题意:
给你不超过8条一端在圆心的半径,求他们组成的凸包的最大面积.
SOL:
正解怎么搞啊不会啊...然后昨天毛爷爷刚讲过模拟退火...那么就打一个吧...
然后就T了,不过三角形的部分分妥妥的...
然后在自信的协助下被他改了改参数然后过了九个点...(对着数据调参也是醉了...
剩下一个点感觉没法搞啊QAQ...差太多了...感觉退完火爬爬山应该会很兹瓷...
90分code:
/*==========================================================================
# Last modified:
# Filename: .cpp
# Description:
==========================================================================*/
#define me AcrossTheSky
#include <cstdio>
#include <cmath>
#include <ctime>
#include <string>
#include <cstring>
#include <cstdlib>
#include <iostream>
#include <algorithm>
#include <set>
#include <map>
#include <stack>
#include <queue>
#include <vector>
#define lowbit(x) (x)&(-x)
#define FOR(i,a,b) for((i)=(a);(i)<=(b);(i)++)
#define FORP(i,a,b) for(int i=(a);i<=(b);i++)
#define FORM(i,a,b) for(int i=(a);i>=(b);i--)
#define ls(a,b) (((a)+(b)) << 1)
#define rs(a,b) (((a)+(b)) >> 1)
#define getlc(a) ch[(a)][0]
#define getrc(a) ch[(a)][1]
#define maxn 10
#define maxm 100000
#define limm 1e-6
#define pi acos(-1)
#define _e 2.718281828459
#define INF 1070000000
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
template<class T> inline
void read(T& num) {
bool start=false,neg=false;
char c;
num=0;
while((c=getchar())!=EOF) {
if(c=='-') start=neg=true;
else if(c>='0' && c<='9') {
start=true;
num=num*10+c-'0';
} else if(start) break;
}
if(neg) num=-num;
}
/*==================split line==================*/
int a[maxn],temp[maxn],tmp[maxn];
double angle[maxn];
int n;
double ans=0;
bool vis[maxn];
set<int> s;
int cmp(int x,int y){return x>y;}
double getang(double x){ return x/180*pi; }
double calc(int ord,double ang,int m){
return temp[ord]*temp[ord%m+1]*sin(getang(ang))/2;
}
int getposb(double c,double b){
double tttt=exp(c/b);
return tttt;
}
void work(int m){
double aaa=360.0/m;
double sum=0;
FORP(i,1,m) { angle[i]=aaa; sum+=calc(i,angle[i],m); }
//angle[m]=360-aaa;
//sum+=calc(m,angle[m],m);
double maxx=sum;
//ans=max(ans,sum);
double T=100;
if (n < 4) T = 1000;
while (fabs(T-0)>1e-5){
if (maxx < 94*ans/100) return;
int pos=rand()%m+1,next=pos%m+1;
double ttemp=calc(pos,angle[pos],m)+calc(next,angle[next],m);
ll cap=trunc(max(angle[pos],angle[next])*100000000/T);
double change=(rand()%cap)*T/100000000;
double dx,dy;
if (angle[pos]-change<0) dx=angle[pos]+change,dy=angle[next]-change;
else dx=angle[pos]-change,dy=angle[next]+change;
double delta=calc(pos,dx,m)+calc(next,dy,m)-ttemp;
if (delta>0){
sum+=delta;
angle[pos]=dx,angle[next]=dy;
}
else{
double posb=getposb(delta,ans*T);
int xxx=10000000/trunc(T);
int rp=rand()%xxx;
if ((double)rp*T/100000000.0<posb) {
sum+=delta;
angle[pos]=dx,angle[next]=dy;
}
}
if (sum>ans) {
//FORP(i,1,m) printf("%d ",temp[i]);
//cout << endl;
//FORP(i,1,m) printf("%lf ",angle[i]);
//cout << endl;
//printf("%lf
",sum);
ans=sum;
}
maxx=max(maxx,sum);
if (n >= 4) T*=0.89;
else T *= 0.999;
}
if (sum>ans) ans=sum;
}
int fpow(int s,int m){
int ret=1;
for (;m;m>>=1,s=s*s) if (m&1) ret*=s;
return ret;
}
void dfs(int x,int m,int tot){
if (x==m+1) {
work(m);work(m);
work(m);work(m);
return;
}
FORP(i,1,n)
if (!vis[i]) {
vis[i]=true; temp[x]=a[i]; dfs(x+1,m,tot*10+i); vis[i]=false;
}
}
int main(){
srand(time(0));
freopen("yist.in","r",stdin);
freopen("yist.out","w",stdout);
read(n); bool flag=true;
if (n==2) {printf("0
"); return 0;}
FORP(i,1,n) read(a[i]);
FORP(i,1,n) { if (i>1 & a[i]!=a[i-1]) flag=false; }
if (flag){
if (n==3) printf("%.8lf
",a[1]*sqrt(3)*(a[1]+a[1]/2.0)/2.0);
else printf("%.8lf",(double)a[1]*a[1]*sin(2*pi/n)*n/2.0);
}
else{
if (n==3){
FORP(i,1,n) temp[i]=a[i];
dfs(1,n,0);
}
else{
FORP(i,3,n-1){
memset(vis,false,sizeof(vis));
//s.clear();
dfs(1,i,0);
}
memset(vis,false,sizeof(vis));
s.clear(); temp[1]=1; vis[1]=1;
dfs(2,n,0);
}
printf("%.10lf
",ans);
}
}