多项式模板 

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector>
#define clr(f, n) memset(f, 0, sizeof(int) * (n))
#define cpy(f, g, n) memcpy(f, g, sizeof(int) * (n))
using namespace std;
const int _G = 3, MOD = 998244353, N = 1 << 20 | 500;
int n, m, tr[N << 1], tf;
long long quickPower (long long x, long long y) {
	long long res = 1;
	while (y) {
		if (y & 1) res = res * x % MOD;
		x = x * x % MOD;
		y >>= 1;
	}
	return res;
}
const int invG = quickPower(_G, MOD - 2);
inline void tpre (int n) {
	if (tf == n) return;
	tf = n;
	for (int i = 0; i < n; i ++) tr[i] = tr[i] = (tr[i >> 1] >> 1) | ((i & 1) ? n >> 1 : 0);
}
unsigned long long F[N << 1], W[N << 1] = {1};
inline void ntt (int *g, bool op, int n) {
	tpre(n);
	for (int i = 0; i < n; i ++) F[i] = (((long long) MOD << 5) + g[tr[i]]) % MOD;
	for (int l = 1; l < n; l <<= 1) {
		unsigned long long tG = quickPower(op ? _G : invG, (MOD - 1) / (l + l));
		for (int i = 1; i < l; i ++) W[i] = W[i - 1] * tG % MOD;
		for (int k = 0; k < n; k += l + l)
			for (int p = 0; p < l; p ++) {
				unsigned long long tt = W[p] * F[k | l | p] % MOD;
				F[k | l | p] = F[k | p] + MOD - tt;
				F[k | p] += tt;
			}
		if (l == (1 << 10))
			for (int i = 0; i < n; i ++) F[i] %= MOD;
	}
	if (!op) {
		unsigned long long invn = quickPower(n, MOD - 2);
		for (int i = 0; i < n; i ++)
			g[i] = F[i] % MOD * invn % MOD;
	} else for (int i = 0; i < n; i ++) g[i] = F[i] % MOD;
}
inline void px (int *f, int *g, int n) {
	for (int i = 0; i < n; i ++)
		f[i] = 1ll * f[i] * g[i] % MOD;
}
#define Poly vector<int>
Poly operator + (const Poly &A, const Poly &B) {
	Poly C = A;
	C.resize(max(A.size(), B.size()));
	for (int i = 0; i < B.size(); i ++) C[i] = (C[i] + B[i]) % MOD;
	return C;
}
Poly operator - (const Poly &A, const Poly &B) {
	Poly C = A;
	C.resize(max(A.size(), B.size()));
	for (int i = 0; i < B.size(); i ++) C[i] = (C[i] + MOD - B[i]) % MOD;
	return C;
}
Poly operator * (const int c, const Poly &A) {
	Poly C;
	C.resize(A.size());
	for (int i = 0; i < A.size(); i ++) C[i] = 1ll * c * A[i] % MOD;
	return C;
}
int lim;
Poly operator * (const Poly &A, const Poly &B) {
	static int a[N << 1], b[N << 1];
	cpy(a, &A[0], A.size());
	cpy(b, &B[0], B.size());
	Poly C;
	C.resize(min(lim, (int)(A.size() + B.size() - 1)));
	int n = 1;
	for (n; n < A.size() + B.size() - 1; n <<= 1);
	ntt(a, 1, n);
	ntt(b, 1, n);
	px(a, b, n);
	ntt(a, 0, n);
	cpy(&C[0], a, C.size());
	clr(a, n);
	clr(b, n);
	return C;
}
inline void pinv (const Poly &A, Poly &B, int n) {
	if (n == 1) B.push_back(quickPower(A[0], MOD - 2));
	else if (n & 1) {
		pinv(A, B, -- n);
		int sav = 0;
		for (int i = 0; i < n; i ++) sav = (sav + 1ll * B[i] * A[n - i]) % MOD;
		B.push_back(1ll * sav * quickPower(MOD - A[0], MOD - 2) % MOD);
	} else {
		pinv(A, B, n / 2);
		Poly sA;
		sA.resize(n);
		cpy(&sA[0], &A[0], n);
		B = 2 * B - B * B * sA;
		B.resize(n);
	}
}
//多项式乘法逆元
Poly pinv (const Poly &A) {
	Poly C;
	pinv(A, C, A.size());
	return C;
}
int inv[N];
inline void Init () {
	inv[1] = 1;
	for (int i = 2; i <= lim; i ++)
		inv[i] = 1ll * inv[MOD % i] * (MOD - MOD / i) % MOD;
}
//多项式求导
Poly dao (const Poly &A) {
	Poly C = A;
	for (int i = 1; i < C.size(); i ++)
		C[i - 1] = 1ll * C[i] * i % MOD;
	C.pop_back();
	return C;
}
//多项式积分
Poly ints (const Poly &A) {
	Poly C = A;
	for (int i = C.size() - 1; i; i --)
		C[i] = 1ll * C[i - 1] * inv[i] % MOD;
	C[0] = 0;
	return C;
}
//多项式ln
Poly ln (const Poly &A) {
	return ints(dao(A) * pinv(A));
}
inline void pexp (const Poly &A, Poly &B, int n) {
	if (n == 1) B.push_back(1);
	else if (n & 1) {
		pexp(A, B, n - 1);
		n -= 2;
		int sav = 0;
		for (int i = 0; i <= n; i ++) sav = (sav + 1ll * (i + 1) * A[i + 1] % MOD * B[n - i]) % MOD;
		B.push_back(1ll * sav * inv[n + 1] % MOD);
	} else {
		pexp(A, B, n / 2);
		Poly lnB = B;
		lnB.resize(n);
		lnB = ln(lnB);
		for (int i = 0; i < lnB.size(); i ++)
			lnB[i] = (MOD + A[i] - lnB[i]) % MOD;
		lnB[0] ++;
		B = B * lnB;
		B.resize(n);
	}
}
//多项式exp
Poly pexp (const Poly &A) {
	Poly C;
	pexp(A, C, A.size());
	return C;
}
Poly f, g;
int main () {
	scanf("%d%d", &n, &m);
	f.resize(n + 1);
	g.resize(m + 1);
	lim = n + m + 1;
	for (int i = 0; i <= n; i ++) scanf("%d", &f[i]);
	for (int i = 0; i <= m; i ++) scanf("%d", &g[i]);
	f = f * g;
	for (int i = 0; i < f.size(); i ++) printf("%d ", f[i]);
	return 0;
}

模数表

//（g 是mod(r*2^k+1)的原根）

素数  r  k  g
3   1   1   2
5   1   2   2
17  1   4   3
97  3   5   5
193 3   6   5
257 1   8   3
7681    15  9   17
12289   3   12  11
40961   5   13  3
65537   1   16  3
786433  3   18  10
5767169 11  19  3
7340033 7   20  3
23068673    11  21  3
104857601   25  22  3
167772161   5   25  3
469762049   7   26  3
1004535809  479 21  3
2013265921  15  27  31
2281701377  17  27  3
3221225473  3   30  5
75161927681 35  31  3
77309411329 9   33  7
206158430209    3   36  22
2061584302081   15  37  7
2748779069441   5   39  3
6597069766657   3   41  5
39582418599937  9   42  5
79164837199873  9   43  5
263882790666241 15  44  7
1231453023109121    35  45  3
1337006139375617    19  46  3
3799912185593857    27  47  5
4222124650659841    15  48  19
7881299347898369    7   50  6
31525197391593473   7   52  3
180143985094819841  5   55  6
1945555039024054273 27  56  5
4179340454199820289 29  57  3

//大模数版
#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector>
#define clr(f, n) memset(f, 0, sizeof(long long) * (n))
#define cpy(f, g, n) memcpy(f, g, sizeof(long long) * (n))
using namespace std;
const long long _G = 6, MOD = 180143985094819841ll, N = 1 << 20 | 500;
int n, m;
long long tr[N << 1], tf;
long long quickPower (long long x, long long y) {
	long long res = 1;
	while (y) {
		if (y & 1) res = (__int128_t) res * x % MOD;
		x = (__int128_t) x * x % MOD;
		y >>= 1;
	}
	return res;
}
const long long invG = quickPower(_G, MOD - 2);
inline void tpre (int n) {
	if (tf == n) return;
	tf = n;
	for (int i = 0; i < n; i ++) tr[i] = tr[i] = (tr[i >> 1] >> 1) | ((i & 1) ? n >> 1 : 0);
}

unsigned long long F[N << 1], W[N << 1] = {1};
inline void ntt (long long *g, bool op, int n) {
	tpre(n);
	for (int i = 0; i < n; i ++) F[i] = (((__int128_t) MOD << 5) + g[tr[i]]) % MOD;
	for (int l = 1; l < n; l <<= 1) {
		unsigned long long tG = quickPower(op ? _G : invG, (MOD - 1) / (l + l));
		for (int i = 1; i < l; i ++) W[i] = (__int128_t) W[i - 1] * tG % MOD;
		for (int k = 0; k < n; k += l + l)
			for (int p = 0; p < l; p ++) {
				unsigned long long tt = (__int128_t) W[p] * F[k | l | p] % MOD;
				F[k | l | p] = F[k | p] + MOD - tt;
				F[k | p] += tt;
			}
		if (l == (1 << 10))
			for (int i = 0; i < n; i ++) F[i] %= MOD;
	}
	if (!op) {
		unsigned long long invn = quickPower(n, MOD - 2);
		for (int i = 0; i < n; i ++)
			g[i] = (__int128_t) F[i] % MOD * invn % MOD;
	} else for (int i = 0; i < n; i ++) g[i] = F[i] % MOD;
}
inline void px (long long *f, long long *g, int n) {
	for (int i = 0; i < n; i ++)
		f[i] = (__int128_t) f[i] * g[i] % MOD;
}
#define Poly vector<long long>
Poly operator + (const Poly &A, const Poly &B) {
	Poly C = A;
	C.resize(max(A.size(), B.size()));
	for (int i = 0; i < B.size(); i ++) C[i] = ((__int128_t) C[i] + B[i]) % MOD;
	return C;
}
Poly operator - (const Poly &A, const Poly &B) {
	Poly C = A;
	C.resize(max(A.size(), B.size()));
	for (int i = 0; i < B.size(); i ++) C[i] = ((__int128_t) C[i] + MOD - B[i]) % MOD;
	return C;
}
Poly operator * (const int c, const Poly &A) {
	Poly C;
	C.resize(A.size());
	for (int i = 0; i < A.size(); i ++) C[i] = (__int128_t) c * A[i] % MOD;
	return C;
}
int lim;
Poly operator * (const Poly &A, const Poly &B) {
	static long long a[N << 1], b[N << 1];
	cpy(a, &A[0], A.size());
	cpy(b, &B[0], B.size());
	Poly C;
	C.resize(min(lim, (int)(A.size() + B.size() - 1)));
	int n = 1;
	for (n; n < A.size() + B.size() - 1; n <<= 1);
	ntt(a, 1, n);
	ntt(b, 1, n);
	px(a, b, n);
	ntt(a, 0, n);
	cpy(&C[0], a, C.size());
	clr(a, n);
	clr(b, n);
	return C;
}
Poly f, g;
int main () {
	scanf("%d%d", &n, &m);
	f.resize(n + 1);
	g.resize(m + 1);
	lim = n + m + 1;
	for (int i = 0; i <= n; i ++) scanf("%lld", &f[i]);
	for (int i = 0; i <= m; i ++) scanf("%lld", &g[i]);
	f = f * g;
	for (int i = 0; i < f.size(); i ++) printf("%lld ", f[i]);
	return 0;
}

ntt分治

#include <iostream>
#include <cstdio>
#include <algorithm>
#include <cstring>
#include <vector>
#define clr(f, n) memset(f, 0, sizeof(int) * (n))
#define cpy(f, g, n) memcpy(f, g, sizeof(int) * (n))
using namespace std;
const int _G = 3, MOD = 998244353, N = 1 << 20 | 500;
int tr[N << 1], tf;
long long quickPower (long long x, long long y) {
	long long res = 1;
	while (y) {
		if (y & 1) res = res * x % MOD;
		x = x * x % MOD;
		y >>= 1;
	}
	return res;
}
const int invG = quickPower(_G, MOD - 2);
inline void tpre (int n) {
	if (tf == n) return;
	tf = n;
	for (int i = 0; i < n; i ++) tr[i] = tr[i] = (tr[i >> 1] >> 1) | ((i & 1) ? n >> 1 : 0);
}
unsigned long long F[N << 1], W[N << 1] = {1};
inline void ntt (int *g, bool op, int n) {
	tpre(n);
	for (int i = 0; i < n; i ++) F[i] = (((long long) MOD << 5) + g[tr[i]]) % MOD;
	for (int l = 1; l < n; l <<= 1) {
		unsigned long long tG = quickPower(op ? _G : invG, (MOD - 1) / (l + l));
		for (int i = 1; i < l; i ++) W[i] = W[i - 1] * tG % MOD;
		for (int k = 0; k < n; k += l + l)
			for (int p = 0; p < l; p ++) {
				unsigned long long tt = W[p] * F[k | l | p] % MOD;
				F[k | l | p] = F[k | p] + MOD - tt;
				F[k | p] += tt;
			}
		if (l == (1 << 10))
			for (int i = 0; i < n; i ++) F[i] %= MOD;
	}
	if (!op) {
		unsigned long long invn = quickPower(n, MOD - 2);
		for (int i = 0; i < n; i ++)
			g[i] = F[i] % MOD * invn % MOD;
	} else for (int i = 0; i < n; i ++) g[i] = F[i] % MOD;
}
inline void px (int *f, int *g, int n) {
	for (int i = 0; i < n; i ++)
		f[i] = 1ll * f[i] * g[i] % MOD;
}
#define Poly vector<int>
Poly operator + (const Poly &A, const Poly &B) {
	Poly C = A;
	C.resize(max(A.size(), B.size()));
	for (int i = 0; i < B.size(); i ++) C[i] = (C[i] + B[i]) % MOD;
	return C;
}
Poly operator - (const Poly &A, const Poly &B) {
	Poly C = A;
	C.resize(max(A.size(), B.size()));
	for (int i = 0; i < B.size(); i ++) C[i] = (C[i] + MOD - B[i]) % MOD;
	return C;
}
Poly operator * (const int c, const Poly &A) {
	Poly C;
	C.resize(A.size());
	for (int i = 0; i < A.size(); i ++) C[i] = 1ll * c * A[i] % MOD;
	return C;
}
int lim;
Poly operator * (const Poly &A, const Poly &B) {
	static int a[N << 1], b[N << 1];
	cpy(a, &A[0], A.size());
	cpy(b, &B[0], B.size());
	Poly C;
	C.resize(min(lim, (int)(A.size() + B.size() - 1)));
	int n = 1;
	for (n; n < A.size() + B.size() - 1; n <<= 1);
	ntt(a, 1, n);
	ntt(b, 1, n);
	px(a, b, n);
	ntt(a, 0, n);
	cpy(&C[0], a, C.size());
	clr(a, n);
	clr(b, n);
	return C;
}
int n;
Poly Ff, Gg;
void cdqntt (int l, int r) {
    if (l == r) return;
    int mid = (l + r) >> 1;
    cdqntt(l, mid);
    Poly f, g;
    for (int i = l; i <= mid; i ++) f.push_back(Ff[i]);
    for (int i = l, j = 0; i <= r; i ++, j ++) g.push_back(Gg[j]);
    lim = r - l + 1;
    f = f * g;
    for (int i = ((r - l) >> 1) + 1; i <= r - l; i ++) Ff[l + i] = (Ff[l + i] + f[i]) % MOD;
    cdqntt(mid + 1, r);
}
int main () {
	scanf("%d", &n);
	Ff.resize(n);
	Gg.resize(n);
    Ff[0] = 1;
    Gg[0] = 0;
	for (int i = 1; i < n; i ++) scanf("%d", &Gg[i]);
    cdqntt(0, n - 1);
    for (int i = 0; i < n; i ++) printf("%d ", Ff[i]);
	return 0;
}
posted @   duoluoluo  阅读(33)  评论(0)  编辑  收藏  举报
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