#660781 (C++17) No.1533 Don't be Negative!

提出ソース

結果

問題	No.1533 Don't be Negative!
ユーザー	tatyam
提出日時	2021-05-28 02:49:04
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	415 ms / 8,000 ms
コード長	10,269 bytes
コンパイル時間	3,044 ms
コンパイル使用メモリ	227,672 KB
実行使用メモリ	18,508 KB
最終ジャッジ日時	2024-11-06 19:39:53
合計ジャッジ時間	12,329 ms
ジャッジサーバーID （参考情報）	judge4 / judge3

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 6,820 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,816 KB
testcase_03	AC	14 ms 6,816 KB
testcase_04	AC	2 ms 6,820 KB
testcase_05	AC	2 ms 6,816 KB
testcase_06	AC	2 ms 6,820 KB
testcase_07	AC	2 ms 6,820 KB
testcase_08	AC	2 ms 6,820 KB
testcase_09	AC	2 ms 6,820 KB
testcase_10	AC	2 ms 6,820 KB
testcase_11	AC	102 ms 6,848 KB
testcase_12	AC	96 ms 6,820 KB
testcase_13	AC	24 ms 6,816 KB
testcase_14	AC	48 ms 6,820 KB
testcase_15	AC	98 ms 6,816 KB
testcase_16	AC	199 ms 9,984 KB
testcase_17	AC	24 ms 6,816 KB
testcase_18	AC	101 ms 6,824 KB
testcase_19	AC	49 ms 6,816 KB
testcase_20	AC	96 ms 6,820 KB
testcase_21	AC	96 ms 6,816 KB
testcase_22	AC	105 ms 7,196 KB
testcase_23	AC	2 ms 6,816 KB
testcase_24	AC	103 ms 6,928 KB
testcase_25	AC	102 ms 7,048 KB
testcase_26	AC	48 ms 6,816 KB
testcase_27	AC	51 ms 6,816 KB
testcase_28	AC	104 ms 7,168 KB
testcase_29	AC	199 ms 9,848 KB
testcase_30	AC	408 ms 18,144 KB
testcase_31	AC	24 ms 6,816 KB
testcase_32	AC	95 ms 6,820 KB
testcase_33	AC	210 ms 11,252 KB
testcase_34	AC	7 ms 6,820 KB
testcase_35	AC	2 ms 6,820 KB
testcase_36	AC	204 ms 10,988 KB
testcase_37	AC	52 ms 6,824 KB
testcase_38	AC	208 ms 11,060 KB
testcase_39	AC	199 ms 10,048 KB
testcase_40	AC	209 ms 11,212 KB
testcase_41	AC	196 ms 9,796 KB
testcase_42	AC	206 ms 10,912 KB
testcase_43	AC	199 ms 9,968 KB
testcase_44	AC	104 ms 7,268 KB
testcase_45	AC	207 ms 10,804 KB
testcase_46	AC	207 ms 10,932 KB
testcase_47	AC	408 ms 16,672 KB
testcase_48	AC	209 ms 11,068 KB
testcase_49	AC	199 ms 9,984 KB
testcase_50	AC	413 ms 18,344 KB
testcase_51	AC	410 ms 16,728 KB
testcase_52	AC	217 ms 11,504 KB
testcase_53	AC	415 ms 18,188 KB
testcase_54	AC	415 ms 18,380 KB
testcase_55	AC	414 ms 18,508 KB
testcase_56	AC	212 ms 11,556 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;
#ifdef DEBUG
int __lg(int n){ return 31 - __builtin_clz(n); }
#endif

template <class T> vector<T> operator-(vector<T> a) {
  for (auto&& e : a) e = -e;
  return a;
}
template <class T> vector<T>& operator+=(vector<T>& a, const vector<T>& b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < (int)b.size(); ++i) a[i] += b[i];
  return a;
}
template <class T> vector<T> operator+(vector<T> a, const vector<T>& b) {
  return a += b;
}
template <class T> vector<T>& operator-=(vector<T>& a, const vector<T>& b) {
  a.resize(max(a.size(), b.size()));
  for (int i = 0; i < (int)b.size(); ++i) a[i] -= b[i];
  return a;
}
template <class T> vector<T> operator-(vector<T> a, const vector<T>& b) {
  return a -= b;
}
template <class T> vector<T>& operator<<=(vector<T>& a, size_t n) {
  return a.insert(begin(a), n, 0), a;
}
template <class T> vector<T> operator<<(vector<T> a, size_t n) {
  return a <<= n;
}
template <class T> vector<T>& operator>>=(vector<T>& a, size_t n) {
  return a.erase(begin(a), begin(a) + min(a.size(), n)), a;
}
template <class T> vector<T> operator>>(vector<T> a, size_t n) {
  return a >>= n;
}
template <class T> vector<T> operator*(const vector<T>& a, const vector<T>& b) {
  if (a.empty() or b.empty()) return {};
  vector<T> res(a.size() + b.size() - 1);
  for (int i = 0; i < (int)a.size(); ++i)
    for (int j = 0; j < (int)b.size(); ++j) res[i + j] += a[i] * b[j];
  return res;
}
template <class T> vector<T>& operator*=(vector<T>& a, const vector<T>& b) {
  return a = a * b;
}
template <class T> vector<T> inverse(const vector<T>& a) {
  assert(not a.empty() and not (a[0] == 0));
  vector<T> b{1 / a[0]};
  while (b.size() < a.size()) {
    vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));
    x *= b * b;
    b.resize(2 * b.size());
    for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = -x[i];
  }
  return {begin(b), begin(b) + a.size()};
}
template <class T> vector<T> operator/(vector<T> a, vector<T> b) {
  if (a.size() < b.size()) return {};
  reverse(begin(a), end(a)), reverse(begin(b), end(b));
  int n = a.size() - b.size() + 1;
  a.resize(n), b.resize(n);
  a *= inverse(b);
  return {rend(a) - n, rend(a)};
}
template <class T> vector<T>& operator/=(vector<T>& a, const vector<T>& b) {
  return a = a / b;
}
template <class T> vector<T> operator%(vector<T> a, const vector<T>& b) {
  if (a.size() < b.size()) return a;
  a -= a / b * b;
  return {begin(a), begin(a) + (b.size() - 1)};
}
template <class T> vector<T>& operator%=(vector<T>& a, const vector<T>& b) {
  return a = a % b;
}
template <class T> vector<T> derivative(const vector<T>& a) {
  vector<T> res(max((int)a.size() - 1, 0));
  for (int i = 0; i < (int)res.size(); ++i) res[i] = (i + 1) * a[i + 1];
  return res;
}
template <class T> vector<T> primitive(const vector<T>& a) {
  vector<T> res(a.size() + 1);
  for (int i = 1; i < (int)res.size(); ++i) res[i] = a[i - 1] / i;
  return res;
}
template <class T> vector<T> logarithm(const vector<T>& a) {
  assert(not a.empty() and a[0] == 1);
  auto res = primitive(derivative(a) * inverse(a));
  return {begin(res), begin(res) + a.size()};
}
template <class T> vector<T> exponent(const vector<T>& a) {
  assert(a.empty() or a[0] == 0);
  vector<T> b{1};
  while (b.size() < a.size()) {
    vector<T> x(begin(a), begin(a) + min(a.size(), 2 * b.size()));
    x[0] += 1;
    b.resize(2 * b.size());
    x -= logarithm(b);
    x *= {begin(b), begin(b) + b.size() / 2};
    for (auto i = b.size() / 2; i < min(x.size(), b.size()); ++i) b[i] = x[i];
  }
  return {begin(b), begin(b) + a.size()};
}

template <class T, class Op = multiplies<T>>
constexpr T power(T a, long long n, Op op = Op(), T e = {1}) {
  assert(n >= 0);
  while (n) {
    if (n & 1) e = op(e, a);
    if (n >>= 1) a = op(a, a);
  }
  return e;
}

template <class T> void ntt(vector<T>& a, bool inverse) {
  int n = size(a);
  assert((n & (n - 1)) == 0);
  if (n < 2) return;
  assert((T::mod - 1) % n == 0);
  static vector<T> w{1}, iw{1};
  for (int m = size(w); m < n / 2; m *= 2) {
    static T root = 2;
    while (power(root, (T::mod - 1) / 2) == 1) root += 1;
    T dw = power(root, (T::mod - 1) / (4 * m)), idw = 1 / dw;
    w.resize(2 * m), iw.resize(2 * m);
    for (int i = 0; i < m; ++i) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * idw;
  }
  if (not inverse) {
    for (int m = n; m >>= 1; ) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j] * w[k];
          a[i] = x + y, a[j] = x - y;
        }
      }
    }
  } else {
    for (int m = 1; m < n; m *= 2) {
      for (int s = 0, k = 0; s < n; s += 2 * m, ++k) {
        for (int i = s, j = s + m; i < s + m; ++i, ++j) {
          T x = a[i], y = a[j];
          a[i] = x + y, a[j] = (x - y) * iw[k];
        }
      }
    }
    auto inv = 1 / T(n);
    for (auto&& e : a) e *= inv;
  }
}

template <unsigned M> struct montgomery {
  using m = montgomery;
  static constexpr unsigned mod = M, neg_inv = [] {
    static_assert(mod < 1 << 30 and mod & 1);
    auto inv = mod;
    while (mod * inv != 1) inv *= 2 - mod * inv;
    return -inv;
  }(), sq = -(uint64_t)mod % mod;
  static unsigned reduce(uint64_t x) {
    return (x + (uint64_t)mod * ((unsigned)x * neg_inv)) >> 32;
  }
  unsigned v;
  montgomery() : v(0) {}
  montgomery(long long x) {
    if ((x %= mod) < 0) x += mod;
    v = reduce((uint64_t)x * sq);
  }
  int get() const {
    auto res = reduce(v);
    return res < mod ? res : res - mod;
  }
  m operator-() const { return m() -= *this; }
  m& operator+=(m b) {
    if ((int)(v += b.v - 2 * mod) < 0) v += 2 * mod;
    return *this;
  }
  m& operator-=(m b) {
    if ((int)(v -= b.v) < 0) v += 2 * mod;
    return *this;
  }
  m& operator*=(m b) {
    v = reduce((uint64_t)v * b.v);
    return *this;
  }
  m& operator/=(m b) { return *this *= power(b, mod - 2); }
  friend m operator+(m a, m b) { return a += b; }
  friend m operator-(m a, m b) { return a -= b; }
  friend m operator*(m a, m b) { return a *= b; }
  friend m operator/(m a, m b) { return a /= b; }
  friend bool operator==(m a, m b) { return a.v == b.v; }
};

using mint = montgomery<998244353>;

vector<mint> fact, inv_fact, minv;
void prepare(int n) {
  fact.resize(n + 1), inv_fact.resize(n + 1), minv.resize(n + 1);
  for (int i = 0; i <= n; ++i) fact[i] = i ? fact[i - 1] * i : 1;
  inv_fact[n] = power(fact[n], mint::mod - 2);
  for (int i = n; i--; ) inv_fact[i] = (i + 1) * inv_fact[i + 1];
  for (int i = 1; i <= n; ++i) minv[i] = inv_fact[i] * fact[i - 1];
}
mint binom(int n, int k) {
  if (k < 0 or k > n) return 0;
  return fact[n] * inv_fact[k] * inv_fact[n - k];
}
template <> mint& mint::operator/=(mint b) {
  return *this *= b.v < minv.size() ? minv[b.v] : power(b, mod - 2);
}

struct dual_vec {
  vector<mint> v;
  void resize(int sz) { v.resize(sz); }
};
dual_vec mfft(const vector<mint>& a, int sz) {
  dual_vec fa{a};
  fa.resize(sz), ntt(fa.v, false);
  return fa;
}
dual_vec operator*(dual_vec a, const dual_vec& b) {
  for (int i = 0; i < (int)a.v.size(); ++i) a.v[i] *= b.v[i];
  return a;
}
vector<mint> ifft(dual_vec fa, int n) {
  ntt(fa.v, true), fa.resize(n);
  return fa.v;
}

vector<mint> operator*(const vector<mint>& a, const vector<mint>& b) {
  if (a.empty() or b.empty()) return {};
  int n = a.size(), m = b.size(), sz = 1 << __lg(2 * (n + m - 1) - 1);
  if (min(n, m) < 30) {
    vector<mint> c(n + m - 1);
    for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j)
      c[i + j] += a[i] * b[j];
    return c;
  }
  if (a == b) {
    dual_vec fl = mfft(a, sz);
    return ifft(fl * fl, n + m - 1);
  }
  return ifft(mfft(a, sz) * mfft(b, sz), n + m - 1);
}
vector<mint> inverse(const vector<mint>& a) {
  assert(not a.empty() and not (a[0] == 0));
  vector<mint> b{1 / a[0]};
  for (int m = 1; m < (int)a.size(); m *= 2) {
    vector<mint> x(begin(a), begin(a) + min<int>(a.size(), 2 * m));
    dual_vec fb = mfft(b, 2 * m);
    x = ifft(mfft(x, 2 * m) * fb, 2 * m);
    fill(begin(x), begin(x) + m, 0);
    x = -ifft(mfft(x, 2 * m) * fb, 2 * m);
    b.insert(end(b), begin(x) + m, end(x));
  }
  return {begin(b), begin(b) + a.size()};
}
vector<mint> exponent(const vector<mint>& a) {
  assert(a.empty() or a[0] == 0);
  vector<mint> b{1, 1 < a.size() ? a[1] : 0}, c{1};
  dual_vec half_fc = mfft(c, 1), fc = mfft(c, 2);
  for (int m = 2; m < (int)a.size(); m *= 2) {
    dual_vec fb = mfft(b, 2 * m), half_fb = fb;
    half_fb.resize(m);
    half_fc = fc;
    vector<mint> z = ifft(half_fb * half_fc, m);
    fill(begin(z), begin(z) + m / 2, 0);
    z = -ifft(mfft(z, m) * half_fc, m);
    c.insert(end(c), begin(z) + m / 2, end(z));
    fc = mfft(c, 2 * m);
    vector<mint> x(begin(a), begin(a) + min<int>(a.size(), m));
    x = derivative(x), x.push_back(0);
    dual_vec fx = mfft(x, m);
    x = ifft(fx * half_fb, m);
    x -= derivative(b);
    x.resize(2 * m);
    for (int i = 0; i < m - 1; ++i) x[m + i] = x[i], x[i] = 0;
    x = ifft(mfft(x, 2 * m) * fc, 2 * m);
    x = primitive(x), x.pop_back();
    for (int i = m; i < min<int>(a.size(), 2 * m); ++i) x[i] += a[i];
    fill(begin(x), begin(x) + m, 0);
    x = ifft(mfft(x, 2 * m) * fb, 2 * m);
    b.insert(end(b), begin(x) + m, end(x));
  }
  return {begin(b), begin(b) + a.size()};
}

vector<mint> power(vector<mint> a, long long m) {
  int n = size(a), tz = 0;
  while (tz < n and a[tz] == 0) ++tz;
  if (n == 0 or (tz and m >= (n + tz - 1) / tz)) return vector<mint>(n);
  a >>= tz;
  auto a0 = a[0];
  a *= vector<mint>{1 / a0};
  a = exponent(logarithm(a) * vector<mint>{m});
  a *= vector<mint>{power(a0, m)};
  return a <<= tz * m;
}
vector<mint> resize(vector<mint> a, int sz) {
    a.resize(sz);
    return a;
}

int main(){
    int N, M, K;
    cin >> N >> M >> K;
    if(M == K) M--;
    if(M == 0)return puts("0") & 0;
    vector<mint> F(M * 2 + 1);
    mint s = 0;
    for(int i = -M; i <= M; i++) if(i != K && i != -K){
        F[i + M] = 1;
        s += 1;
    }
    vector<mint> S(M + 1);
    S[M] = s;
    auto Q = vector<mint>{1, -1} * (F - S) * (F - S);
    F.resize(N * M);
    auto P = power(F, N + 2);
    Q.resize(N * M);
    cout << (P * inverse(Q))[M * N - 1].get() << endl;
}

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結果

テストケース

ソースコード