(1) / (T)(f.size());
  for (int i = 0; i < (int)f.size(); i++) f[i] *= iz;
  return f;
}
}  // namespace po167
namespace po167 {
template <class T>
std::pair<std::vector<T>, std::vector<T>> count_square(std::vector<T> L, std::vector<T> D) {
  assert(!L.empty() && !D.empty());
  int N = L.size();
  int M = D.size();
  if (std::min(N, M) <= 200) {
    int sw = 0;
    if (N > M) std::swap(N, M), std::swap(L, D), sw = 1;
    std::vector<T> R(N);
    for (int i = 0; i < N; i++) {
      D[0] += L[i];
      for (int j = 1; j < M; j++) D[j] += D[j - 1];
      R[i] = D.back();
    }
    if (sw) std::swap(R, D);
    return {R, D};
  }
  po167::Binomial<T> table(N + M);
  std::vector<T> R(N), U(M);
  int z = 0;
  while ((1 << z) < (N + M - 1)) z++;
  {
    std::vector<T> tmp(N);
    for (int i = 0; i < N; i++) tmp[i] = table.C(M - 1 + i, i);
    tmp = atcoder::convolution(tmp, L);
    for (int i = 0; i < N; i++) R[i] += tmp[i];
  }
  {
    std::vector<T> tmp(1 << z);
    for (int i = 0; i < N; i++) L[i] *= table.invfact(N - 1 - i);
    for (int i = 0; i < N + M - 1; i++) tmp[i] = table.fact(i);
    L.resize(1 << z, 0);
    tmp = po167::FPS_cyclic_convolution(tmp, L);
    for (int i = 0; i < M; i++) U[i] += tmp[N - 1 + i] * table.invfact(i);
  }
  {
    std::vector<T> tmp(M);
    for (int i = 0; i < M; i++) tmp[i] = table.C(N - 1 + i, i);
    tmp = atcoder::convolution(tmp, D);
    for (int i = 0; i < M; i++) U[i] += tmp[i];
  }
  {
    std::vector<T> tmp(1 << z);
    for (int i = 0; i < M; i++) D[i] *= table.invfact(M - i - 1);
    for (int i = 0; i < N + M - 1; i++) tmp[i] = table.fact(i);
    D.resize(1 << z, 0);
    tmp = po167::FPS_cyclic_convolution(tmp, D);
    for (int i = 0; i < N; i++) R[i] += tmp[M - 1 + i] * table.invfact(i);
  }
  return {R, U};
}
template <class T>
std::vector<T> count_increase_sequences_with_upper_bounds(std::vector<int> A, std::vector<T> C) {
  int N = A.size();
  assert((int)C.size() == N);
  assert(N);
  for (int i = (int)(A.size()) - 1; i > 0; i--) A[i - 1] = std::min(A[i - 1], A[i]);
  if (A.back() == 0) return {};
  if (std::min(A.back(), N) <= 200) {
    std::vector<T> dp(0);
    dp.reserve(A.back());
    for (int i = 0; i < N; i++) {
      dp.resize(A[i], 0);
      if (A[i]) dp[0] += C[i];
      for (int j = 1; j < (int)dp.size(); j++) {
        dp[j] += dp[j - 1];
      }
    }
    return dp;
  }
  if (N == 1) {
    std::vector<T> res(A[0]);
    for (int i = 0; i < A[0]; i++) res[i] = C[0];
    return res;
  }
  int m = N / 2;
  std::vector<int> LA(m), RA(N - m);
  std::vector<T> LC(m), RC(N - m);
  for (int i = 0; i < m; i++) {
    LA[i] = A[i];
    LC[i] = C[i];
  }
  for (int i = 0; i < N - m; i++) {
    RA[i] = A[i + m] - A[m - 1];
    RC[i] = C[i + m];
  }
  std::vector<T> res;
  res.reserve(A.back());
  auto L = count_increase_sequences_with_upper_bounds(LA, LC);
  if (!L.empty()) {
    auto [R, U] = count_square(L, RC);
    for (int i = 0; i < (int)R.size(); i++) res.push_back(R[i]);
    std::swap(U, RC);
  }
  auto R = count_increase_sequences_with_upper_bounds(RA, RC);
  for (auto x : R) res.push_back(x);
  return res;
}
template <class T>
std::vector<T> NAIVE_count_increase_sequences_with_upper_lower_bounds(std::vector<int> A, std::vector<int> B, std::vector<T> C = {}) {
  std::vector<T> tmp(B.back() - A[0]);
  if (C.empty()) {
    int b = B[0];
    for (int i = 1; i < (int)B.size(); i++) b = std::min(b, B[i]);
    for (int i = 0; i < b - A[0]; i++) tmp[i] = 1;
  } else
    for (int i = 0; i < (int)std::min(tmp.size(), C.size()); i++) tmp[i] = C[i];
  int N = A.size();
  for (int i = 1; i < N; i++) {
    for (int j = 1; j < (int)tmp.size(); j++) {
      tmp[j] += tmp[j - 1];
    }
    for (int j = 0; j < (int)tmp.size(); j++) {
      if (j < A[i] - A[0] || B[i] - A[0] <= j) tmp[j] = 0;
    }
  }
  std::vector<T> res(B.back() - A.back());
  for (int i = 0; i < B.back() - A.back(); i++) {
    res[i] = tmp[A.back() - A[0] + i];
  }
  return res;
}

template <class T>
std::vector<T> count_increase_sequences_with_upper_lower_bounds(std::vector<int> A, std::vector<int> B, std::vector<T> C = {}) {
  int N = A.size();
  assert(A.size() == B.size());
  for (int i = 0; i < N - 1; i++) {
    A[i + 1] = std::max(A[i], A[i + 1]);
  }
  for (int i = N - 1; i > 0; i--) {
    B[i - 1] = std::min(B[i], B[i - 1]);
  }
  if (A.back() >= B.back()) return {};
  std::vector<T> res(B.back() - A.back(), 0);
  {
    int tmp = A[0];
    for (int i = 0; i < N; i++) {
      A[i] -= tmp;
      B[i] -= tmp;
      if (A[i] >= B[i]) return res;
    }
  }
  if (C.empty()) {
    C.resize(B[0] - A[0], 1);
  } else
    assert((int)(C.size()) == B[0] - A[0]);
  int l = 0;
  while (B[l] <= A.back()) {
    for (int i = (int)(C.size()) - 1; i > 0; i--) C[i] -= C[i - 1];
    int nl = l;
    while (A[nl] < B[l]) nl++;
    std::vector<int> tmp(B[l] - A[l]);
    tmp[0] = 1;
    for (int i = l; i < nl; i++) {
      tmp[A[i] - A[l]]++;
    }
    for (int i = 1; i < B[l] - A[l]; i++) tmp[i] += tmp[i - 1];
    auto X = count_increase_sequences_with_upper_bounds(tmp, C);
    std::vector<int> nB(nl - l + 1);
    for (int i = l; i <= nl; i++) {
      nB[i - l] = B[i] - B[l];
    }
    auto Y = count_increase_sequences_with_upper_bounds(nB, X);
    C.resize(B[nl] - A[nl]);
    for (int i = 0; i < B[nl] - A[nl]; i++) {
      C[i] = Y[i + A[nl] - B[l]];
    }
    l = nl;
  }
  {
    int a = A[l];
    for (int i = l; i < N; i++) {
      A[i] -= a;
      B[i] -= a;
    }
  }
  for (int i = (int)(C.size()) - 1; i > 0; i--) C[i] -= C[i - 1];
  std::vector<T> D(N - l, 0);
  if (A.back() != 0) {
    std::vector<T> L(A.back());
    for (int i = 0; i < (int)L.size(); i++) L[i] = C[i];
    std::vector<int> tmp(L.size());
    tmp[0] = 1;
    for (int i = l; i < N; i++) {
      if (A[i] < (int)tmp.size()) tmp[A[i]]++;
    }
    for (int i = 1; i < (int)tmp.size(); i++) {
      tmp[i] += tmp[i - 1];
    }
    auto nD = count_increase_sequences_with_upper_bounds(tmp, L);
    for (int i = 0; i < (int)nD.size(); i++) D[i] = nD[i];
  }
  for (int i = A.back(); i < B[l]; i++) C[i - A.back()] = C[i];
  C.resize(B[l] - A.back());
  auto [R, U] = count_square(C, D);
  res = R;
  std::vector<int> nB(N - l);
  for (int i = 0; i < N - l; i++) nB[i] = B[i + l] - B[l];
  R = count_increase_sequences_with_upper_bounds(nB, U);
  for (auto x : R) res.push_back(x);
  return res;
}
}  // namespace po167
namespace po167 {
int main(int N, int M, std::vector<int> A, std::vector<int> B) {
  using mint = atcoder::modint998244353;
  auto tmp = po167::count_increase_sequences_with_upper_lower_bounds<mint>(A, B);
  mint ans = 0;
  for (auto x : tmp) ans += x;
  return ans.val();
}

}  // namespace po167

#include <atcoder/modint.hpp>

template <class T> concept MyRange = std::ranges::range<T> && !std::convertible_to<T, std::string_view>;
template <class T> concept MyTuple = std::__is_tuple_like<T>::value && !MyRange<T>;

namespace std {

istream& operator>>(istream& is, MyRange auto&& r) {
  for (auto&& e : r) is >> e;
  return is;
}
istream& operator>>(istream& is, MyTuple auto&& t) {
  apply([&](auto&... xs) { (is >> ... >> xs); }, t);
  return is;
}

ostream& operator<<(ostream& os, MyRange auto&& r) {
  auto sep = "";
  for (auto&& e : r) os << exchange(sep, " ") << e;
  return os;
}
ostream& operator<<(ostream& os, MyTuple auto&& t) {
  auto sep = "";
  apply([&](auto&... xs) { ((os << exchange(sep, " ") << xs), ...); }, t);
  return os;
}

template <class T, atcoder::internal::is_modint_t<T>* = nullptr>
istream& operator>>(istream& is, T& x) {
  int v;
  is >> v;
  x = T::raw(v);
  return is;
}

template <class T, atcoder::internal::is_modint_t<T>* = nullptr>
ostream& operator<<(ostream& os, const T& x) {
  return os << x.val();
}

}  // namespace std

using namespace std;

#define Rep(...) [](int l, int r) { return views::iota(min(l, r), r); }(__VA_ARGS__)
#define Sz(r) int(size(r))
#define IN(...) (cin >> forward_as_tuple(__VA_ARGS__))
#define OUT(...) (cout << forward_as_tuple(__VA_ARGS__) << '\n')

#endif  // __INCLUDE_LEVEL__ == 1
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