Chrysanthemum's Blog

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Input

Output

Sample Input

Sample Output

HINT

我们发现高精度乘法的每一位是满足卷积的形式的，所以我们先fft搞出c数组，然后再一位一位进位上去就可以了。

代码：

#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;
double pi=acos(-1);
int n,m,l,c[500010];
char s[100010];
struct cp{double x,y;};
cp a[500010],b[500010],cur[500010];
cp operator *(cp x,cp y){return (cp){x.x*y.x-x.y*y.y,x.x*y.y+x.y*y.x};}
cp operator +(cp x,cp y){return (cp){x.x+y.x,x.y+y.y};}
cp operator -(cp x,cp y){return (cp){x.x-y.x,x.y-y.y};}
void fft(cp *a,int n,int fl)
{
    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)
    {
        cp w=(cp){cos(2*pi*fl/m),sin(2*pi*fl/m)};
        cur[0]=(cp){1,0};
        for (int i=1;i<m;i++) cur[i]=cur[i-1]*w;
        for (int i=0;i<n;i+=m)
            for (int j=i;j<i+(m>>1);j++)
            {
                cp u=a[j],v=a[j+(m>>1)]*cur[j-i];
                a[j]=u+v;
                a[j+(m>>1)]=u-v;
            }
    }
}
int main()
{
    scanf("%d",&n);
    scanf("%s",s);
    for (int i=0;i<n;i++)
        a[i].x=s[n-i-1]-'0';
    scanf("%s",s);
    for (int i=0;i<n;i++)
        b[i].x=s[n-i-1]-'0';
    m=1;while (m<=n*2) m*=2;
    fft(a,m,1);fft(b,m,1);
    for (int i=0;i<=m;i++) a[i]=a[i]*b[i];
    fft(a,m,-1);
    for (int i=0;i<=m;i++)
        c[i]=(int)(a[i].x/m+0.5);
    for (int i=0;i<=m;i++)
    {
        c[i+1]+=c[i]/10;
        c[i]%=10;
    }
    l=m;while (!c[l]) l--;
    for (int i=l;i>=0;i--) printf("%d",c[i]);printf("\n");
}