FFT模板

#define pi acos(-1)
#define maxn 222222
using namespace std;
struct plex { ///定义一个复数类
double x, y;
plex (double _x = 0.0, double _y = 0.0) : x (_x), y (_y) {}
plex operator + (const plex &a) const {
return plex (x+a.x, y+a.y);
}
plex operator - (const plex &a) const {
return plex (x-a.x, y-a.y);
}
plex operator * (const plex &a) const {
return plex (x*a.x-y*a.y, x*a.y+y*a.x);
}
};
void change (plex *y, int len) {
int i, j, k;
for(i = 1, j = len / 2; i < len - 1; i++) {
if (i < j) swap(y[i], y[j]);
k = len / 2;
while (j >= k) {
j -= k;
k /= 2;
}
if (j < k) j += k;
}
}
void fft(plex y[],int len,int on)
{
change(y,len);
for(int h = 2; h <= len; h <<= 1)
{
plex wn(cos(-on*2*pi/h),sin(-on*2*pi/h)); ///根据欧拉公式求wn
for(int j = 0;j < len;j+=h)
{
plex w(1,0);
for(int k = j;k < j+h/2;k++)
{
plex u = y[k];
plex t = w*y[k+h/2];
y[k] = u+t;
y[k+h/2] = u-t;
w = w*wn;
}
}
}
if(on == -1)            ///看是dft还是idft
for(int i = 0;i < len;i++)
y[i].x /= len;
}