P3803 [模板] 多项式乘法 (FFT)
阅读原文时间:2023年07月08日阅读:3

Rt

注意len要为2的幂

#include
using namespace std;
const double PI = acos(-1.0);

inline int read()
{
char c=getchar();int x=0,f=1;
while(c<'0'||c>'9'){if(c=='-')f=-1;c=getchar();}
while(c>='0'&&c<='9'){x=x*10+c-'0';c=getchar();}
return x*f;
}

int n, m;
struct Complex {
double x, y;
Complex(double _x = 0.0, double _y = 0.0) {
x = _x;
y = _y;
}
Complex operator + (const Complex &b) const {
return Complex(x + b.x, y + b.y);
}
Complex operator - (const Complex &b) const {
return Complex(x - b.x, y - b.y);
}
Complex operator * (const Complex &b) const {
return Complex(x * b.x - y * b.y, x * b.y + y * b.x);
}
};

void change(Complex 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(Complex y[], int len, int on)
{
change(y, len);
for(int h = 2; h <= len; h <<= 1)
{
Complex wn(cos(-on * 2 * PI / h), sin(-on * 2 * PI / h));
for(int j = 0; j < len; j += h)
{
Complex w(1, 0);
for(int k = j; k < j + h / 2; k++)
{
Complex u = y[k];
Complex t = w * y[k + h / 2];
y[k] = u + t;
y[k + h / 2] = u - t;
w = w * wn;
}
}
}

if(on == -1)  
    for(int i = 0; i < len; i++)  
        y\[i\].x /= len;  

}

Complex x1[4000005], x2[4000005];

int main()
{
scanf("%d%d", &n, &m);
for(int i = 0; i <= n; i++) {
int u; u = read();
x1[i] = Complex(1.0 * u, 0);
}
for(int i = 0; i <= m; i++) {
int u; u = read();
x2[i] = Complex(1.0 * u, 0);
}

int len = 1;  
while(len <= n + m) len <<= 1;

fft(x1, len, 1);  
fft(x2, len, 1);  
for(int i = 0; i <= len; i++) x1\[i\] = x1\[i\] \* x2\[i\];  
fft(x1, len, -1);

for(int i = 0; i <= n + m; i++) printf("%d ", (int)(x1\[i\].x + 0.5));  
return 0;  

}

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