快速傅里叶变换（FFT）板子

递归版

//UOJ 34
//Luogu 3803
//By Hany01
#include<bits/stdc++.h>
#define For(i ,j , k) for (int i = (j) ; i <= (k) ; ++ i)
#ifdef hany01
#define debug(...) fprintf(stderr , __VA_ARGS__)
#else
#define debug(...)
#endif
typedef long long LL;
using namespace std;
typedef complex<double>cpx;

inline void file()
{
freopen("fft.in" , "r" , stdin);
freopen("fft.out" , "w" , stdout);
}

template <typename T> inline bool chkmax(T &a , const T &b) { return a < b ? a = b , 1 : 0; }
template <typename T> inline bool chkmin(T &a , const T &b) { return a > b ? a = b , 1 : 0; }

char c_;
int _ , __;
inline int read()
{
for (_ = 0 , __ = 1 , c_ = getchar() ; !isdigit(c_) ; c_ = getchar()) if (c_ == '-') __ = -1;
for ( ; isdigit(c_) ; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
return _ * __;
}

const int maxn = (1 << 22) + 10;
const double Pi = acos(-1.0);
int n , m;
cpx a[maxn] , b[maxn];

inline void Init()
{
n = read();
m = read();
For(i , 0 , n)
a[i] = read();
For(i , 0 , m)
b[i] = read();
m += n;
for (n = 1 ; n <= m ; n <<= 1) ;
}

inline void FFT(cpx *x , int n , int type)
{
if (n == 1)
return ;
cpx l[n >> 1] , r[n >> 1];
for (int i = 0 ; i < n ; i += 2)
l[i >> 1] = x[i] ,
r[i >> 1] = x[i + 1];
FFT(l , n >> 1 , type);
FFT(r , n >> 1 , type);
cpx wn(cos(2 * Pi / n) , sin(type * 2 * Pi / n)) , w(1 , 0) , t;
for (int i = 0 ; i < n >> 1 ; ++ i , w *= wn)
{
t = w * r[i];
x[i] = l[i] + t;
x[i + (n >> 1)] = l[i] - t;
}
}

int main()
{
#ifdef hany01
file();
#endif
Init();
FFT(a , n , 1);
FFT(b , n , 1);
For(i , 0 , n)
debug("%lf\n" , a[i].real());
For(i , 0 , n)
a[i] *= b[i];
FFT(a , n , -1);
For(i , 0 , m)
printf("%d " , (int)round(a[i].real() / n));
return 0;
}
//千里黄云白日曛，北风吹雁雪纷纷。
//    -- 高适《别董大二首》

迭代版(faster)

#include<bits/stdc++.h>

using namespace std;

#define rep(i, j) for (register int i = 0, i##_end_ = j; i < i##_end_; ++ i)
#define getchar getchar_unlocked
#define putchar putchar_unlocked

inline int read()
{
register int _, __; register char c_;
for (_ = 0 , __ = 1 , c_ = getchar() ; !isdigit(c_) ; c_ = getchar()) if (c_ == '-') __ = -1;
for ( ; isdigit(c_) ; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48);
return _ * __;
}

const double pi = acos(-1.0);
const int maxn = 1<<21;

struct Complex
{
double real, imag;
}a[maxn], b[maxn];
inline Complex operator + (const Complex &A, const Complex &B) { return (Complex){A.real + B.real, A.imag + B.imag}; }
inline Complex operator - (const Complex &A, const Complex &B) { return (Complex){A.real - B.real, A.imag - B.imag}; }
inline Complex operator * (const Complex &A, const Complex &B) { return (Complex){A.real * B.real - A.imag * B.imag, A.real * B.imag + A.imag * B.real}; }

int n, r[maxn];

inline void fft(Complex *a, int type)
{
rep(i, n) if (i < r[i]) swap(a[i], a[r[i]]);
for (register int i = 2; i <= n; i <<= 1)
{
register Complex wn = Complex{cos(2 * pi / i), sin(2 * pi / i * type)};
for (register int j = 0; j < n; j += i)
{
register Complex w = Complex{1, 0};
rep(k, i >> 1) {
register Complex x = a[j + k], y = a[j + k + (i >> 1)] * w;
a[j + k] = x + y; a[j + k + (i >> 1)] = x - y;
w = w * wn;
}
}
}
}

int main()
{
int n1, n2, m, cnt;
n1 = read() + 1; n2 = read() + 1; m = n1 + n2 - 1;
rep(i, n1) a[i].real = read();
rep(i, n2) b[i].real = read();
for (n = 1; n < m; n <<= 1) ++ cnt;
rep(i, n) r[i] = (r[i >> 1] >> 1) | ((i & 1) << (cnt - 1));
fft(a, 1);
fft(b, 1);
rep(i, n) a[i] = a[i] * b[i];
fft(a, -1);
rep(i, m) printf("%d", (int)(a[i].real / n + 0.5)), putchar(' ');
return 0;
}
//楚塞三湘接，荆门九派通。
//江流天地外，山色有无中。
//郡邑浮前浦，波澜动远空。
//襄阳好风日，留醉与山翁。
//--王维《汉江临泛》