多项式汇总[巨常数]

一个多月前写的板子，忘了放上来了，今天莫名其妙地想起来了

包含多项式乘法，多项式求逆，多项式除法/取模，多项式exp，多项式ln，多项式求导，多项式积分等基本操作

由于懒癌，这里直接开vector表示多项式，常数贼大(然后我把一机房人带坏了

以后可能会写一个常数小的多项式板子

#include <bits/stdc++.h>
using namespace std;

const int p = 998244353;

int qpow(int x, int y)
{
	int res = 1;
	while (y > 0)
	{
		if (y & 1)
			res = 1LL * res * x % p;
		x = 1LL * x * x % p;
		y >>= 1;
	}
	return res;
}

void FNTT(vector<int> &A, int len, int flag)
{
	A.resize(len);
	int *r = new int[len];
	r[0] = 0;
	for (int i = 0; i < len; i++)
		r[i] = (r[i >> 1] >> 1) | ((i & 1) * (len >> 1));
	for (int i = 0; i < len; i++)
		if (i < r[i])
			swap(A[i], A[r[i]]);
	int gn, g, t, A0, A1;
	for (int i = 1; i < len; i <<= 1)
	{
		gn = qpow(3, (p - 1) / (i * 2));
		for (int j = 0; j < len; j += (i << 1))
		{
			g = 1;
			A0 = j;
			A1 = A0 + i;
			for (int k = 0; k < i; k++, A0++, A1++, g = (1LL * g * gn) % p)
			{
				t = (1LL * A[A1] * g) % p;
				A[A1] = ((A[A0] - t) % p + p) % p;
				A[A0] = (A[A0] + t) % p;
			}
		}
	}
	if (flag == -1)
	{
		reverse(A.begin() + 1, A.end());
		int inv = qpow(len, p - 2);
		for (int i = 0; i < len; i++)
			A[i] = 1LL * A[i] * inv % p;
	}
	delete []r;
}

vector<int> operator+(vector<int> a, vector<int> b)
{
	vector<int> res;
	res.resize(max(a.size(), b.size()));
	a.resize(res.size());
	b.resize(res.size());
	for (int i = 0; i < (int)res.size(); i++)
		res[i] = (a[i] + b[i]) % p;
	return res;
}

vector<int> operator-(vector<int> a, vector<int> b)
{
	vector<int> res;
	res.resize(max(a.size(), b.size()));
	a.resize(res.size());
	b.resize(res.size());
	for (int i = 0; i < (int)res.size(); i++)
		res[i] = ((a[i] - b[i]) % p + p) % p;
	return res;
}

vector<int> operator*(vector<int> a, vector<int> b)
{
	int len = 1;
	int sz = a.size() + b.size() - 1;
	while (len <= sz) len <<= 1;
	FNTT(a, len, 1);
	FNTT(b, len, 1);
	vector<int> res;
	res.resize(len);
	for (int i = 0; i < len; i++)
		res[i] = 1LL * a[i] * b[i] % p;
	FNTT(res, len, -1);
	res.resize(sz);
	return res;
}

vector<int> poly_inv(vector<int> a)
{
	if (a.size() == 1)
	{
		a[0] = qpow(a[0], p - 2);
		return a;
	}
	int n = a.size(), newsz = (n + 1) >> 1;
	vector<int> b(a);
	b.resize(newsz);
	b = poly_inv(b);
	int len = 1;
	while (len <= (n << 1)) len <<= 1;
	vector<int> c(a);
	FNTT(a, len, 1);
	FNTT(b, len, 1);
	for (int i = 0; i < len; i++)
		a[i] = ((1LL * b[i] * (2 - 1LL * a[i] * b[i] % p)) % p + p) % p;
	FNTT(a, len, -1);
	a.resize(n);
	return a;
}

vector<int> intergal(vector<int> a)
{
	int sz = a.size();
	a.resize(sz + 1);
	for (int i = sz; i >= 1; i--)
		a[i] = 1LL * a[i - 1] * qpow(i, p - 2) % p;
	a[0] = 0;
	return a;
}

vector<int> derivation(vector<int> a)
{
	int sz = a.size();
	for (int i = 1; i < sz; i++)
		a[i - 1] = 1LL * a[i] * i % p;
	a.resize(sz - 1);
	return a;
}

vector<int> ln(vector<int> a)
{
	return intergal(derivation(a) * poly_inv(a));
}

vector<int> poly_r(vector<int> a)
{
	reverse(a.begin(), a.end());
	return a;
}

void div(vector<int> f, vector<int> g, vector<int> &q, vector<int> &r)
{
	int n = f.size() - 1, m = g.size() - 1;
	vector<int> gr = poly_r(g);
	gr.resize(n - m + 1);
	q = poly_r(f) * poly_inv(gr);
	q.resize(n - m + 1);
	q = poly_r(q);
	vector<int> gq = g * q;
	r.resize(m);
	gq.resize(m);
	f.resize(m);
	for (int i = 0; i < m; i++)
		r[i] = ((f[i] - gq[i]) % p + p) % p;
}

vector<int> poly_exp(vector<int> a)
{
	if (a.size() == 1)
	{
		a[0]++;
		return a;
	}
	vector<int> f0 = a;
	f0.resize((a.size() + 1) / 2);
	f0 = poly_exp(f0);
	vector<int> f;
	a[0]++;
	f = (a - ln(f0));
	f = f0 * f;
	f.resize(a.size());
	return f;
}

int main_luogu3803()
{
	vector<int> a, b;
	int n, m;
	scanf("%d%d", &n, &m);
	a.resize(n + 1);
	b.resize(m + 1);
	for (int i = 0; i <= n; i++)
		scanf("%d", &a[i]);
	for (int i = 0; i <= m; i++)
		scanf("%d", &b[i]);
	vector<int> res = a * b;
	for (int i = 0; i <= n + m; i++)
		printf("%d%c", res[i], i == n + m ? '\n' : ' ');
	return 0;
}

int main_luogu4238()
{
	vector<int> a;
	int n;
	scanf("%d", &n);
	a.resize(n);
	for (int i = 0; i < n; i++)
		scanf("%d", &a[i]);
	a = poly_inv(a);
	for (int i = 0; i < n; i++)
		printf("%d%c", a[i], i == n - 1 ? '\n' : ' ');
	return 0;
}

int main_luogu4725()
{
	vector<int> a;
	int n;
	scanf("%d", &n);
	a.resize(n);
	for (int i = 0; i < n; i++)
		scanf("%d", &a[i]);
	a = ln(a);
	for (int i = 0; i < n; i++)
		printf("%d%c", a[i], i == n - 1 ? '\n' : ' ');
	return 0;
}

int main_luogu4512()
{
	vector<int> f, g;
	int n, m;
	scanf("%d%d", &n, &m);
	f.resize(n + 1);
	g.resize(m + 1);
	for (int i = 0; i <= n; i++)
		scanf("%d", &f[i]);
	for (int i = 0; i <= m; i++)
		scanf("%d", &g[i]);
	vector<int> q, r;
	div(f, g, q, r);
	for (int i = 0; i <= n - m; i++)
		printf("%d%c", q[i], i == n - m ? '\n' : ' ');
	for (int i = 0; i < m; i++)
		printf("%d%c", r[i], i == m - 1 ? '\n' : ' ');
	return 0;
}

int main_luogu4726()
{
	vector<int> a;
	int n;
	scanf("%d", &n);
	a.resize(n * 2);
	for (int i = 0; i < n; i++)
		scanf("%d", &a[i]);
	a = poly_exp(a);
	for (int i = 0; i < n; i++)
		printf("%d%c", a[i], i == n - 1 ? '\n' : ' ');
	return 0;
}


int main()
{
	main_luogu4726();
	return 0;
}