标签：namespace cos using scan str def ati 大型 cto
# include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int mod(998244353);
const int inv2(499122177);
const int maxn(1 << 18);
/*
const double pi(acos(-1));
struct Complex {
double a, b;
inline Complex() {
a = b = 0;
}
inline Complex(double _a, double _b) {
a = _a, b = _b;
}
inline Complex operator +(Complex x) const {
return Complex(a + x.a, b + x.b);
}
inline Complex operator -(Complex x) const {
return Complex(a - x.a, b - x.b);
}
inline Complex operator *(Complex x) const {
return Complex(a * x.a - b * x.b, a * x.b + b * x.a);
}
inline Complex Conj() {
return Complex(a, -b);
}
};
*/
inline int Pow(ll x, int y) {
register ll ret = 1;
for (; y; y >>= 1, x = x * x % mod)
if (y & 1) ret = ret * x % mod;
return ret;
}
inline void Inc(int &x, const int y) {
if ((x += y) >= mod) x -= mod;
}
namespace FFT {
/* all module
Complex ma[maxn], mb[maxn], w[maxn], a1[maxn], a2[maxn];
int r[maxn], l, len, a[maxn], b[maxn];
inline void DFT(Complex *p, int opt) {
register int i, j, k, t;
register Complex wn, x, y;
for (i = 0; i < len; ++i) if (r[i] < i) swap(p[r[i]], p[i]);
for (i = 1; i < len; i <<= 1)
for(t = i << 1, j = 0; j < len; j += t)
for (k = 0; k < i; ++k) {
wn = w[len / i * k];
if (opt == -1) wn.b *= -1;
x = p[j + k], y = wn * p[i + j + k];
p[j + k] = x + y, p[i + j + k] = x - y;
}
}
inline void Init(const int n) {
register int i, x, y;
for (l = 0, len = 1; len < n; len <<= 1) ++l;
for (i = 0; i < len; ++i) r[i] = (r[i >> 1] >> 1) | ((i & 1) << (l - 1));
for (i = 0; i < len; ++i) a1[i] = a2[i] = ma[i] = mb[i] = Complex(0, 0), a[i] = b[i] = 0;
for (i = 0; i < len; ++i) w[i] = Complex(cos(pi * i / len), sin(pi * i / len));
}
inline void Calc1() {
register int i, k, v1, v2, v3;
register Complex ca, cb, da1, da2, db1, db2;
for (i = 0; i < len; ++i) ma[i] = Complex(a[i] & 32767, a[i] >> 15), mb[i] = Complex(b[i] & 32767, b[i] >> 15);
for (DFT(ma, 1), DFT(mb, 1), i = 0; i < len; ++i) {
k = (len - i) & (len - 1), ca = ma[k].Conj(), cb = mb[k].Conj();
da1 = (ca + ma[i]) * Complex(0.5, 0), da2 = (ma[i] - ca) * Complex(0, -0.5);
db1 = (cb + mb[i]) * Complex(0.5, 0), db2 = (mb[i] - cb) * Complex(0, -0.5);
a1[i] = da1 * db1 + (da1 * db2 + da2 * db1) * Complex(0, 1), a2[i] = da2 * db2;
}
for (DFT(a1, -1), DFT(a2, -1), i = 0; i < len; ++i) {
v1 = (ll)(a1[i].a / len + 0.5) % mod, v2 = (ll)(a1[i].b / len + 0.5) % mod;
v3 = (ll)(a2[i].a / len + 0.5) % mod, a[i] = (((ll)v3 << 30) + ((ll)v2 << 15) + v1) % mod;
if (a[i] < 0) a[i] += mod;
}
}
inline void Calc2() {
register int i, k, v1, v2, v3;
register Complex ca, cb, da1, da2, db1, db2;
for (i = 0; i < len; ++i) ma[i] = Complex(a[i] & 32767, a[i] >> 15), mb[i] = Complex(b[i] & 32767, b[i] >> 15);
for (DFT(ma, 1), DFT(mb, 1), i = 0; i < len; ++i) {
k = (len - i) & (len - 1), ca = ma[k].Conj(), cb = mb[k].Conj();
da1 = (ca + ma[i]) * Complex(0.5, 0), da2 = (ma[i] - ca) * Complex(0, -0.5);
db1 = (cb + mb[i]) * Complex(0.5, 0), db2 = (mb[i] - cb) * Complex(0, -0.5);
a1[i] = da1 * db1 + (da1 * db2 + da2 * db1) * Complex(0, 1), a2[i] = da2 * db2;
}
for (DFT(a1, -1), DFT(a2, -1), i = 0; i < len; ++i) {
v1 = (ll)(a1[i].a / len + 0.5) % mod, v2 = (ll)(a1[i].b / len + 0.5) % mod;
v3 = (ll)(a2[i].a / len + 0.5) % mod, a[i] = (((ll)v3 << 30) + ((ll)v2 << 15) + v1) % mod;
if (a[i] < 0) a[i] += mod;
}
for (i = 0; i < len; ++i) ma[i] = Complex(a[i] & 32767, a[i] >> 15), mb[i] = Complex(b[i] & 32767, b[i] >> 15);
for (DFT(ma, 1), DFT(mb, 1), i = 0; i < len; ++i) {
k = (len - i) & (len - 1), ca = ma[k].Conj(), cb = mb[k].Conj();
da1 = (ca + ma[i]) * Complex(0.5, 0), da2 = (ma[i] - ca) * Complex(0, -0.5);
db1 = (cb + mb[i]) * Complex(0.5, 0), db2 = (mb[i] - cb) * Complex(0, -0.5);
a1[i] = da1 * db1 + (da1 * db2 + da2 * db1) * Complex(0, 1), a2[i] = da2 * db2;
}
for (DFT(a1, -1), DFT(a2, -1), i = 0; i < len; ++i) {
v1 = (ll)(a1[i].a / len + 0.5) % mod, v2 = (ll)(a1[i].b / len + 0.5) % mod;
v3 = (ll)(a2[i].a / len + 0.5) % mod, a[i] = (((ll)v3 << 30) + ((ll)v2 << 15) + v1) % mod;
if (a[i] < 0) a[i] += mod;
}
}
*/
int a[maxn], b[maxn], len, r[maxn], l, w[2][maxn];
inline void Init(const int n) {
register int i, x, y;
for (l = 0, len = 1; len < n; len <<= 1) ++l;
for (i = 0; i < len; ++i) r[i] = (r[i >> 1] >> 1) | ((i & 1) << (l - 1));
for (i = 0; i < len; ++i) a[i] = b[i] = 0;
w[1][0] = w[0][0] = 1, x = Pow(3, (mod - 1) / len), y = Pow(x, mod - 2);
for (i = 1; i < len; ++i) w[0][i] = (ll)w[0][i - 1] * x % mod, w[1][i] = (ll)w[1][i - 1] * y % mod;
}
inline void NTT(int *p, const int opt) {
register int i, j, k, wn, t, x, y;
for (i = 0; i < len; ++i) if (r[i] < i) swap(p[r[i]], p[i]);
for (i = 1; i < len; i <<= 1)
for (t = i << 1, j = 0; j < len; j += t)
for (k = 0; k < i; ++k) {
wn = w[opt == -1][len / t * k];
x = p[j + k], y = (ll)wn * p[i + j + k] % mod;
p[j + k] = x + y >= mod ? x + y - mod : x + y;
p[i + j + k] = x - y < 0 ? x - y + mod : x - y;
}
if (opt == -1) for (wn = Pow(len, mod - 2), i = 0; i < len; ++i) p[i] = (ll)p[i] * wn % mod;
}
inline void Calc1() {
register int i;
NTT(a, 1), NTT(b, 1);
for (i = 0; i < len; ++i) a[i] = (ll)a[i] * b[i] % mod;
NTT(a, -1);
}
inline void Calc2() {
register int i;
NTT(a, 1), NTT(b, 1);
for (i = 0; i < len; ++i) a[i] = (ll)a[i] * b[i] % mod * b[i] % mod;
NTT(a, -1);
}
}
struct Poly {
vector <int> v;
inline Poly() {
v.resize(1);
}
inline Poly(const int d) {
v.resize(d);
}
inline int Length() const {
return v.size();
}
inline void Adjust() {
register int n = v.size(), len;
for (len = 1; len < n; len <<= 1);
v.resize(len);
}
inline Poly operator +(Poly b) const {
register int i, l1 = Length(), l2 = b.Length(), l3 = max(l1, l2);
register Poly c(l3);
for (i = 0; i < l1; ++i) c.v[i] = v[i];
for (i = 0; i < l2; ++i) Inc(c.v[i], b.v[i]);
return c;
}
inline Poly operator -(Poly b) const {
register int i, l1 = Length(), l2 = b.Length(), l3 = max(l1, l2);
register Poly c(l3);
for (i = 0; i < l1; ++i) c.v[i] = v[i];
for (i = 0; i < l2; ++i) Inc(c.v[i], mod - b.v[i]);
return c;
}
inline void InvMul(Poly b) {
register int i, l1 = Length(), l2 = b.Length(), l3 = l1 + l2 - 1;
FFT :: Init(l3);
for (i = 0; i < l1; ++i) FFT :: a[i] = v[i];
for (i = 0; i < l2; ++i) FFT :: b[i] = b.v[i];
FFT :: Calc2();
}
inline Poly operator *(Poly b) const {
register int i, l1 = Length(), l2 = b.Length(), l3 = l1 + l2 - 1;
register Poly c(l3);
FFT :: Init(l3);
for (i = 0; i < l1; ++i) FFT :: a[i] = v[i];
for (i = 0; i < l2; ++i) FFT :: b[i] = b.v[i];
FFT :: Calc1();
for (i = 0; i < l3; ++i) c.v[i] = FFT :: a[i];
return c;
}
inline Poly operator *(int b) const {
register int i, l = Length();
register Poly c(l);
for (i = 0; i < l; ++i) c.v[i] = (ll)v[i] * b % mod;
return c;
}
inline int Calc(const int x) {
register int i, ret = v[0], l = Length(), now = x;
for (i = 1; i < l; ++i) Inc(ret, (ll)now * v[i] % mod), now = (ll)now * x % mod;
return ret;
}
};
inline void Calc(Poly p, Poly &q, int len) {
register int i;
for (i = len - 1; i; --i) q.v[i] = (ll)p.v[i - 1] * Pow(i, mod - 2) % mod;
q.v[0] = 0;
}
inline void ICalc(Poly p, Poly &q, int len) {
register int i;
for (i = len - 2; ~i; --i) q.v[i] = (ll)p.v[i + 1] * (i + 1) % mod;
q.v[len - 1] = 0;
}
void Inv(Poly p, Poly &q, int len) {
if (len == 1) {
q.v[0] = Pow(p.v[0], mod - 2);
return;
}
Inv(p, q, len >> 1);
register int i;
p.InvMul(q);
for (i = 0; i < len; ++i) q.v[i] = ((ll)2 * q.v[i] + mod - FFT :: a[i]) % mod;
}
void Ln(Poly p, Poly &q, int len) {
static Poly c, a;
c.v.resize(len), a.v.resize(len);
Inv(p, c, len), ICalc(p, a, len);
c = c * a, c.v.resize(len), Calc(c, q, len);
}
void Exp(Poly p, Poly &q, int len) {
if (len == 1) {
q.v[0] = 1;
return;
}
static Poly d;
Exp(p, q, len >> 1), q.v.resize(len);
d.v.resize(len), Ln(q, d, len), Inc(d.v[0], mod - 1);
d = p - d, d.v.resize(len), q = q * d, q.v.resize(len);
}
void Sqrt(Poly p, Poly &q, int len) {
if (len == 1) {
q.v[0] = sqrt(p.v[0]);
return;
}
static Poly c, a;
Sqrt(p, q, len >> 1), c.v.resize(len), Inv(q, c, len);
a = p, a.v.resize(len), a = a * c, a.v.resize(len);
q = (q + a) * inv2, q.v.resize(len);
}
inline Poly operator %(const Poly &a, const Poly &b) {
if (a.Length() < b.Length()) return a;
register Poly x = a, y = b, z;
register int n = a.Length(), m = b.Length(), res = n - m + 1;
reverse(x.v.begin(), x.v.end()), reverse(y.v.begin(), y.v.end());
x.v.resize(res), y.v.resize(res), y.Adjust();
z.v.resize(y.Length()), Inv(y, z, y.Length());
z.v.resize(res), x = x * z;
x.v.resize(res), reverse(x.v.begin(), x.v.end());
y = a - x * b, y.v.resize(m - 1);
return y;
}
Poly f[maxn], a, b;
int n, m, x[maxn], y[maxn], ans[maxn];
void Build(int o, int l, int r) {
if (l == r) {
f[o].v.resize(2), f[o].v[0] = mod - x[l], f[o].v[1] = 1;
return;
}
register int mid = (l + r) >> 1;
Build(o << 1, l, mid), Build(o << 1 | 1, mid + 1, r);
f[o] = f[o << 1] * f[o << 1 | 1];
}
void Solve_val(Poly cur, int o, int l, int r) {
if (r - l + 1 <= 2000) {
for (; l <= r; ++l) ans[l] = 1LL * y[l] * Pow(cur.Calc(x[l]), mod - 2) % mod;
return;
}
register int mid = (l + r) >> 1;
Solve_val(cur % f[o << 1], o << 1, l, mid);
Solve_val(cur % f[o << 1 | 1], o << 1 | 1, mid + 1, r);
}
void Solve(Poly &cur, int o, int l, int r) {
if (l == r) {
cur.v[0] = ans[l];
return;
}
register int mid = (l + r) >> 1;
register Poly lp(mid - l + 1), rp(r - mid);
Solve(lp, o << 1, l, mid);
Solve(rp, o << 1 | 1, mid + 1, r);
cur = lp * f[o << 1 | 1] + rp * f[o << 1];
}
inline void Lagrange() {
register int i, len;
scanf("%d", &n);
for (i = 1; i <= n; ++i) scanf("%d%d", &x[i], &y[i]);
Build(1, 1, n), a = f[1], len = a.Length();
for (i = 0; i < len - 1; ++i) a.v[i] = (ll)a.v[i + 1] * (i + 1) % mod;
if (a.Length() > 1) a.v.pop_back();
else a.v[0] = 0;
b.v.resize(n), Solve_val(a, 1, 1, n), Solve(b, 1, 1, n);
for (i = 0; i < n; ++i) printf("%d ", b.v[i]);
puts("");
}
int main() {
return 0;
}标签：namespace cos using scan str def ati 大型 cto
原文地址：https://www.cnblogs.com/cjoieryl/p/10158721.html
