hdu_2202_凸包求最大三角形

//先求凸包,枚举凸包上的点求最大三角形

#include<iostream>

#include<cmath>

#include<cstdio>

#include<algorithm>

using namespace std;

 

struct point

{

int x,y;

}a[50001],stack[50001],flag;

int n;

 

int sect(point a,point b,point c)

{

return (a.x-c.x)*(b.y-c.y)-(b.x-c.x)*(a.y-c.y);

}

 

double dis(point a,point b)

{

return sqrt((double)((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y)));

}

 

double area(point a,point b,point c)

{

double x=dis(a,b),y=dis(a,c),z=dis(b,c);

double p=(x+y+z)/2.0;

double s=p*(p-x)*(p-y)*(p-z);

return sqrt(s);

}

 

int cmp(point a,point b)

{

return sect(a,b,flag)>1e-8;

}

 

double graham()

{

int top=1;

stack[0]=a[0];

stack[1]=a[1];

int i,j,k;

for(i=2;i<n;i++)

{

while(top>0&&sect(a[i],stack[top],stack[top-1])>0)top--;

stack[++top]=a[i];

}

/*printf("/n");

for(i=0;i<=top;i++)

printf("%d %d/n",stack[i].x,stack[i].y);

printf("/n");

*/

double max=0.0,s;

for(i=0;i<top;i++)

for(j=i+1;j<top;j++)

for(k=j+1;k<=top;k++)

{

s=area(stack[i],stack[j],stack[k]);

if(s>max)

max=s;

}

 

return max;

}

 

int main()

{

while(scanf("%d",&n)!=EOF&&n!=-1)

{

flag.x=flag.y=100000;

int i,j,index;

for(i=0;i<n;i++)

{

scanf("%d%d",&a[i].x,&a[i].y);

if(a[i].x<flag.x||flag.x==a[i].x&&flag.y>a[i].y)

{

index=i;

flag=a[i];

}

}

a[index]=a[0];

a[0]=flag;

sort(a+1,a+n,cmp);

printf("%.2lf/n",graham());

}

return 0;

}