結果

問題 No.1195 数え上げを愛したい（文字列編）
ユーザー SHIJOUSHIJOU
提出日時 2020-09-10 22:03:17
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 569 ms / 3,000 ms
コード長 13,864 bytes
コンパイル時間 3,300 ms
コンパイル使用メモリ 233,204 KB
実行使用メモリ 17,688 KB
最終ジャッジ日時 2024-06-06 12:14:55
合計ジャッジ時間 12,805 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 569 ms
17,432 KB
testcase_01 AC 567 ms
17,560 KB
testcase_02 AC 569 ms
17,572 KB
testcase_03 AC 76 ms
12,900 KB
testcase_04 AC 77 ms
12,972 KB
testcase_05 AC 66 ms
14,400 KB
testcase_06 AC 15 ms
11,004 KB
testcase_07 AC 15 ms
11,008 KB
testcase_08 AC 104 ms
12,000 KB
testcase_09 AC 542 ms
17,688 KB
testcase_10 AC 309 ms
14,428 KB
testcase_11 AC 499 ms
17,408 KB
testcase_12 AC 469 ms
17,516 KB
testcase_13 AC 399 ms
14,244 KB
testcase_14 AC 267 ms
14,776 KB
testcase_15 AC 297 ms
14,296 KB
testcase_16 AC 267 ms
14,148 KB
testcase_17 AC 110 ms
12,004 KB
testcase_18 AC 468 ms
17,388 KB
testcase_19 AC 470 ms
17,512 KB
testcase_20 AC 399 ms
14,372 KB
testcase_21 AC 497 ms
17,404 KB
testcase_22 AC 378 ms
14,352 KB
testcase_23 AC 16 ms
10,972 KB
testcase_24 AC 15 ms
10,900 KB
testcase_25 AC 15 ms
10,904 KB
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 # 

//#define _GLIBCXX_DEBUG
#include <bits/stdc++.h>
#define rep(i, n) for(int i=0; i<n; ++i)
#define all(v) v.begin(), v.end()
#define rall(v) v.rbegin(), v.rend()
using namespace std;
using ll = int64_t;
using ld = long double;
using P = pair<int, int>;
using vs = vector<string>;
using vi = vector<int>;
using vvi = vector<vi>;
template<class T> using PQ = priority_queue<T>;
template<class T> using PQG = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0xccccccc;
const ll LINF = 0xcccccccccccccccLL;
template<typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {return a < b && (a = b, true);}
template<typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {return a > b && (a = b, true);}
template<typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) { return is >> p.first >> p.second;}
template<typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) { return os << p.first << ' ' << p.second;}

namespace fft {

constexpr unsigned int modulo1 = 998244353;
constexpr unsigned int modulo2 = 1000000007;
constexpr long double PI = acos(-1);

struct modint_base {};
template<class C> using is_modint = is_base_of<modint_base, C>;
template<class C> using is_modint_t = enable_if_t<is_modint<C>::value>;
template<class C> using is_complex = typename conditional<is_same<C, complex<double>>::value || is_same<C, complex<long double>>::value, true_type, false_type>::type;

//begin NTT
template<int m>
struct mint : modint_base {
  unsigned int x;
  static constexpr int mod() {return m;}
  static constexpr unsigned int umod() {return m;}
  mint():x(0) {}
  mint(int64_t x_) {
    int64_t v = int64_t(x_ % umod());
    if(v < 0) v += umod();
    x = (unsigned int)v;
  }
  static mint row(int v) {
    mint v_;
    v_.x = v;
    return v_;
  }
  mint operator-() const { return mint(-x);}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= umod()) x -= umod();
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += umod()-a.x) >= umod()) x -= umod();
    return *this;
  }
  mint& operator*=(const mint a) {
    uint64_t z = x;
    z *= a.x;
    x = (unsigned int)(z % umod());
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a;}
  mint operator-(const mint a) const { return mint(*this) -= a;}
  mint operator*(const mint a) const { return mint(*this) *= a;}
  mint &operator++() {
    x++;
    if(x == umod()) x = 0;
    return *this;
  }
  mint &operator--() {
    if(x == 0) x = umod();
    x--;
    return *this;
  }
  mint operator++(int) {
    mint result = *this;
    ++*this;
    return result;
  }
  mint operator--(int) {
    mint result = *this;
    --*this;
    return result;
  }
  mint pow(int64_t t) const {
    mint x_ = *this, r = 1;
    while(t) {
      if(t&1) r *= x_;
      x_ *= x_;
      t >>= 1;
    }
    return r;
  }
  mint inv() const { return pow(umod()-2);}
  mint& operator/=(const mint a) { return *this *= a.inv();}
  mint operator/(const mint a) {return mint(*this) /= a;}
  friend bool operator==(const mint &a, const mint &b) {return a.x == b.x;}
  friend bool operator!=(const mint &a, const mint &b) {return a.x != b.x;}
};

constexpr int64_t safe_mod(int64_t x, int64_t m) {
  x %= m;
  if(x < 0) x += m;
  return x;
}

constexpr int64_t pow_mod_constexpr(int64_t x, int64_t n, int m) {
  if(m == 1) return 0;
  unsigned int _m = (unsigned int)(m);
  uint64_t r = 1;
  uint64_t y = safe_mod(x, m);
  while(n) {
    if(n&1) r = (r*y)%_m;
    y = (y*y)%_m;
    n >>= 1;
  }
  return r;
}

constexpr int primitive_root_constexpr(int m) {
  if(m == 2) return 1;
  if(m == 167772161) return 3;
  if(m == 469762049) return 3;
  if(m == 754974721) return 11;
  if(m == 998244353) return 3;
  int divs[20] = {};
  divs[0] = 2;
  int cnt = 1;
  int x = (m-1)>>1;
  while(~x&1) x >>= 1;
  for(int i = 3; (int64_t)(i)*i <= x; i += 2) {
    if(x%i == 0) {
      divs[cnt++] = i;
      while(x%i == 0) x /= i;
    }
  }
  if(x > 1) divs[cnt++] = x;
  for(int g = 2;; g++) {
    bool ok = true;
    for(int i = 0; i < cnt; i++) {
      if(pow_mod_constexpr(g, (m-1)/divs[i], m) == 1) {
        ok = false;
        break;
      }
    }
    if(ok) return g;
  }
}
template<int m> constexpr int primitive_root = primitive_root_constexpr(m);

constexpr pair<int64_t, int64_t> inv_gcd(int64_t a, int64_t b) {
  a = safe_mod(a, b);
  if(a == 0) return {b, 0};
  int64_t s = b, t = a;
  int64_t m0 = 0, m1 = 1;
  while(t) {
    int64_t u = s/t;
    s -= t*u;
    m0 -= m1*u;
    int64_t tmp = s;
    s = t;
    t = tmp;
    tmp = m0;
    m0 = m1;
    m1 = tmp;
  }
  if(m0 < 0) m0 += b/s;
  return {s, m0};
}

int ceil_pow2(int n) {
  int x = 0;
  while((1U << x) < (unsigned int)(n)) x++;
  return x;
}

template<class mint, is_modint_t<mint>* = nullptr>
void butterfly(vector<mint> &ary) {
  static constexpr int g = primitive_root<mint::mod()>;
  int n = int(ary.size());
  int h = ceil_pow2(n);

  static bool first = true;
  static mint sum_e[30];
  if(first) {
    first = false;
    mint es[30], ies[30];
    int cnt2 = __builtin_ctz(mint::mod()-1);
    mint e = mint(g).pow((mint::mod()-1)>>cnt2), ie = e.inv();
    for(int i = cnt2; i >= 2; i--) {
      es[i-2] = e;
      ies[i-2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now(1);
    for(int i = 0; i < cnt2-2; i++) {
      sum_e[i] = es[i] * now;
      now *= ies[i];
    }
  }
  for(int ph = 1; ph <= h; ph++) {
    int w = 1<<(ph-1), p = 1<<(h-ph);
    mint now(1);
    for(int s = 0; s < w; s++) {
      int offset = s << (h-ph+1);
      for(int i = 0; i < p; i++) {
        mint l = ary[i+offset];
        mint r = ary[i+offset+p] * now;
        ary[i+offset] = l+r;
        ary[i+offset+p] = l-r;
      }
      now *= sum_e[__builtin_ctz(~(unsigned int)(s))];
    }
  }
}

template<class mint, is_modint_t<mint>* = nullptr>
void butterfly_inv(vector<mint> &ary) {
  static constexpr int g = primitive_root<mint::mod()>;
  int n = int(ary.size());
  int h = ceil_pow2(n);

  static bool first = true;
  static mint sum_ie[30];
  if(first) {
    first = false;
    mint es[30], ies[30];
    int cnt2 = __builtin_ctz(mint::mod()-1);
    mint e = mint(g).pow((mint::mod()-1)>>cnt2), ie = e.inv();
    for(int i = cnt2; i >= 2; i--) {
      es[i-2] = e;
      ies[i-2] = ie;
      e *= e;
      ie *= ie;
    }
    mint now(1);
    for(int i = 0; i < cnt2-2; i++) {
      sum_ie[i] = ies[i] * now;
      now *= es[i];
    }
  }
  for(int ph = h; ph >= 1; ph--) {
    int w = 1<<(ph-1), p = 1<<(h-ph);
    mint inow(1);
    for(int s = 0; s < w; s++) {
      int offset = s<<(h-ph+1);
      for(int i = 0; i < p; i++) {
        mint l = ary[i+offset];
        mint r = ary[i+offset+p];
        ary[i+offset] = l+r;
        ary[i+offset+p] = (uint64_t)(mint::mod() + l.x - r.x) * inow.x;
      }
      inow *= sum_ie[__builtin_ctz(~(unsigned int)(s))];
    }
  }
}

template<class mint, is_modint_t<mint>* = nullptr>
vector<mint> convolution(vector<mint> a, vector<mint> b) {
  int n = int(a.size()), m = int(b.size());
  if(!n || !m) return {};
  if(min(n, m) <= 60) {
    if(n < m) {
      swap(n, m);
      swap(a, b);
    }
    vector<mint> ans(n+m-1);
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < m; j++) {
        ans[i+j] += a[i] * b[j];
      }
    }
    return ans;
  }
  int z = 1<<ceil_pow2(n+m-1);
  a.resize(z);
  butterfly(a);
  b.resize(z);
  butterfly(b);
  for(int i = 0; i < z; i++) {
    a[i] *= b[i];
  }
  butterfly_inv(a);
  a.resize(n+m-1);
  mint iz = mint(z).inv();
  for(int i = 0; i < n+m-1; i++) a[i] *= iz;
  return a;
}

template<unsigned int mod = modulo1, class T, enable_if_t<is_integral<T>::value>* = nullptr>
vector<T> convolution(const vector<T> &a, const vector<T> &b) {
  int n = int(a.size()), m = int(b.size());
  if(!n || !m) return {};

  using Mint = mint<mod>;
  vector<Mint> a2(n), b2(m);
  for(int i = 0; i < n; i++) {
    a2[i] = Mint(a[i]);
  }
  for(int i = 0; i < m; i++) {
    b2[i] = Mint(b[i]);
  }
  vector<Mint> c2 = convolution<Mint>(move(a2), move(b2));
  vector<T> c(n+m-1);
  for(int i = 0; i < n+m-1; i++) c[i] = c2[i].x;
  return c;
}

vector<int64_t> convolution_ll(const vector<int64_t> &a, vector<int64_t> &b) {
  int n = int(a.size()), m = int(b.size());
  if(!n || !m) return {};

  static constexpr uint64_t MOD1 = 754974721;  // 2^24
  static constexpr uint64_t MOD2 = 167772161;  // 2^25
  static constexpr uint64_t MOD3 = 469762049;  // 2^26
  static constexpr uint64_t M2M3 = MOD2 * MOD3;
  static constexpr uint64_t M1M3 = MOD1 * MOD3;
  static constexpr uint64_t M1M2 = MOD1 * MOD2;
  static constexpr uint64_t M1M2M3 = MOD1 * MOD2 * MOD3;

  static constexpr uint64_t i1 = inv_gcd(M2M3, MOD1).second;
  static constexpr uint64_t i2 = inv_gcd(M1M3, MOD2).second;
  static constexpr uint64_t i3 = inv_gcd(M1M2, MOD3).second;

  vector<int64_t> c1 = convolution<MOD1>(a, b);
  vector<int64_t> c2 = convolution<MOD2>(a, b);
  vector<int64_t> c3 = convolution<MOD3>(a, b);

  vector<int64_t> c(n+m-1);
  for(int i = 0; i < n+m-1; i++) {
    uint64_t x = 0;
    x += (c1[i] * i1) % MOD1 * M2M3;
    x += (c2[i] * i2) % MOD2 * M1M3;
    x += (c3[i] * i3) % MOD3 * M1M2;
    int64_t diff = c1[i] - safe_mod(int64_t(x), int64_t(MOD1));
    if(diff < 0) diff += MOD1;
    static constexpr uint64_t offset[5] = {0, 0, M1M2M3, 2*M1M2M3, 3*M1M2M3};
    x -= offset[diff%5];
    c[i] = x;
  }
  return c;
}

//begin FFT
template<class Float, enable_if_t<is_floating_point<Float>::value>* = nullptr>
void butterfly(vector<complex<Float>>& ary) {
  int n = int(ary.size());
  int h = ceil_pow2(n);

  using Complex = complex<Float>;
  static bool first = true;
  static Complex sum_e[30];
  if(first) {
    first = false;
    Complex now = 1.0;
    for(int i = 0; i < 28; i++) {
      Complex es = polar(Float(1.0), Float(PI)/(1<<(i+1)));
      sum_e[i] = es * now;
      now *= conj(es);
    }
  }
  for(int ph = 1; ph <= h; ph++) {
    int w = 1<<(ph-1), p = 1<<(h-ph);
    Complex now = Complex(1.0, 0);
    for(int s = 0; s < w; s++) {
      int offset = s<<(h-ph+1);
      for(int i = 0; i < p; i++) {
        Complex l = ary[i+offset];
        Complex r = ary[i+offset+p] * now;
        ary[i+offset] = l+r;
        ary[i+offset+p] = l-r;
      }
      now *= sum_e[__builtin_ctz(~(unsigned int)(s))];
    }
  }
}

template<class Float, enable_if_t<is_floating_point<Float>::value>* = nullptr>
void butterfly_inv(vector<complex<Float>> &ary) {
  int n = int(ary.size());
  int h = ceil_pow2(n);

  using Complex = complex<Float>;
  static bool first = true;
  static Complex sum_ie[30];
  if(first) {
    first = false;
    Complex now = 1.0;
    for(int i = 0; i < 28; i++) {
      Complex es = polar(Float(1.0), Float(PI)/(1<<(i+1)));
      sum_ie[i] = conj(es) * now;
      now *= es;
    }
  }
  for(int ph = h; ph >= 1; ph--) {
    int w = 1<<(ph-1), p = 1<<(h-ph);
    Complex inow = Complex(1.0, 0);
    for(int s = 0; s < w; s++) {
      int offset = s<<(h-ph+1);
      for(int i = 0; i < p; i++) {
        Complex l = ary[i+offset];
        Complex r = ary[i+offset+p];
        ary[i+offset] = l+r;
        ary[i+offset+p] = (l-r) * inow;
      }
      inow *= sum_ie[__builtin_ctz(~(unsigned int)(s))];
    }
  }
  Complex in(1.0/n, 0);
  for(int i = 0; i < n; i++) ary[i] *= in;
}

template<class Complex, enable_if_t<is_complex<Complex>::value>* = nullptr>
vector<Complex> convolution(vector<Complex> a, vector<Complex> b) {
  int n = int(a.size()), m = int(b.size());
  if(!n || !m) return {};
  if(min(n, m) <= 60) {
    if(n < m) {
      swap(n, m);
      swap(a, b);
    }
    vector<Complex> ans(n+m-1);
    for(int i = 0; i < n; i++) {
      for(int j = 0; j < m; j++) {
        ans[i+j] += a[i] * b[j];
      }
    }
    return ans;
  }
  int z = 1<<ceil_pow2(n+m-1);
  a.resize(z);
  butterfly(a);
  b.resize(z);
  butterfly(b);
  for(int i = 0; i < z; i++) {
    a[i] *= b[i];
  }
  butterfly_inv(a);
  a.resize(n+m-1);
  return a;
}

template<class Float, enable_if_t<is_floating_point<Float>::value>* = nullptr>
vector<Float> convolution(vector<Float> &a, vector<Float> &b) {
  int n = int(a.size()), m = int(b.size());
  if(!n || !m) return {};

  using Complex = complex<Float>;
  vector<Complex> a2(n), b2(m);
  for(int i = 0; i < n; i++) a2[i] = Complex(a[i], 0);
  for(int i = 0; i < m; i++) b2[i] = Complex(b[i], 0);
  vector<Complex> c2 = convolution(move(a2), move(b2));
  vector<Float> c(n+m-1);
  for(int i = 0; i < n+m-1; i++) c[i] = c2[i].real();
  return c;
}

//modulo1 998244353
//modulo2 1000000007
//vector<mint<m>> convolution(vector<mint<m>>, vector<mint<m>>)
//vector<T> convolution<mod = modulo1>(vector<T>&, vector<T>&) ##is_integral<T>::value == true
//vector<int64_t> convolution_ll(vector<int64_t>&, vector<int64_t>&)
//vector<Complex> convolution(vector<Complex>, vector<Complex>)
//vector<Float> convolution(vector<Float>&, vector<Float>&)

} // namespace fft

struct combination {
  using Mint = fft::mint<fft::modulo1>;
  vector<Mint> frac, ifrac;
  combination(int n):frac(n+1), ifrac(n+1) {
    frac[0] = 1;
    for (int i = 1; i <= n; ++i) frac[i] = frac[i-1]*i;
    ifrac[n] = frac[n].inv();
    for (int i = n; i >= 1; --i) ifrac[i-1] = ifrac[i]*i;
  }
  Mint operator()(int n, int k) {
    if (k < 0 || k > n) return 0;
    return frac[n]*ifrac[k]*ifrac[n-k];
  }
} c(1000000);

#define AL 26

//head

string s;
int cnt[AL];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> s;
  rep(i, s.size()) cnt[s[i]-'a']++;
  vector<fft::mint<fft::modulo1>> ans(1, 1);
  rep(i, AL) {
    rep(j, ans.size()) {
      ans[j] *= c.ifrac[j];
    }
    vector<fft::mint<fft::modulo1>> now(cnt[i]+1);
    rep(j, cnt[i]+1) now[j] = c.ifrac[j];
    ans = fft::convolution(ans, now);
    rep(j, ans.size()) ans[j] *= c.frac[j];
  }
  cout << accumulate(ans.begin()+1, ans.end(), fft::mint<fft::modulo1>()).x << endl;
}
0