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IDProblemSubmitterResultTimeMemoryLanguageFile sizeSubmit timeJudge time
#180714#6513. Expression 3ClHg2TL 1ms5664kbC++146.8kb2023-09-16 10:46:392023-09-16 10:46:39

Judging History

你现在查看的是最新测评结果

  • [2024-02-14 13:23:19]
  • hack成功,自动添加数据
  • (/hack/531)
  • [2023-09-16 10:46:39]
  • 评测
  • 测评结果:TL
  • 用时:1ms
  • 内存:5664kb
  • [2023-09-16 10:46:39]
  • 提交

answer

#include <algorithm>
#include <cstdint>
#include <iostream>
#include <string>
#include <utility>
#include <vector>

namespace {
using std::cin;
using std::cout;
using std::int64_t;
using int128_t = __int128;

const int kP = 998244353, kInv2 = (kP + 1) / 2, kG = 3, kInvG = 332748118;

namespace mod {
inline int Mod(int x) { return x >= kP ? x - kP : x; }
inline void Add(int& x, int y) { x = Mod(x + y); }
inline int Fix(int x) { return x + (x >> 31 & kP); }
inline void Sub(int& x, int y) { x = Fix(x - y); }
inline int Unm(int x) { return x ? kP - x : x; }
inline void Neg(int& x) { x = Unm(x); }

int64_t Pow(int64_t a, int b) {
  int64_t ans = 1;

  while (b) {
    if (b & 1) ans = ans * a % kP;
    a = a * a % kP, b >>= 1;
  }

  return ans;
}

inline int64_t Inv(int64_t a) { return Pow(a, kP - 2); }
}  // namespace mod

namespace poly {
inline int Ceil(int n) {
  if (n == 1) return 1;
  return 1 << (32 - __builtin_clz(n - 1));
}

struct Poly {
  std::vector<int> c;
  int Size() const { return c.size(); }
  void Resize(int n) { c.resize(n); }
  void Reverse() { std::reverse(c.begin(), c.end()); }
  int operator[](int i) const { return c[i]; }
  int& operator[](int i) { return c[i]; }
};

Poly& operator+=(Poly& f, const Poly& g) {
  int n = f.Size(), m = g.Size(), len = std::max(n, m);
  f.Resize(len);
  for (int i = 0; i < m; ++i) mod::Add(f[i], g[i]);
  return f;
}

Poly operator+(Poly f, const Poly& g) { return f += g; }

Poly& operator-=(Poly& f, const Poly& g) {
  int n = f.Size(), m = g.Size(), len = std::max(n, m);
  f.Resize(len);
  for (int i = 0; i < m; ++i) mod::Sub(f[i], g[i]);
  return f;
}

Poly operator-(Poly f, const Poly& g) { return f -= g; }

Poly operator-(Poly f) {
  int n = f.Size();
  for (int i = 0; i < n; ++i) mod::Neg(f[i]);
  return f;
}

Poly& operator*=(Poly& f, int64_t k) {
  int n = f.Size();
  for (int i = 0; i < n; ++i) f[i] = f[i] * k % kP;
  return f;
}

Poly operator*(Poly f, int64_t k) { return f *= k; }

Poly rev;

void InitRev(int n) {
  int m = rev.Size();
  if (m == n) return;
  rev.Resize(n);
  int e = __builtin_ctz(n);

  for (int i = 1; i < n; ++i) {
    rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (e - 1));
  }
}

Poly w = {{0}};

void InitW(int n, int g) {
  int m = w.Size();
  if (m == n && w[0] == g) return;
  w[0] = g, w.Resize(n);

  for (int i = 1; i < n; i <<= 1) {
    int64_t w_i = mod::Pow(g, (kP - 1) / (i << 1)), w_i_j = 1;
    for (int j = 0; j < i; ++j) w[i | j] = w_i_j, w_i_j = w_i_j * w_i % kP;
  }
}

void Ntt(Poly& f, int type) {
  int n = f.Size();
  InitRev(n);
  InitW(n, type == 1 ? kG : kInvG);

  for (int i = 0; i < n; ++i) {
    if (i < rev[i]) std::swap(f[i], f[rev[i]]);
  }

  for (int i = 1; i < n; i <<= 1) {
    for (int j = 0; j < n; j += (i << 1)) {
      for (int k = 0; k < i; ++k) {
        int x = f[j | k], y = int64_t{f[i | j | k]} * w[i | k] % kP;
        f[j | k] = mod::Mod(x + y), f[i | j | k] = mod::Fix(x - y);
      }
    }
  }

  if (type == -1) {
    int64_t inv = mod::Inv(n);
    for (int i = 0; i < n; ++i) f[i] = f[i] * inv % kP;
  }
}

Poly& operator*=(Poly& f, Poly g) {
  int n = f.Size(), m = g.Size(), len = Ceil(n + m - 1);
  f.Resize(len), g.Resize(len);
  Ntt(f, 1), Ntt(g, 1);
  for (int i = 0; i < len; ++i) f[i] = int64_t{f[i]} * g[i] % kP;
  Ntt(f, -1);
  f.Resize(n + m - 1);
  return f;
}

Poly operator*(Poly f, const Poly& g) { return f *= g; }

Poly Slice(const Poly& f, int l, int r) {
  Poly g;
  g.Resize(r - l + 1);
  for (int i = 0; i <= r - l; ++i) g[i] = f[i + l];
  return g;
}

Poly Inv(Poly f) {
  int n = f.Size(), len = Ceil(n);
  f.Resize(len);
  Poly g = {{static_cast<int>(mod::Inv(f[0]))}};

  for (int w = 2; w <= len; w <<= 1) {
    g = g * 2 - g * g * Slice(f, 0, w - 1);
    g.Resize(w);
  }

  g.Resize(n);
  return g;
}

Poly& operator/=(Poly& f, Poly g) {
  int n = f.Size(), m = g.Size(), len = n - m + 1;
  f.Reverse(), g.Reverse();
  f.Resize(len), g.Resize(len);
  f *= Inv(g);
  f.Resize(len), f.Reverse();
  return f;
}

Poly operator/(Poly f, const Poly& g) { return f /= g; }

Poly Sqrt(Poly f) {
  int n = f.Size(), len = Ceil(n);
  f.Resize(len);
  Poly g = {{1}};

  for (int w = 2; w <= len; w <<= 1) {
    Poly h = g;
    h.Resize(w);
    g = (g * g + Slice(f, 0, w - 1)) * Inv(h) * kInv2;
    g.Resize(w);
  }

  g.Resize(n);
  if (g[0] * 2 > kP) return -g;
  return g;
}

Poly Derivative(const Poly& f) {
  int n = f.Size();
  if (n == 1) return {{0}};
  Poly g;
  g.Resize(n - 1);
  for (int i = 0; i < n - 1; ++i) g[i] = int64_t{f[i + 1]} * (i + 1) % kP;
  return g;
}

Poly inv = {{0, 1}};

void InitInv(int n) {
  int m = inv.Size();
  if (m - 1 >= n) return;
  inv.Resize(n + 1);

  for (int i = m; i <= n; ++i) {
    inv[i] = int64_t{inv[kP % i]} * (kP - kP / i) % kP;
  }
}

Poly Integration(const Poly& f) {
  int n = f.Size();
  InitInv(n);
  Poly g;
  g.Resize(n + 1), g[0] = 0;
  for (int i = 1; i <= n; ++i) g[i] = int64_t{f[i - 1]} * inv[i] % kP;
  return g;
}

Poly Ln(const Poly& f) {
  int n = f.Size();
  Poly g = Integration(Derivative(f) * Inv(f));
  g.Resize(n);
  return g;
}

Poly Exp(Poly f) {
  int n = f.Size(), len = Ceil(n);
  f.Resize(len);
  Poly g = {{1}};

  for (int w = 2; w <= len; w <<= 1) {
    Poly h = g;
    h.Resize(w);
    g -= (Ln(h) - Slice(f, 0, w - 1)) * g;
    g.Resize(w);
  }

  g.Resize(n);
  return g;
}

Poly Pow(Poly f, int k) {
  int n = f.Size(), p = 0;
  while (p < n && f[p] == 0) ++p;
  if (p == n) return f;
  int x = f[p];
  f = Slice(f, p, n - 1) * mod::Inv(x);
  f = Exp(Ln(f) * k);
  Poly g;
  g.Resize(n);
  for (int i = p * k; i < n; ++i) g[i] = f[i - p * k];
  return g * mod::Pow(x, k);
}
}  // namespace poly

using poly::Poly;

const int kMaxN = 2.0e5 + 5;
int n;
int fac[kMaxN], inv_fac[kMaxN], a[kMaxN], b[kMaxN], c[kMaxN];
std::string str;
Poly f = {{1}};

void InitChoose() {
  fac[0] = 1;
  for (int i = 1; i <= n; ++i) fac[i] = int64_t{fac[i - 1]} * i % kP;
  inv_fac[n] = mod::Inv(fac[n]);
  for (int i = n; i >= 1; --i) inv_fac[i - 1] = int64_t{inv_fac[i]} * i % kP;
}
}  // namespace

int main() {
  cin.tie(nullptr);
  std::ios::sync_with_stdio(false);
  cin >> n;
  for (int i = 0; i < n; ++i) cin >> a[i];
  cin >> str, str = std::string(" ").append(str);
  for (int i = 1; i < n; ++i) c[i] = mod::Fix((str[i] == '+' ? 1 : -1) - i);
  InitChoose();

  for (int i = 1; i < n; ++i) {
    int64_t val = 0;
    for (int j = f.Size() - 1; j >= 0; --j) val = (val * i + f[j]) % kP;
    b[i] = (str[i] == '+' ? val : -val), f *= Poly{{c[i], 1}};
  }

  int128_t ans = a[0];
  for (int i = 1; i < n; ++i) ans += int64_t{a[i]} * b[i] % kP * inv_fac[i];
  cout << mod::Fix(ans % kP * fac[n - 1] % kP) << "\n";
  return 0;
}

Details

Tip: Click on the bar to expand more detailed information

Test #1:

score: 100
Accepted
time: 1ms
memory: 5664kb

input:

4
9 1 4 1
-+-

output:

46

result:

ok 1 number(s): "46"

Test #2:

score: 0
Accepted
time: 0ms
memory: 3644kb

input:

5
1 2 3 4 5
+-+-

output:

998244313

result:

ok 1 number(s): "998244313"

Test #3:

score: -100
Time Limit Exceeded

input:

100000
664815434 205025136 871445392 797947979 379688564 336946672 231295524 401655676 526374414 670533644 156882283 372427821 700299596 166140732 677498490 44858761 185182210 559696133 813911251 842364231 681916958 114039865 222372111 784286397 437994571 152137641 650875922 613727135 209302742 5321...

output:


result: