多项式相关算法模板

多项式乘法

#include <bits/stdc++.h>
using namespace std;
const double pi = acos(-1);
const int LEN = 1e5 + 5;
int n, m, N;
namespace ploy {
    struct comp {
        double x, y;
    } a[LEN * 4], b[LEN * 4];
    comp operator + (const comp &x,const comp &y) {
        return (comp){x.x + y.x, x.y + y.y};
    }
    comp operator - (const comp &x,const comp &y) {
        return (comp){x.x - y.x, x.y - y.y};
    }
    comp operator * (const comp &x,const comp &y) {
        return (comp){x.x * y.x - x.y * y.y, x.x * y.y + x.y * y.x};
    }
    void FFT(comp *a, int n, int x) {
        for (int i = n >> 1, j = 1; j < n; j++) {
            if (i < j) swap(a[i], a[j]);
            int k = n >> 1;
            for (; k & i; i ^= k, k >>= 1);
            i ^= k;
        }
        for (int m = 2; m <= n; m <<= 1) {
            comp w = (comp){cos(2.0 * pi * x / m), sin(2.0 * pi * x / m)};
            for (int i = 0; i + m <= n; i += m) {
                comp t = (comp){1, 0};
                for (int j = i; j < i + (m >> 1); j++) {
                    comp u = a[j];
                    comp v = t * a[j + (m >> 1)];
                    a[j] = u + v;
                    a[j + (m >> 1)] = u - v;
                    t = t * w;
                }
            }
        }
        if (x == -1) {
            for (int i = 0; i < n; i++) a[i].x /= n;
        }
    }
}
using namespace ploy;
int main() {
    scanf("%d %d", &n, &m);
    n++, m++;
    N = 1;
    while (N < n + m - 1) N <<= 1;
    for (int i = 0; i < n; i++) scanf("%lf", &a[i].x);
    for (int i = 0; i < m; i++) scanf("%lf", &b[i].x);
    FFT(a, N, 1);
    FFT(b, N, 1);
    for (int i = 0; i < N; i++) a[i] = a[i] * b[i];
    FFT(a, N, -1);
    for (int i = 0; i < n + m - 2; i++) printf("%d ", (int)(a[i].x + 0.5));
    printf("%d
", (int)(a[n + m - 2].x + 0.5));
    return 0;
}