多项式求逆入门 板题(Luogu P4238)

• 下面是代码，推导详见 传送门

模板Code

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;
const int mod = 998244353, g = 3, MAXN = 1<<18;
typedef long long LL;

inline void change(int arr[], const int &len)
{
	register int i, j, k;
	for(i = 1, j = len/2; i < len-1; ++i)
	{
		if(i < j) swap(arr[i], arr[j]);
		k = len/2;
		while(j >= k) j -= k, k >>= 1;
		j += k;
	}
}

inline int qmul(int a, int b, const int &c)
{
	register int ret = 1;
	while(b)
	{
		if(b&1) ret = (LL)ret * a % c;
		a = (LL)a * a % c; b >>= 1;
	}
	return ret;
}

inline void NTT(int arr[], const int &len, const int &flg)
{
	change(arr, len);
	register int wn, w, A0, wA1, i, j, k;
	for(i = 2; i <= len; i <<= 1)
	{
		if(~flg) wn = qmul(g, (mod-1)/i, mod);
		else wn = qmul(g, (mod-1) - (mod-1)/i, mod);
		for(j = 0; j < len; j += i)
		{
			w = 1;
			for(k = j; k < j + i/2; ++k)
			{
				A0 = arr[k], wA1 = (LL)w * arr[k + i/2]% mod;
				arr[k] = (A0 + wA1) % mod;
				arr[k + i/2] = ((A0 - wA1) % mod + mod) % mod;
				w = (LL)w * wn % mod;
			}
		}
	}
	if(flg == -1)
	{
		register int rev = qmul(len, mod-2, mod);
		for(i = 0; i < len; ++i)
			arr[i] = (LL)arr[i] * rev % mod;
	}
}
int a[MAXN], b[MAXN], c[MAXN];

void work(const int &deg, int a[], int b[])
{
	if(deg == 1) { b[0] = qmul(a[0], mod-2, mod); return; }
	work(deg+1>>1, a, b);
	register int len = 1;
	while(len < deg<<1) len <<= 1;
	for(int i = 0; i < deg; ++i) c[i] = a[i];
	for(int i = deg; i < len; ++i) c[i] = 0;
	NTT(c, len, 1); NTT(b, len, 1);
	for(int i = 0; i < len; ++i)
		b[i] = (2 - (LL)b[i]*c[i]%mod + mod) % mod * b[i] % mod;
	NTT(b, len, -1);
	for(int i = deg; i < len; ++i) b[i] = 0;
}
int n;
void init()
{
	scanf("%d", &n);
	for(int i = 0; i < n; ++i)
		scanf("%d", &a[i]);
}

void solve()
{
	work(n, a, b);
	for(int i = 0; i < n; ++i)
		printf("%d%c", b[i], i == n-1 ? '
' : ' ');
}

int main ()
{
	init(); solve();
}