HDU1392 Surround the Trees 简单凸包

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=1392

题目大意：平面上有n个点代表n棵树，现在要把这些树用绳子围起来，求最少需要的绳子长度。

分析：简单求凸包问题。

实现代码如下：

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
using namespace std;
typedef struct
{
    double x,y;
}POINT;
POINT result[110];
POINT tree[110];
int n,top;
double Distance(POINT p1,POINT p2)
{
    return sqrt( (p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y) );
}
double Multiply(POINT p1,POINT p2,POINT p3)
{
    return (p2.x-p1.x)*(p3.y-p1.y)-(p2.y-p1.y)*(p3.x-p1.x);
}
int cmp(const void *p1,const void *p2)
{
    POINT *p3,*p4;
    double m;
    p3=(POINT *)p1;
    p4=(POINT *)p2;
    m=Multiply(tree[0],*p3,*p4);
    if(m<0) return 1;
    else if(m==0&&(Distance(tree[0],*p3)<Distance(tree[0],*p4)))
      return 1;
    else return -1;
}
void Tubao()
{
    result[0].x=tree[0].x,result[0].y=tree[0].y;
    result[1].x=tree[1].x,result[1].y=tree[1].y;
    result[2].x=tree[2].x,result[2].y=tree[2].y;
    top=2;
    for(int i=3;i<=n;i++)
    {
        while(Multiply(result[top-1],result[top],tree[i])<=0)
          top--;
        result[top+1].x=tree[i].x;
        result[top+1].y=tree[i].y;
        top++;
    }
}
int main()
{
    int pos;
    double px,py;
    while(scanf("%d",&n)!=-1&&n)
    {
        py=-1;
        for(int i=0;i<n;i++)
          scanf("%lf%lf",&tree[i].x,&tree[i].y);
        if(n==1)
        {
            printf("0.00\n");
            continue;
        }
        else if(n==2)
        {
            printf("%.2lf\n",Distance(tree[0],tree[1]));
            continue;
        }
        for(int i=0;i<n;i++)
        {
            if(py==-1||tree[i].y<py)
            {
                px=tree[i].x;
                py=tree[i].y;
                pos=i;
            }
            else if(tree[i].y==py&&tree[i].x<px)
            {
                px=tree[i].x;
                py=tree[i].y;
                pos=i;
            }
        }
        double tmp=tree[0].x;
        tree[0].x=tree[pos].x;
        tree[pos].x=tmp;
        tmp=tree[0].y;
        tree[0].y=tree[pos].y;
        tree[pos].y=tmp;
        qsort(&tree[1],n-1,sizeof(POINT),cmp);
        tree[n].x=tree[0].x;
        tree[n].y=tree[0].y;
        Tubao();
        double len=0.0;
        for(int i=0;i<top;i++)
          len+=Distance(result[i],result[i+1]);
        printf("%.2f\n",len);
    }
    return 0;
}