UOJ 34: 多项式乘法（FFT模板题）

关于FFT

这个博客的讲解超级棒

http://blog.miskcoo.com/2015/04/polynomial-multiplication-and-fast-fourier-transform

算法导论上的讲解也不错

模板就是抄一抄别人的啦

首先是递归版本

 #include <cstdio>
 #include <complex>
 #include <cmath>
 using namespace std;

 const double pi = acos(-);
 const int N = ( << ) + ;
 typedef complex<double> cp;
 cp A[N], B[N];
 int n, m;

 void FFT(cp *y, int n, int o) {
     if (n == )    return ;
     cp l[n >> ], r[n >> ];
     for (int i = ; i <= n; i++)
         if (i & )    r[i >> ] = y[i];
         else    l[i >> ] = y[i];
     FFT(l, n >> , o); FFT(r, n >> , o);
     cp omegan(cos( * pi / n), sin( * pi * o / n)), omega(, );
     for (int i = ; i < n >> ; i++) {
         y[i] = l[i] + omega * r[i];
         y[i + (n >> )] = l[i] - omega * r[i];
         omega *= omegan;
     }
 }

 int main() {
     scanf("%d %d", &n, &m);
     for (int i = ; i <= n; i++)
         scanf("%lf", &A[i].real());
     for (int i = ; i <= m; i++)
         scanf("%lf", &B[i].real());
     m += n;
     for (n = ; n <= m; n <<= );
     FFT(A, n, ); FFT(B, n, );
     for (int i = ; i <= n; i++)
         A[i] *= B[i];
     FFT(A, n, -);
     for (int i = ; i <= m; i++)
         printf("%d ", (int)(A[i].real() / n + 0.5));
     return ;
 }

迭代版本

 #include <cstdio>
 #include <cmath>
 #include <complex>
 #include <iostream>
 using namespace std;

 const int N =  << ;
 typedef complex<double> cp;
 const double pi = acos(-1.0);
 cp A[N], B[N];
 bool flag;
 int a[N], b[N], n, m, tar[N], bit;

 inline void read(int &ans) {
     static char buf = getchar();
     ans = ;
     for (; !isdigit(buf); buf = getchar());
     for (; isdigit(buf); buf = getchar())
         ans = ans *  + buf - '';
 }

 inline int rev(int val) {
     int rst = ;
     for (int i = ; i < bit; i++) {
         rst <<= ; rst |= val & ; val >>= ;
     } return rst;
 }

 inline void FFT(cp *y) {
     for (int i = ; i <= bit; i++) {
         int fac =  << i;
         cp omegan(cos( * pi / fac), sin( * pi / fac));
         if (flag)    omegan.imag() *= -;
         for (int j = ; j < n; j += fac) {
             cp omega(, );
             for (int k = ; k < fac >> ; k++) {
                 cp t = omega * y[j + k + (fac >> )];
                 cp u = y[j + k]; y[j + k] = u + t;
                 y[j + k + (fac >> )] = u - t;
                 omega *= omegan;
             }
         }
     }
 }
 int main() {
     read(n); read(m); n++; m++;
     for (int i = ; i < n; i++)    read(a[i]);
     for (int i = ; i < m; i++)    read(b[i]);
     m += n; for (n = ; n < m; n <<= )    bit++;
     for (int i = ; i < n; i++)    tar[i] = rev(i);
     for (int i = ; i < n; i++)    A[i].real() = a[tar[i]];
     for (int i = ; i < n; i++)    B[i].real() = b[tar[i]];
     FFT(A); FFT(B);
     for (int i = ; i < n; i++)    A[i] *= B[i];
     for (int i = ; i < n; i++)    if (i < tar[i])    swap(A[i], A[tar[i]]);
     flag = true; FFT(A);
     for (int i = ; i < m - ; i++)
         printf("%.0lf ", 0.0001 + A[i].real() / n);
        puts("");
     return ;
 }