P4035 [JSOI2008]球形空间产生器

爬山算法

#include <bits/stdc++.h>
#define inf 2333333333333333
#define N 1000010
#define p(a) putchar(a)
#define For(i,a,b) for(int i=a;i<=b;++i)

using namespace std;
int n,m;
long double tot,f[20][20],ans[20],d[20],cans[20];
void in(int &x){
    int y=1;char c=getchar();x=0;
    while(c<'0'||c>'9'){if(c=='-')y=-1;c=getchar();}
    while(c<='9'&&c>='0'){ x=(x<<1)+(x<<3)+c-'0';c=getchar();}
    x*=y;
}
void o(int x){
    if(x<0){p('-');x=-x;}
    if(x>9)o(x/10);
    p(x%10+'0');
}

void check(){
    tot=0;
    For(i,1,m){
        d[i]=0;cans[i]=0;
        For(j,1,n){
            d[i]+=(f[i][j]-ans[j])*(f[i][j]-ans[j]);
        }
        tot+=d[i];
    }
    tot/=(long double)m;
    For(i,1,m){
        For(j,1,n){
            cans[j]+=(d[i]-tot)*(f[i][j]-ans[j])/tot;
        }
    }
}

signed main(){
    in(n);m=n+1;
    For(i,1,m)
        For(j,1,n){
            cin>>f[i][j];
            ans[j]+=f[i][j];
        }
    For(j,1,n) ans[j]/=(long double)m;
    for(long double t=1000;t>=1e-1;t*=0.9999){
        check();
        For(j,1,n) ans[j]+=cans[j]*t;
    }
    For(j,1,n) printf("%.3Lf ",ans[j]);
    return 0;
}