FFT模板

大佬的FFT详解（点击打开链接）

复根的设置：typedef complex E;

π=acos(-1)：

#define pi acos(-1)

const double pi=3.14159265358979;

单位复根：

E wn(cos(pi/i),f*sin(pi/i)); (快) 

E wn=exp(E(0,f*pi/i));（慢）exp（x）为e的x次方

//ω单位复根 

FFT

#include
#define N 2621450
#define pi acos(-1) 
using namespace std;
typedef complex E;
int n,m,l,r[N];
E a[N],b[N];
void fft(E *a,int f){
    for(int i=0;i'9');
    do{x=x*10+ch-'0';ch=getchar();}while(ch>='0'&&ch<='9');
    return f*x;
}
int main(){
    n=read();m=read();
    for(int i=0;i<=n;i++)a[i]=read();
    for(int i=0;i<=m;i++)b[i]=read();
    m+=n;for(n=1;n<=m;n<<=1)l++;
    for(int i=0;i>1]>>1)|((i&1)<<(l-1));
    fft(a,1);fft(b,1);
    for(int i=0;i<=n;i++)a[i]=a[i]*b[i];
    fft(a,-1);
    for(int i=0;i<=m;i++)printf("%d ",(int)(a[i].real()/n+0.5));
}

NFT（快速数论变换）

1

#include
#define getchar() (p1 == p2 && (p2 = (p1 = buf) + fread(buf, 1, 1<<21, stdin), p1 == p2) ? EOF : *p1++)
#define swap(x,y) x ^= y, y ^= x, x ^= y
#define LL long long 
const int MAXN = 3 * 1e6 + 10, P = 998244353, G = 3, Gi = 332748118; 
char buf[1<<21], *p1 = buf, *p2 = buf;
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, limit = 1, L, r[MAXN];
LL a[MAXN], b[MAXN];
inline LL fastpow(LL a, LL k) {
    LL base = 1;
    while(k) {
        if(k & 1) base = (base * a ) % P;
        a = (a * a) % P;
        k >>= 1;
    }
    return base % P;
}
inline void NTT(LL *A, int type) {
    for(int i = 0; i < limit; i++) 
        if(i < r[i]) swap(A[i], A[r[i]]);
    for(int mid = 1; mid < limit; mid <<= 1) {  
        LL Wn = fastpow( type == 1 ? G : Gi , (P - 1) / (mid << 1));
        for(int j = 0; j < limit; j += (mid << 1)) {
            LL w = 1;
            for(int k = 0; k < mid; k++, w = (w * Wn) % P) {
                 int x = A[j + k], y = w * A[j + k + mid] % P;
                 A[j + k] = (x + y) % P,
                 A[j + k + mid] = (x - y + P) % P;
            }
        }
    }
}
int main() {
    N = read(); M = read();
    for(int i = 0; i <= N; i++) a[i] = (read() + P) % P;
    for(int i = 0; i <= M; i++) b[i] = (read() + P) % P;
    while(limit <= N + M) limit <<= 1, L++;
    for(int i = 0; i < limit; i++) r[i] = (r[i >> 1] >> 1) | ((i & 1) << (L - 1));  
    NTT(a, 1);NTT(b, 1);    
    for(int i = 0; i < limit; i++) a[i] = (a[i] * b[i]) % P;
    NTT(a, -1); 
    LL inv = fastpow(limit, P - 2);
    for(int i = 0; i <= N + M; i++)
        printf("%d ", (a[i] * inv) % P);
    return 0;
}

2

#include
#include
#include
#include
//#include
using namespace std;
//typedef complex cd;

typedef long long LL;

void exgcd(int a,int b,int& x,int& y){
    if(b==0){
        x=1;
        y=0;
        return;
    }
    int x0,y0;
    exgcd(b,a%b,x0,y0);
    x=y0;y=x0-int(a/b)*y0;
}

int Inv(int a,int p){
    int x,y;
    exgcd(a,p,x,y);
    x%=p;
    while(x<0)x+=p;
    return x;
}

int qpow(int a,int b,int p){
    if(b<0){
        b=-b;
        a=Inv(a,p);
    }
    LL ans=1,mul=a%p;
    while(b){
        if(b&1)ans=ans*mul%p;
        mul=mul*mul%p;
        b>>=1;
    }
    return ans;
}

#define maxn (65537*2)
const int MOD=479*(1<<21)+1,G=3;

int rev[maxn];
void get_rev(int bit){
    for(int i=0;i<(1<>1]>>1)|((i&1)<<(bit-1));
    }
}

//from internet
//for(int i=0; i
char s1[maxn],s2[maxn];

int main(){
    //scanf("%*d");
    scanf("%s%s",s1,s2);
    int l1=strlen(s1),l2=strlen(s2);
    for(int i=0;i=0 && a[cnt]==0)cnt--;
    if(cnt==-1)printf("0");
    for(int i=cnt;i>=0;i--){
        printf("%d",a[i]);
    }
    putchar('\n');
    return 0;
}