# FFT与NTT

## 递归版FFT

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cstdlib>
#include <cmath>
using namespace std;
const int MAXN = 4000005;
const double PI = acos(-1);
int init() {
int rv = 0, fh = 1;
char c = getchar();
while(c < '0' || c > '9') {
if(c == '-') fh = -1;
c = getchar();
}
while(c >= '0' && c <= '9') {
rv = (rv<<1) + (rv<<3) + c - '0';
c = getchar();
}
return rv * fh;
}
struct Complex{
double x, y;
Complex (double xx = 0.0, double yy = 0.0) {
x = xx; y = yy;
}
Complex operator + (const Complex &u) const{
return Complex(x + u.x, y + u.y);
}
Complex operator - (const Complex &u) const{
return Complex(x - u.x, y - u.y);
}
Complex operator * (const Complex &u) const{
return Complex(x * u.x - y * u.y, x * u.y + y * u.x);
}
}a[MAXN], b[MAXN], buf[MAXN];
int n, m;
void fft(Complex a[], int lim, int opt) {
if(lim == 1) return;
int tmp = lim / 2;
for(int i = 0; i < tmp; i++) {
buf[i] = a[i * 2];
buf[tmp + i] = a[i * 2 + 1];
}
for(int i = 0; i < lim; i++) {
a[i] = buf[i];
}
fft(a, tmp, opt);
fft(a + tmp, tmp, opt);
Complex wn = Complex(cos(PI * 2.0 / lim), opt * sin(PI * 2.0 / lim)), w = Complex(1.0, 0.0);
for(int i = 0; i < tmp; i++) {
buf[i] = a[i] + w * a[i + tmp];
buf[i + tmp] = a[i] - w * a[i + tmp];
w = w * wn;
}
for(int i = 0; i < lim; i++) {
a[i] = buf[i];
}
}
int main() {
n = init(); m = init();
for(int i = 0; i <= n; i++) a[i].x = init();
for(int i = 0; i <= m; i++) b[i].x = init();
int lim = 1;
while(lim <= n + m) lim <<= 1;
fft(a, lim, 1);
fft(b, lim, 1);
for(int i = 0; i <= lim; i++) {
a[i] = a[i] * b[i];
}
fft(a, lim, -1);
for(int i = 0; i <= n + m; i++) {
printf("%d ", (int)(a[i].x / lim + 0.5));
}
printf("\n");
return 0;
}

## 迭代版FFT

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <cstdlib>
#include <algorithm>
using namespace std;
const int MAXN = 4000005;
const double PI = acos(-1);
int init() {
int rv = 0, fh = 1;
char c = getchar();
while(c < '0' || c > '9') {
if(c == '-') fh = -1;
c = getchar();
}
while(c >= '0' && c <= '9') {
rv = (rv<<1) + (rv<<3) + c - '0';
c = getchar();
}
return rv * fh;
}
struct Complex{
double x, y;
Complex (double xx = 0.0, double yy = 0.0) {
x = xx; y = yy;
}
Complex operator + (const Complex &u) const {
return Complex(x + u.x, y + u.y);
}
Complex operator - (const Complex &u) const{
return Complex(x - u.x, y - u.y);
}
Complex operator * (const Complex &u) const{
return Complex(x * u.x - y * u.y, x * u.y + y * u.x);
}
}a[MAXN], b[MAXN], buf[MAXN];
int n, m, rev[MAXN], lim, limcnt;
void fft(Complex a[], int opt) {
for(int i = 0; i <= lim; i++) {
if(i < rev[i]) swap(a[i], a[rev[i]]);
}
for(int mid = 1; mid < lim; mid <<= 1) {
Complex wn = Complex(cos(PI / mid), opt * sin(PI / mid));
for(int R = mid << 1, j = 0; j < lim; j += R) {
Complex w = Complex(1.0, 0.0);
for(int k = 0; k < mid; k++) {
Complex x = a[j + k], y = w * a[j + mid + k];
a[j + k] = x + y;
a[j + mid + k] = x - y;
w = w * wn;
}
}
}
}
int main() {
n = init(); m = init();
for(int i = 0; i <= n; i++) a[i].x = init();
for(int i = 0; i <= m; i++) b[i].x = init();
lim = 1;
while(lim <= n + m) {lim <<= 1; limcnt++;}
for(int i = 0; i <= lim; i++) rev[i] = (rev[i >> 1] >> 1) | ((i & 1) << (limcnt - 1));
fft(a, 1);
fft(b, 1);
for(int i = 0; i <= lim; i++) a[i] = a[i] * b[i];
fft(a, -1);
for(int i = 0; i <= n + m; i++) {
printf("%d ", (int)(a[i].x / lim + 0.5));
}
return 0;
}

## NTT

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#define ll long long
using namespace std;
const int MAXN = 4000005, MOD = 998244353, gg = 3, gi = 332748118;
ll init() {
ll rv = 0, fh = 1;
char c = getchar();
while(c < '0' || c > '9') {
if(c == '-') fh = -1;
c = getchar();
}
while(c >= '0' && c <= '9') {
rv = (rv<<1) + (rv<<3) + c - '0';
c = getchar();
}
return fh * rv;
}
ll lim = 1, limcnt, rev[MAXN], n, m, a[MAXN], b[MAXN];
ll ksm(ll a, ll k) {
ll ans = 1;
while(k) {
if(k & 1ll) {
(ans *= a) %= MOD;
}
(a *= a) %= MOD;
k >>= 1;
}
return ans;
}
void ntt(ll a[], int opt) {
for(int i = 0; i <= lim; i++) {
if(i < rev[i]) swap(a[i], a[rev[i]]);
}
for(int mid = 1; mid < lim; mid <<= 1) {
ll wn = ksm(opt == 1 ? gg : gi, (MOD - 1) / (mid << 1));
for(int R = mid << 1, j = 0; j < lim; j += R) {
ll w = 1;
for(int k = 0; k < mid; k++) {
ll x = a[j + k], y = w * a[j + mid + k] % MOD;
a[j + k] = (x + y) % MOD;
a[j + mid + k] = (x - y + MOD) % MOD;
(w *= wn) %= MOD;
}
}
}
if(opt == -1) {
ll inv = ksm(lim, MOD - 2);
for(int i = 0; i <= lim; i++) {
(a[i] *= inv) %= MOD;
}
}
}
int main() {
n = init(); m = init();
for(int i = 0; i <= n; i++) {
a[i] = init();
}
for(int i = 0; i <= m; i++) b[i] = init();
while(lim <= (n + m)) lim <<= 1, limcnt++;
for(int i = 0; i <= lim; i++)
rev[i] = (rev[i>>1]>>1) | ((i&1)<<(limcnt-1));
ntt(a, 1);
ntt(b, 1);
for(int i = 0; i <= lim; i++) (a[i] = a[i] * b[i]) %= MOD;
ntt(a, -1);
for(int i = 0; i <= n + m; i++) {
printf("%lld ", a[i]);
}
printf("\n");
return 0;
}
posted @ 2018-05-23 16:50  Mr_Wolfram  阅读(...)  评论(...编辑  收藏