zoukankan      html  css  js  c++  java
  • [计算几何][求解凸包]Surround the Trees

    Problem Description
    There are a lot of trees in an area. A peasant wants to buy a rope to surround all these trees. So at first he must know the minimal required length of the rope. However, he does not know how to calculate it. Can you help him?
    The diameter and length of the trees are omitted, which means a tree can be seen as a point. The thickness of the rope is also omitted which means a rope can be seen as a line.



    There are no more than 100 trees.
     
    Input
    The input contains one or more data sets. At first line of each input data set is number of trees in this data set, it is followed by series of coordinates of the trees. Each coordinate is a positive integer pair, and each integer is less than 32767. Each pair is separated by blank.

    Zero at line for number of trees terminates the input for your program.
     
    Output
    The minimal length of the rope. The precision should be 10^-2.
     
    Sample Input
    9 12 7 24 9 30 5 41 9 80 7 50 87 22 9 45 1 50 7 0
     
    Sample Output
    243.06
     
    思路:Graham扫描法求解凸包——https://max.book118.com/html/2017/0409/99594646.shtm(讲得炒鸡生动!!)
    AC代码:
    #include <iostream>
    #include<cstdio>
    #include<algorithm>
    #include<cmath>
    using namespace std;
    int n;
    int top;
    double ans;
    
    struct Point{
      int x,y;
    }point[110],stk[110];
    
    double dis(Point a,Point b){//求两点距离
       return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
    }
    
    double cross(Point a,Point b,Point c){//向量ab与向量ac的叉积
       return (b.x-a.x)*(c.y-a.y)-(c.x-a.x)*(b.y-a.y);
    }
    
    void find_miny(){//找point[0]
       Point tmp=point[0];
       int flag=0;
       for(int i=1;i<n;i++){
         if(point[i].y<tmp.y||(point[i].y==tmp.y&&point[i].x<tmp.x)){
             tmp=point[i]; flag=i;
         }
       }
       if(flag) swap(point[0],point[flag]);
    }
    
    bool cmp(Point a,Point b){//点的排序
       double n=cross(point[0],a,b);
       if(n>0||(n==0&&dis(point[0],a)<dis(point[0],b))) return true;
       return false;
    }
    
    void Graham(){//Graham扫描法
       top=-1;
       stk[++top]=point[0]; stk[++top]=point[1];
       for(int i=2;i<n;i++){
          while(top&&cross(stk[top-1],stk[top],point[i])<0) top--;
          stk[++top]=point[i];
       }
    }
    
    void sum(){//求凸包的周长
       ans=0;
       stk[++top]=point[0];
       for(int i=0;i<top;i++){
         ans+=dis(stk[i],stk[i+1]);
       }
    }
    
    int main()
    {
        while(scanf("%d",&n)!=EOF&&n){
            for(int i=0;i<n;i++){
                scanf("%d%d",&point[i].x,&point[i].y);
            }
            if(n==1) {
                printf("0.00
    "); continue;
            }
            if(n==2) {
                printf("%.2f
    ",dis(point[0],point[1])); continue;
            }
            find_miny();
            sort(point+1,point+n,cmp);
            Graham();
            sum();
            printf("%.2f
    ",ans);
        }
        return 0;
    }
    转载请注明出处:https://www.cnblogs.com/lllxq/
  • 相关阅读:
    JMeter做接口测试几个简单实例
    1
    Ubuntu基本命令学习
    commons-codec对字符串进行编码解码
    Python入门学习-DAY15-模块
    Python入门学习-DAY14-生成器,生成器表达式,内置函数,面向过程编程
    Python入门学习-DAY13-迭代器
    Python入门学习-DAY12-递归、三元表达式、列表生成式、字典生成式、匿名函数
    Python入门学习-DAY11-装饰器
    DAY10-Python入门学习-函数的对象与嵌套、名称空间与作用域、闭包函数
  • 原文地址:https://www.cnblogs.com/lllxq/p/8983263.html
Copyright © 2011-2022 走看看