QOJ.ac
QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#180733 | #6513. Expression 3 | ClHg2 | TL | 2682ms | 73808kb | C++14 | 7.3kb | 2023-09-16 11:00:38 | 2023-09-16 11:00:39 |
Judging History
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, kMax4N = kMaxN * 4;
int n;
int fac[kMaxN], inv_fac[kMaxN], a[kMaxN], b[kMaxN], c[kMaxN];
std::string str;
Poly f[kMax4N], g[kMax4N];
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;
}
#define LC p << 1
#define RC (p << 1 | 1)
void Build(int p, int l, int r) {
if (l == r) {
f[p] = {{c[l], 1}}, g[p] = {{kP - l, 1}};
return;
}
int mid = (l + r) >> 1;
Build(LC, l, mid), Build(RC, mid + 1, r);
f[p] = f[LC] * f[RC], g[p] = g[LC] * g[RC];
}
void Solve(int p, int l, int r, Poly h) {
if (h.Size() >= g[p].Size()) h -= h / g[p] * g[p], h.Resize(g[p].Size() - 1);
if (l == r) {
b[l] = h[0];
return;
}
int mid = (l + r) >> 1;
Solve(LC, l, mid, h), Solve(RC, mid + 1, r, h * f[LC]);
}
#undef LC
#undef RC
} // 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();
Build(1, 1, n - 1);
Solve(1, 1, n - 1, Poly({{1}}));
int128_t ans = a[0];
for (int i = 1; i < n; ++i) {
int64_t val = int64_t{a[i]} * b[i] % kP * inv_fac[i];
ans += (str[i] == '+' ? val : -val);
}
cout << mod::Fix(ans % kP * fac[n - 1] % kP) << "\n";
return 0;
}
详细
Test #1:
score: 100
Accepted
time: 2ms
memory: 44680kb
input:
4 9 1 4 1 -+-
output:
46
result:
ok 1 number(s): "46"
Test #2:
score: 0
Accepted
time: 7ms
memory: 43892kb
input:
5 1 2 3 4 5 +-+-
output:
998244313
result:
ok 1 number(s): "998244313"
Test #3:
score: 0
Accepted
time: 2682ms
memory: 73808kb
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:
178167352
result:
ok 1 number(s): "178167352"
Test #4:
score: -100
Time Limit Exceeded
input:
200000 109044620 745578941 396599814 756923982 940933214 875346257 378089839 792684563 491924893 782192923 208569108 421583135 814903710 690275542 15773609 364566266 12890134 661702679 640270667 615999192 13352194 325560419 385152885 265008089 570536451 282429805 331946208 255056541 813809151 150995...