#646646 (C++17) No.1474 かさまＪ

提出ソース
結果

問題	No.1474 かさまＪ
ユーザー	opt
提出日時	2021-04-09 23:27:24
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	158 ms / 2,500 ms
コード長	15,596 bytes
コンパイル時間	3,986 ms
コンパイル使用メモリ	270,836 KB
実行使用メモリ	6,840 KB
最終ジャッジ日時	2023-09-07 13:18:17
合計ジャッジ時間	6,152 ms
ジャッジサーバーID （参考情報）	judge11 / judge13
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	2 ms 4,384 KB
testcase_01	AC	1 ms 4,380 KB
testcase_02	AC	1 ms 4,380 KB
testcase_03	AC	2 ms 4,380 KB
testcase_04	AC	2 ms 4,376 KB
testcase_05	AC	67 ms 5,472 KB
testcase_06	AC	13 ms 4,376 KB
testcase_07	AC	2 ms 4,380 KB
testcase_08	AC	1 ms 4,376 KB
testcase_09	AC	95 ms 5,388 KB
testcase_10	AC	6 ms 4,376 KB
testcase_11	AC	2 ms 4,376 KB
testcase_12	AC	2 ms 4,376 KB
testcase_13	AC	99 ms 5,912 KB
testcase_14	AC	31 ms 4,380 KB
testcase_15	AC	15 ms 4,376 KB
testcase_16	AC	5 ms 4,380 KB
testcase_17	AC	34 ms 4,900 KB
testcase_18	AC	126 ms 6,472 KB
testcase_19	AC	150 ms 6,748 KB
testcase_20	AC	158 ms 6,840 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

raw source code
#include <bits/stdc++.h>
using namespace std;
#include <atcoder/all>
using namespace atcoder;
// input and output of modint
istream &operator>>(istream &is, modint998244353 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); }
istream &operator>>(istream &is, modint1000000007 &a) { long long v; is >> v; a = v; return is; }
ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); }
template<int m> istream &operator>>(istream &is, static_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> ostream &operator<<(ostream &os, const static_modint<m> &a) { return os << a.val(); }
template<int m> istream &operator>>(istream &is, dynamic_modint<m> &a) { long long v; is >> v; a = v; return is; }
template<int m> ostream &operator<<(ostream &os, const dynamic_modint<m> &a) { return os << a.val(); }
#define rep_(i, a_, b_, a, b, ...) for (int i = (a), lim##i = (b); i < lim##i; ++i)
#define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
#define drep_(i, a_, b_, a, b, ...) for (int i = (a)-1, lim##i = (b); i >= lim##i; --i)
#define drep(i, ...) drep_(i, __VA_ARGS__, __VA_ARGS__, __VA_ARGS__, 0)
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#ifdef LOCAL
void debug_out() { cerr << endl; }
template <class Head, class... Tail> void debug_out(Head H, Tail... T) { cerr << ' ' << H; debug_out(T...); }
#define debug(...) cerr << 'L' << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#define dump(x) cerr << 'L' << __LINE__ << " " << #x << " = " << (x) << endl
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
template<class T> using V = vector<T>;
using ll = long long;
using ld = long double;
using Vi = V<int>;  using VVi = V<Vi>;
using Vl = V<ll>;   using VVl = V<Vl>;
using Vd = V<ld>;   using VVd = V<Vd>;
using Vb = V<bool>; using VVb = V<Vb>;
template<class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
template<class T> vector<T> make_vec(size_t n, T a) { return vector<T>(n, a); }
template<class... Ts> auto make_vec(size_t n, Ts... ts) { return vector<decltype(make_vec(ts...))>(n, make_vec(ts...)); }
template<class T> inline int sz(const T &x) { return x.size(); }
template<class T> inline bool chmin(T &a, const T b) { if (a > b) { a = b; return true; } return false; }
template<class T> inline bool chmax(T &a, const T b) { if (a < b) { a = b; return true; } return false; }
template<class T1, class T2> istream &operator>>(istream &is, pair<T1, T2> &p) { is >> p.first >> p.second; return is; }
template<class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p) { os << '(' << p.first << ", " << p.second << ')'; return os; }
template<class T, size_t n> istream &operator>>(istream &is, array<T, n> &v) { for (auto &e : v) is >> e; return is; }
template<class T, size_t n> ostream &operator<<(ostream &os, const  array<T, n> &v) { for (auto &e : v) os << e << ' '; return os; }
template<class T> istream &operator>>(istream &is, vector<T> &v) { for (auto &e : v) is >> e; return is; }
template<class T> ostream &operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
template<class T> inline void deduplicate(vector<T> &a) { sort(all(a)); a.erase(unique(all(a)), a.end()); }
template<class T> inline int count_between(const vector<T> &a, T l, T r) { return lower_bound(all(a), r) - lower_bound(all(a), l); } // [l, r)
inline ll ceil_div(const ll x, const ll y) { return (x+y-1) / y; } // ceil(x/y)
inline int floor_log2(const ll x) { assert(x > 0); return 63-__builtin_clzll(x); } // floor(log2(x))
inline int ceil_log2(const ll x) { assert(x > 0); return (x == 1) ? 0 : 64-__builtin_clzll(x-1); } // ceil(log2(x))
inline int popcount(const ll x) { return __builtin_popcountll(x); }
inline void fail() { cout << -1 << '\n'; exit(0); }
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
// const int INF  = (1<<30) - 1;
// const ll INFll = (1ll<<60) - 1;
// const ld EPS   = 1e-10;
// const ld PI    = acos(-1.0);
// using mint = modint998244353;
using mint = modint1000000007;
// using mint = modint;
using Vm = V<mint>; using VVm = V<Vm>;



template<typename T> struct Factorial {
  int MAX;
  vector<T> fac, finv;
  Factorial(int m = 0) : MAX(m), fac(m+1, 1), finv(m+1, 1) {
    rep(i, 2, MAX+1) fac[i] = fac[i-1] * i;
    finv[MAX] /= fac[MAX];
    drep(i, MAX+1, 3) finv[i-1] = finv[i] * i;
  }
  T binom(int n, int k) {
    if (k < 0 || n < k) return 0;
    return fac[n] * finv[k] * finv[n-k];
  }
  T perm(int n, int k) {
    if (k < 0 || n < k) return 0;
    return fac[n] * finv[n-k];
  }
};
Factorial<mint> fc;


template<class T>
struct formal_power_series : vector<T> {
  using vector<T>::vector;
  using vector<T>::operator=;
  using F = formal_power_series;

  F operator-() const {
    F res(*this);
    for (auto &e : res) e = -e;
    return res;
  }
  F &operator*=(const T &g) {
    for (auto &e : *this) e *= g;
    return *this;
  }
  F &operator/=(const T &g) {
    assert(g != T(0));
    *this *= g.inv();
    return *this;
  }
  F &operator+=(const F &g) {
    int n = this->size(), m = g.size();
    rep(i, min(n, m)) (*this)[i] += g[i];
    return *this;
  }
  F &operator-=(const F &g) {
    int n = this->size(), m = g.size();
    rep(i, min(n, m)) (*this)[i] -= g[i];
    return *this;
  }
  F &operator<<=(const int d) {
    int n = this->size();
    if (d >= n) *this = F(n);
    this->insert(this->begin(), d, 0);
    this->resize(n);
    return *this;
  }
  F &operator>>=(const int d) {
    int n = this->size();
    this->erase(this->begin(), this->begin() + min(n, d));
    this->resize(n);
    return *this;
  }

  // O(n log n)
  F inv(int d = -1) const {
    int n = this->size();
    assert(n != 0 && (*this)[0] != 0);
    if (d == -1) d = n;
    assert(d >= 0);
    F res{(*this)[0].inv()};
    for (int m = 1; m < d; m *= 2) {
      F f(this->begin(), this->begin() + min(n, 2*m));
      F g(res);
      f.resize(2*m), internal::butterfly(f);
      g.resize(2*m), internal::butterfly(g);
      rep(i, 2*m) f[i] *= g[i];
      internal::butterfly_inv(f);
      f.erase(f.begin(), f.begin() + m);
      f.resize(2*m), internal::butterfly(f);
      rep(i, 2*m) f[i] *= g[i];
      internal::butterfly_inv(f);
      T iz = T(2*m).inv(); iz *= -iz;
      rep(i, m) f[i] *= iz;
      res.insert(res.end(), f.begin(), f.begin() + m);
    }
    res.resize(d);
    return res;
  }

  // fast: FMT-friendly modulus only
  // O(n log n)
  F &multiply_inplace(const F &g, int d = -1) {
    int n = this->size();
    if (d == -1) d = n;
    assert(d >= 0);
    *this = convolution(move(*this), g);
    this->resize(d);
    return *this;
  }
  F multiply(const F &g, const int d = -1) const { return F(*this).multiply_inplace(g, d); }
  // O(n log n)
  F &divide_inplace(const F &g, int d = -1) {
    int n = this->size();
    if (d == -1) d = n;
    assert(d >= 0);
    *this = convolution(move(*this), g.inv(d));
    this->resize(d);
    return *this;
  }
  F divide(const F &g, const int d = -1) const { return F(*this).divide_inplace(g, d); }

  // // naive
  // // O(n^2)
  // F &multiply_inplace(const F &g) {
  //   int n = this->size(), m = g.size();
  //   drep(i, n) {
  //     (*this)[i] *= g[0];
  //     rep(j, 1, min(i+1, m)) (*this)[i] += (*this)[i-j] * g[j];
  //   }
  //   return *this;
  // }
  // F multiply(const F &g) const { return F(*this).multiply_inplace(g); }
  // // O(n^2)
  // F &divide_inplace(const F &g) {
  //   assert(g[0] != T(0));
  //   T ig0 = g[0].inv();
  //   int n = this->size(), m = g.size();
  //   rep(i, n) {
  //     rep(j, 1, min(i+1, m)) (*this)[i] -= (*this)[i-j] * g[j];
  //     (*this)[i] *= ig0;
  //   }
  //   return *this;
  // }
  // F divide(const F &g) const { return F(*this).divide_inplace(g); }

  // sparse
  // O(nk)
  F &multiply_inplace(vector<pair<int, T>> g) {
    int n = this->size();
    auto [d, c] = g.front();
    if (d == 0) g.erase(g.begin());
    else c = 0;
    drep(i, n) {
      (*this)[i] *= c;
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] += (*this)[i-j] * b;
      }
    }
    return *this;
  }
  F multiply(const vector<pair<int, T>> &g) const { return F(*this).multiply_inplace(g); }
  // O(nk)
  F &divide_inplace(vector<pair<int, T>> g) {
    int n = this->size();
    auto [d, c] = g.front();
    assert(d == 0 && c != T(0));
    T ic = c.inv();
    g.erase(g.begin());
    rep(i, n) {
      for (auto &[j, b] : g) {
        if (j > i) break;
        (*this)[i] -= (*this)[i-j] * b;
      }
      (*this)[i] *= ic;
    }
    return *this;
  }
  F divide(const vector<pair<int, T>> &g) const { return F(*this).divide_inplace(g); }

  // multiply and divide (1 + cz^d)
  // O(n)
  void multiply_inplace(const int d, const T c) { 
    int n = this->size();
    if (c == T(1)) drep(i, n-d) (*this)[i+d] += (*this)[i];
    else if (c == T(-1)) drep(i, n-d) (*this)[i+d] -= (*this)[i];
    else drep(i, n-d) (*this)[i+d] += (*this)[i] * c;
  }
  // O(n)
  void divide_inplace(const int d, const T c) {
    int n = this->size();
    if (c == T(1)) rep(i, n-d) (*this)[i+d] -= (*this)[i];
    else if (c == T(-1)) rep(i, n-d) (*this)[i+d] += (*this)[i];
    else rep(i, n-d) (*this)[i+d] -= (*this)[i] * c;
  }

  // O(n)
  T eval(const T &a) const {
    T x(1), res(0);
    for (auto e : *this) res += e * x, x *= a;
    return res;
  }

  // O(n)
  F &integral_inplace() {
    int n = this->size();
    assert(n > 0);
    if (n == 1) return *this = F{0};
    this->insert(this->begin(), 0);
    this->pop_back();
    vector<T> inv(n);
    inv[1] = 1;
    int p = T::mod();
    rep(i, 2, n) inv[i] = - inv[p%i] * (p/i);
    rep(i, 2, n) (*this)[i] *= inv[i];
    return *this;
  }
  F integral() const { return F(*this).integral_inplace(); }

  // O(n)
  F &derivative_inplace() {
    int n = this->size();
    assert(n > 0);
    rep(i, 2, n) (*this)[i] *= i;
    this->erase(this->begin());
    this->push_back(0);
    return *this;
  }
  F derivative() const { return F(*this).derivative_inplace(); }

  // O(n log n)
  F &log_inplace(int d = -1) {
    int n = this->size();
    assert(n > 0 && (*this)[0] == 1);
    if (d == -1) d = n;
    assert(d >= 0);
    if (d < n) this->resize(d);
    F f_inv = this->inv();
    this->derivative_inplace();
    this->multiply_inplace(f_inv);
    this->integral_inplace();
    return *this;
  }
  F log(const int d = -1) const { return F(*this).log_inplace(d); }

  // O(n log n)
  // https://arxiv.org/abs/1301.5804 (Figure 1, right)
  F &exp_inplace(int d = -1) {
    int n = this->size();
    assert(n > 0 && (*this)[0] == 0);
    if (d == -1) d = n;
    assert(d >= 0);
    F g{1}, g_fft{1, 1};
    (*this)[0] = 1;
    this->resize(d);
    F h_drv(this->derivative());
    for (int m = 2; m < d; m *= 2) {
      // prepare
      F f_fft(this->begin(), this->begin() + m);
      f_fft.resize(2*m), internal::butterfly(f_fft);

      // Step 2.a'
      {
        F _g(m);
        rep(i, m) _g[i] = f_fft[i] * g_fft[i];
        internal::butterfly_inv(_g);
        _g.erase(_g.begin(), _g.begin() + m/2);
        _g.resize(m), internal::butterfly(_g);
        rep(i, m) _g[i] *= g_fft[i];
        internal::butterfly_inv(_g);
        _g.resize(m/2);
        _g /= T(-m) * m;
        g.insert(g.end(), _g.begin(), _g.begin() + m/2);
      }

      // Step 2.b'--d'
      F t(this->begin(), this->begin() + m);
      t.derivative_inplace();
      {
        // Step 2.b'
        F r{h_drv.begin(), h_drv.begin() + m-1};
        // Step 2.c'
        r.resize(m); internal::butterfly(r);
        rep(i, m) r[i] *= f_fft[i];
        internal::butterfly_inv(r);
        r /= -m;
        // Step 2.d'
        t += r;
        t.insert(t.begin(), t.back()); t.pop_back();
      }

      // Step 2.e'
      if (2*m < d) {
        t.resize(2*m); internal::butterfly(t); 
        g_fft = g; g_fft.resize(2*m); internal::butterfly(g_fft);
        rep(i, 2*m) t[i] *= g_fft[i];
        internal::butterfly_inv(t);
        t.resize(m);
        t /= 2*m;
      }
      else { // この場合分けをしても数パーセントしか速くならない
        F g1(g.begin() + m/2, g.end());
        F s1(t.begin() + m/2, t.end());
        t.resize(m/2);
        g1.resize(m), internal::butterfly(g1);
        t.resize(m),  internal::butterfly(t);
        s1.resize(m), internal::butterfly(s1);
        rep(i, m) s1[i] = g_fft[i] * s1[i] + g1[i] * t[i];
        rep(i, m) t[i] *= g_fft[i];
        internal::butterfly_inv(t);
        internal::butterfly_inv(s1);
        rep(i, m/2) t[i+m/2] += s1[i];
        t /= m;
      }
      
      // Step 2.f'
      F v(this->begin() + m, this->begin() + min<int>(d, 2*m)); v.resize(m);
      t.insert(t.begin(), m-1, 0); t.push_back(0);
      t.integral_inplace();
      rep(i, m) v[i] -= t[m+i];

      // Step 2.g'
      v.resize(2*m); internal::butterfly(v);
      rep(i, 2*m) v[i] *= f_fft[i];
      internal::butterfly_inv(v);
      v.resize(m);
      v /= 2*m;

      // Step 2.h'
      rep(i, min(d-m, m)) (*this)[m+i] = v[i];
    }
    return *this;
  }
  F exp(const int d = -1) const { return F(*this).exp_inplace(d); }

  // O(n log n)
  F &pow_inplace(const ll k, int d = -1) {
    int n = this->size();
    if (d == -1) d = n;
    assert(d >= 0 && k >= 0);
    if (d == 0) return *this = F(0);
    if (k == 0) {
      *this = F(d);
      (*this)[0] = 1;
      return *this;
    }
    int l = 0;
    while (l < n && (*this)[l] == 0) ++l;
    if (l == n || l > (d-1)/k) return *this = F(d);
    T c{(*this)[l]};
    this->erase(this->begin(), this->begin() + l);
    *this /= c;
    this->log_inplace(d - l*k);
    *this *= k;
    this->exp_inplace();
    *this *= c.pow(k);
    this->insert(this->begin(), l*k, 0);
    return *this;
  }
  F pow(const ll k, const int d = -1) const { return F(*this).pow_inplace(k, d); }

  // O(n log n)
  F &shift_inplace(const T c) {
    int n = this->size();
    fc = Factorial<T>(n);
    rep(i, n) (*this)[i] *= fc.fac[i];
    reverse(this->begin(), this->end());
    F g(n);
    T cp = 1;
    rep(i, n) g[i] = cp * fc.finv[i], cp *= c;
    this->multiply_inplace(g, n);
    reverse(this->begin(), this->end());
    rep(i, n) (*this)[i] *= fc.finv[i];
    return *this;
  }
  F shift(const T c) const { return F(*this).shift_inplace(c); }

  F operator*(const T &g) const { return F(*this) *= g; }
  F operator/(const T &g) const { return F(*this) /= g; }
  F operator+(const F &g) const { return F(*this) += g; }
  F operator-(const F &g) const { return F(*this) -= g; }
  F operator<<(const int d) const { return F(*this) <<= d; }
  F operator>>(const int d) const { return F(*this) >>= d; }

  // for multivariable FPS
  // F operator*(const F &g) const { return this->multiply(g); }
  // F operator*=(const F &g) { return this->multiply_inplace(g); }
};


using fps = formal_power_series<mint>;


mint solve() {
  int n, mp, mq, l; cin >> n >> mp >> mq >> l;
  fc = Factorial<mint>(n + mp + mq);

  V<fps> f(n+1, fps(mq+1));
  f[0][0] = 1;
  rep(i, n) {
    int s; cin >> s;
    drep(j, n) {
      auto g = f[j];
      g.multiply_inplace(s, -1);
      g.divide_inplace(1, -1);
      g <<= 1;
      f[j+1] += g;
    }
  }

  mint ans = 0;
  rep(i, n+1) rep(j, mq+1) {
    int dz = mq - j;
    int dx = mp + mq - dz - l*i;
    ans += f[i][j] * fc.binom(n + dx - 1, dx);
  }
  return ans;
}


int main() {
  // solve();
  cout << solve() << '\n';
}
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結果

テストケース

ソースコード
