[模板] 多项式ln

提交至 【模板】多项式对数函数

代码特别丑。

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#include <cstring>
#include <cstdio>
#include <algorithm>

using namespace std;

const int maxn = 100010;
const int mod = 998244353;
const int g = 3;

int (int x, int y) {
int ret = 1;
while (y) {
if (y & 1) ret = 1LL*ret*x%mod;
x = 1LL*x*x%mod;
y >>= 1;
}
return ret;
}

int n = 0;

struct poly {
int *a, len;
poly(int l) {
len = l;
a = new int[l];
for (int i = 0; i < l; i++)
a[i] = 0;
}
};

int w_a[maxn*4], w_b[maxn*4], w_c[maxn*4], rev[maxn*4];

void ntt(int *a, int t, int ty) {
int len = (1 << t);
for (int i = 1; i < len; i++) rev[i] = (rev[i>>1]>>1)|((i&1)<<(t-1));
for (int i = 0; i < len; i++) if (rev[i] > i) swap(a[i], a[rev[i]]);
for (int l = 2; l <= len; l <<= 1) {
int wn = qpow(g, (mod-1)/l);
for (int s = 0; s < len; s += l) {
int w = 1;
for (int i = s; i < (s+(l>>1)); i++) {
int v1 = a[i], v2 = 1LL*w*a[i+(l>>1)]%mod;
a[i] = (v1+v2) % mod;
a[i+(l >> 1)] = (v1-v2+mod)%mod;
w = 1LL*w*wn%mod;
}
}
}
if (ty == -1) {
for (int i = 1; i < len/2; i++) swap(a[i], a[len-i]);
int r = qpow(len, mod-2);
for (int i = 0; i < len; i++) a[i] = 1LL*a[i]*r%mod;
}
}

poly operator*(poly a, poly b) {
poly ret(a.len + b.len - 1);
int t = 0;
while ((1<<t) < ret.len) ++ t;
for (int i = 0; i < (1<<t); i++) w_a[i] = w_b[i] = 0;
for (int i = 0; i < a.len; i++) w_a[i] = a.a[i];
for (int i = 0; i < b.len; i++) w_b[i] = b.a[i];
ntt(w_a, t, 1);
ntt(w_b, t, 1);
for (int i = 0; i < (1<<t); i++) w_c[i] = 1LL*w_a[i]*w_b[i]%mod;
ntt(w_c, t, -1);
for (int i = 0; i < ret.len; i++) ret.a[i] = w_c[i];
return ret;
}

poly poly_inverse(poly a) {
if (a.len == 1) {
poly ret(1);
ret.a[0] = qpow(a.a[0], mod-2);
return ret;
}
int nl = (a.len+1)/2;
poly na(nl);
for (int i = 0; i < nl; i++) na.a[i] = a.a[i];
poly r = poly_inverse(na);
poly t = r*a;
t.len = a.len;
for (int i = 0; i < t.len; i++) t.a[i] = (mod-t.a[i])%mod;
t.a[0] = (t.a[0] + 2) % mod;
poly ret = t*r;
ret.len = a.len;
return ret;
}

poly poly_ln(poly a) {
poly t(a.len-1);
for (int i = 1; i < a.len; i++) {
t.a[i-1] = 1LL * a.a[i] * i % mod;
}
poly x = poly_inverse(a);
poly s = x*t;
s.len = a.len;
poly ret(a.len);
for (int i = 1; i < a.len; i++) {
ret.a[i] = 1LL*qpow(i, mod-2)*s.a[i-1]%mod;
}
return ret;
}

int main() {
scanf("%d", &n);
poly A(n);
for (int i = 0; i < n; i++) scanf("%d", &A.a[i]);
poly P = poly_ln(A);
for (int i = 0; i < n; i++) printf("%d ", P.a[i]);
printf("n");
return 0;
}