HUOJ-10857 最大的面积 凸包+DP

　　题目链接：http://acm.hunnu.edu.cn/online/?action=problem&type=show&id=10857&courseid=55

　　比赛的时候把题目看成取恰好K个点了，，，悲剧。。然后按照正确的题意的话，是比较好做的，求个凸包，然后DP就可以了，f[i][j][k]表示第 i 个点到第 j 点选择k个点的多边形的最大面积，那么f[i][j][k]=Max{ f[i][j][k], f[i][y][k-1]+area(p[i],p[y],p[j]) }就可以了。。

　　这题相当悲剧，题目的数据范围描述错了，k应该是小于等于30，因为题目sb，看了一晚上的代码= =！

 //STATUS:C++_AC_0MS_1284KB
 #include <functional>
 #include <algorithm>
 #include <iostream>
 //#include <ext/rope>
 #include <fstream>
 #include <sstream>
 #include <iomanip>
 #include <numeric>
 #include <cstring>
 #include <cassert>
 #include <cstdio>
 #include <string>
 #include <vector>
 #include <bitset>
 #include <queue>
 #include <stack>
 #include <cmath>
 #include <ctime>
 #include <list>
 #include <set>
 #include <map>
 using namespace std;
 //#pragma comment(linker,"/STACK:102400000,102400000")
 //using namespace __gnu_cxx;
 //define
 #define pii pair<int,int>
 #define mem(a,b) memset(a,b,sizeof(a))
 #define lson l,mid,rt<<1
 #define rson mid+1,r,rt<<1|1
 #define PI acos(-1.0)
 //typedef
 typedef long long LL;
 typedef unsigned long long ULL;
 //const
 const int N=;
 const int INF=0x3f3f3f3f;
 const int MOD=,STA=;
 const LL LNF=1LL<<;
 const double EPS=1e-;
 const double OO=1e60;
 const int dx[]= {-,,,};
 const int dy[]= {,,,-};
 const int day[]= {,,,,,,,,,,,,};
 //Daily Use ...
 //End

 struct point{
     double x, y;
 }p[N],res[N];

 double f[N][N];
 int T,n,k;

 bool mult(point sp, point ep, point op)
 {
     return (sp.x - op.x) * (ep.y - op.y)>= (ep.x - op.x) * (sp.y - op.y);
 }

 bool operator < (const point &l, const point &r)
 {
     return l.y < r.y || (l.y == r.y && l.x < r.x);
 }

 int graham(point pnt[], int n, point res[])
 {
     int i, len, k = , top = ;
     sort(pnt, pnt + n);
     if (n == ) return ;
     res[] = pnt[];
     if (n == ) return ;
     res[] = pnt[];
     if (n == ) return ;
     res[] = pnt[];
     for (i = ; i < n; i++){
         while (top && mult(pnt[i], res[top], res[top-]))top--;
         res[++top] = pnt[i];
     }
     len = top;
     res[++top] = pnt[n - ];
     for (i = n - ; i >= ; i--){
         while (top!=len && mult(pnt[i], res[top], res[top-])) top--;
         res[++top] = pnt[i];
     }
     return top; // 返回凸包中点的个数
 }

 double arear(point& a,point& b,point& c)
 {
     double ret=;
     ret+=a.x*b.y-a.y*b.x;
     ret+=b.x*c.y-b.y*c.x;
     ret+=c.x*a.y-c.y*a.x;
     return ret/;
 }

 int main()
 {
  //   freopen("in.txt","r",stdin);
     int i,j,x,y,cnt;
     double ans;
     scanf("%d",&T);
     while(T--)
     {
         scanf("%d%d",&n,&k);
         for(i=; i<n; i++){
             scanf("%lf%lf",&p[i].x,&p[i].y);
         }
         cnt=graham(p,n,res);
         if(cnt<= || k<=){
             printf("0.00\n");
             continue;
         }
         if(cnt<=k){
             double sum=;
             for(i=;i<cnt;i++)
                 sum+=res[i].x*res[(i+)%cnt].y-res[i].y*res[(i+)%cnt].x;
             printf("%.2lf\n",sum/=);
             continue;
         }
         ans=;
         int m=cnt;
         while(m--){
             mem(f,);
             point t=res[];
             for(j=;j<cnt-;j++)res[j]=res[j+];
             res[j]=t;
             for(j=;j<cnt;j++){
                 for(x=;x<=j+ && x<=k;x++){
                     for(y=x-;y<j;y++){
                         f[j][x]=max(f[j][x],f[y][x-]+arear(res[],res[y],res[j]));
                     }
                 }
                 ans=max(ans,f[j][k]);
             }
         }

         printf("%.2lf\n",ans);
     }
     return ;
 }