p3723 [AH2017/HNOI2017]礼物

分析

https://www.luogu.org/blog/dedicatus545/solution-p3723

代码

#include<bits/stdc++.h>
using namespace std;
#define pi acos(-1.0)
#define int long long
const int inf = 1e17+9;
int n,m,r[2000100],len;
struct node {
    double x,y;
};
node a[2000100],b[2000100];
inline node operator + (const node x,const node y){return (node){x.x+y.x,x.y+y.y};}
inline node operator - (const node x,const node y){return (node){x.x-y.x,x.y-y.y};}
inline node operator * (const node x,const node y){return (node){x.x*y.x-x.y*y.y,x.x*y.y+x.y*y.x};}
inline void fft(node a[],int f){
    int i,j,k;
    for(i=0;i<n;i++)if(i<r[i])swap(a[i],a[r[i]]);
    for(i=1;i<n;i<<=1){
          node wn=(node){cos(pi/i),f*sin(pi/i)};
      for(j=0;j<n;j+=(i<<1)){
          node w=(node){1,0},p,q;
          for(k=0;k<i;k++,w=w*wn){
            p=a[j+k],q=a[i+j+k]*w;
            a[j+k]=p+q,a[i+j+k]=p-q;
        }
      }
    }
    if(f==-1)for(i=0;i<n;i++)a[i].x=a[i].x/n;
}
signed main(){
    int i,j,k;
    scanf("%d%d",&n,&m);
    for(i=1;i<=n;i++)scanf("%lf",&a[i].x);
    for(i=1;i<=n;i++)scanf("%lf",&b[i].x);
    int res=0,Ans=inf,sum=0;
    for(i=1;i<=n;i++)res+=a[i].x*a[i].x+b[i].x*b[i].x,sum+=2*(a[i].x-b[i].x);
    reverse(a+1,a+n+1);
    for(i=1;i<=n;i++)a[i+n]=a[i];
    int n1=3*n;
    for(n=1;n<=n1;n<<=1)len++;
    for(i=0;i<n;i++)r[i]=((r[i>>1]>>1)|((i&1)<<(len-1)));
    fft(a,1),fft(b,1);
    for(i=0;i<n;i++)a[i]=a[i]*b[i];
    fft(a,-1);
    n=n1/3;
    for(i=1;i<=n;i++)
      for(j=-m;j<=m;j++)
        Ans=min(Ans,res+j*j*n+j*sum-2*(int)(a[i+n].x+0.5));
    cout<<Ans<<"\n";
    return 0;
}