FFT

struct Complex
{
    double r,i;
    Complex(double _r = 0,double _i = 0)
    {
        r = _r; i = _i;
    }
    Complex operator +(const Complex &b)
    {
        return Complex(r+b.r,i+b.i);
    }
    Complex operator -(const Complex &b)
    {
        return Complex(r-b.r,i-b.i);
    }
    Complex operator *(const Complex &b)
    {
        return Complex(r*b.r-i*b.i,r*b.i+i*b.r);
    }
};
void change(Complex y[],ll len)   //二进制平摊反转置换 O(logn)
{
    ll i,j,k;
    for(i = 1, j = len/2;i < len-1;i++)
    {
        if(i < j)swap(y[i],y[j]);
        k = len/2;    // Rader算法 二进制反转
        while( j >= k)
        {
            j -= k;
            k /= 2;
        }
        /*if(j < k)*/j += k;
    }
}
/*
* *len必须为2^k形式,不够的话,就补0
* * on为1的话就是DFT,为-1就是IDFT
*/
void fft(Complex y[],ll len,ll on)
{
    change(y,len);                                        //调用反转置换
    for(ll h = 2;h <= len;h <<= 1)
    {
        Complex wn(cos(-on*2*PI/h),sin(-on*2*PI/h));      //初始化单位复根
        for(ll j = 0;j < len;j += h)
        {
            Complex w(1,0);
            for(ll k = j;k < j+h/2;k++)    // 蝶形运算
            {
                Complex u = y[k];
                Complex t = w*y[k+h/2];
                y[k] = u+t;
                y[k+h/2] = u-t;
                w = w*wn;                                  //更新螺旋因子
            }
        }
    }
    if(on == -1)
        for(ll i = 0;i < len;i++)
            y[i].r /= len;                //IDFT
}