FFT多项式乘法

[LuoguP3803]

学了好久才懂了那么一点点哎

Code：

#include <bits/stdc++.h>
#define ll long long
using namespace std;
const int N = 1e7 + 7;
const double Pi = acos(-1.0);
ll read() {
    ll re = 0, f = 1;
    char ch = getchar();
    while (ch < '0' || ch > '9') {if (ch == '-') f = -f; ch = getchar();}
    while ('0' <= ch && ch <= '9') {re = re * 10 + ch - '0'; ch = getchar();}
    return re * f;
}
int n, m;
int l, pos[N], limit = 1;
struct Complex{
    double x, y;
    Complex (double nx = 0, double ny = 0) {x = nx, y = ny;}
}a[N], b[N];
Complex operator +(Complex a, Complex b) {return Complex(a.x + b.x, a.y + b.y);}
Complex operator -(Complex a, Complex b) {return Complex(a.x - b.x, a.y - b.y);}
Complex operator *(Complex a, Complex b) {return Complex(a.x*b.x-a.y*b.y, a.x*b.y+b.x*a.y);}
void FFT(Complex *A, int f) {
    for (int i = 0; i < limit; i++) {
        if (i < pos[i]) swap(A[i], A[pos[i]]);
    }
    for (int mid = 1; mid < limit; mid <<= 1) {
        Complex wn(cos(Pi / mid), f * sin(Pi / mid));
        for (int r = mid << 1, i = 0; i < limit; i += r) {
            Complex w(1, 0);
            for (int k = 0; k < mid; k++, w = w * wn) {
                Complex u = A[i + k], v = w * A[i + k + mid];
                A[i + k] = u + v;
                A[i + k + mid] = u - v;
            }
        }
    }
    if (f == -1) {
        for (int i = 0; i < limit; i++) A[i].x /= limit;
    }
}
int main () {
    n = read(), m = read();
    for (int i = 0; i <= n; i++) {
        a[i].x = read();
    }
    for (int i = 0; i <= m; i++) {
        b[i].x = read();
    }
    while (limit <= n + m) l++, limit <<= 1;
    for (int i = 0; i < limit; i++) {
        pos[i] = (pos[i >> 1] >> 1) | ((i & 1) << (l - 1));
    }
    FFT(a, 1), FFT(b, 1);
    for (int i = 0; i < limit; i++) {
        a[i] = a[i] * b[i];
    }
    FFT(a, -1);
    for (int i = 0; i <= n + m; i++) {
        printf("%d%c", (int)(a[i].x + 0.5), i == n + m ? '
' : ' ');
    }
    return 0;
}