poj2079Triangle(N点中三点组成三角形面积最大）

链接

根据旋转卡壳的思想，找到当前边的最远点。

确定i,j找到最远的k使 cross(i,j,k)最大，那么i,j+1时只需从k+1开始找即可 。

 #include <iostream>
 #include<cstdio>
 #include<cstring>
 #include<algorithm>
 #include<stdlib.h>
 #include<vector>
 #include<cmath>
 #include<queue>
 #include<set>
 using namespace std;
 #define N 50010
 #define LL long long
 #define INF 0xfffffff
 const double eps = 1e-;
 const double pi = acos(-1.0);
 const double inf = ~0u>>;
 struct point
 {
     int x,y;
     point(int x=,int y=):x(x),y(y) {}
 } p[N],ch[N];
 typedef point pointt;
 pointt operator - (point a,point b)
 {
     return point(a.x-b.x,a.y-b.y);
 }
 int dcmp(double x)
 {
     if(fabs(x)<eps) return ;
     return x<?-:;
 }
 double cross(point a,point b)
 {
     return 1.0*a.x*b.y-1.0*a.y*b.x;
 }
 double getarea(point a,point b,point c)
 {
     return fabs(cross(b-a,c-a))/;
 }
 double mul(point p0,point p1,point p2)
 {
     return cross(p1-p0,p2-p0);
 }
 double dis(point a)
 {
     return sqrt(1.0*a.x*a.x+a.y*a.y);
 }
 bool cmp(point a,point b)
 {
     if(dcmp(mul(p[],a,b))==) return dis(a-p[])<dis(b-p[]);
     return dcmp(mul(p[],a,b))>;
 }
 int graham(int n)
 {
     int i,k=,top;
     point tmp;
     for(i = ;  i< n; i++)
     {
         if(p[i].y<p[k].y||(p[i].y==p[k].y&&p[i].x<p[k].x))
             k = i;
     }
     if(k!=)
         swap(p[],p[k]);
     sort(p+,p+n,cmp);
     ch[] = p[];
     ch[] = p[];
     top = ;
     for(i = ; i < n; i++)
     {
         while(top>&&dcmp(mul(ch[top-],ch[top],p[i]))<=)
             top--;
         ch[++top] = p[i];
     }
     return top;
 }
 int main()
 {
     int n,i,j,k,kk;
     while(scanf("%d",&n)!=EOF)
     {
         if(n==-) break;
         for(i = ; i < n; i++)
             scanf("%d%d",&p[i].x,&p[i].y);
         int top = graham(n);
         double maxz=,area;
     ++top;
     ch[top] = ch[];
     for(i=; i<top; ++i)
     {
         j=(i+)%top;
         k=(j+)%top;
         while(k!=i && getarea(ch[i],ch[j],ch[k])<getarea(ch[i],ch[j],ch[k+]))
             k=(k+)%top;
         maxz = max(maxz,getarea(ch[i],ch[j],ch[k]));
         if(k == i)
             continue;
         kk=(k+)%top;
         while(j!=kk && k!=i)
         {
             area=getarea(ch[i],ch[j],ch[k]);
             if(area>maxz)
                 area=maxz;
             while(k!=i && getarea(ch[i],ch[j],ch[k])<getarea(ch[i],ch[j],ch[k+]))
                 k=(k+)%top;
             maxz = max(maxz,getarea(ch[i],ch[j],ch[k]));
             j=(j+)%top;
         }
     }
     printf("%.2f\n",maxz);

     }return ;
 }