给定平面上的N个点，寻找距离最远的两个点

 转：http://blog.csdn.net/wangyangkobe/article/details/6081975

主要是凸包算法、卡壳算法

http://blog.csdn.net/kaytowin/archive/2010/01/06/5140111.aspx

 

http://www.cppblog.com/staryjy/archive/2010/09/25/101412.html

 

http://www.cnblogs.com/devymex/archive/2010/08/09/1795392.html

 

http://iamhuiam.blog.sohu.com/132378792.html

 

 

 

 

#include "stdafx.h"
#include <iostream>
#include <vector>
#include <stack>
#include <algorithm>
#include <iterator>
#include <cmath>
using namespace std;
class Point
{
public:
    Point(){}
    Point(int m_x, int m_y):x(m_x),y(m_y){}
    int x;
    int y;
    friend ostream& operator<< (ostream &out, const Point &point);
};
/************************************************************************/
/* 函数功能：比较两个点（先以y坐标比较，若y相同按x比较）        */
/************************************************************************/
bool Cmp(const Point &left, const Point &right)
{
    return ((left.y < right.y) || ((left.y == right.y) && (left.x < right.x)));
}
/************************************************************************/
/* 函数功能：求两个向量的内积                                  */
/************************************************************************/
int CrossProduct(const Point &pre, const Point &cur, const Point &next)//pre是上一个点，cur是当前点，next是将要选择的点
{
    int x1 = cur.x - pre.x;
    int y1 = cur.y - pre.y;
    int x2 = cur.x - next.x;
    int y2 = cur.y - next.y;
    return (x1*x2 + y1*y2); //<0是满足凸包的点
}
ostream& operator<< (ostream &out, const Point &point)
{
    out<<"("<<point.x<<","<<point.y<<")";
    return out;
}
/************************************************************************/
/* 函数功能：求两点间的距离                                    */
/************************************************************************/
int Distance(const Point &point1, const Point &point2)
{
    return (point1.x - point2.x)*(point1.x - point2.x) + (point1.y - point2.y)*(point1.y - point2.y);
}
/************************************************************************/
/* 函数功能：获取凸包
   参数vec存放输入的点，result存放凸包上的点*/
/************************************************************************/
void GetConvexHull(vector<Point> vec, vector<Point> &result)
{
    sort(vec.begin(), vec.end(), Cmp); //排序
    int size = vec.size();
    if(size < 3)
    {
        copy(vec.begin(), vec.end(), back_inserter(result));
    }
    else
    {
        result.push_back(vec.at(0));
        result.push_back(vec.at(1));
        result.push_back(vec.at(2));
        int top = 2;
        for(int i=3; i<size; i++)
        {
            while((top>0) && (CrossProduct(result.at(top-1), result.at(top), vec.at(i)) >= 0))
            {
                result.pop_back();
                top--;
            }
            result.push_back(vec.at(i));
            top++;
        }
    }
}
/************************************************************************/
/* 函数功能:卡壳算法（我也没搞懂）                             */
/************************************************************************/
int RotatingCalipers(vector<Point> vec, int n)
{
    int j = 1;
    int maxLength = 0;//存储最大值
    vec[n] = vec[0];
    for(int i = 0; i<n; i++)
    {
        while(CrossProduct(vec[i+1], vec[j+1], vec[i]) > CrossProduct(vec[i+1], vec[j], vec[i]))
            j = (j+1)%n;
        maxLength = max(maxLength, max(Distance(vec[i], vec[j]), Distance(vec[i+1], vec[j+1])));
    }
    return maxLength;
}
int main()
{
    vector<Point> vec;
    const int N = 20;
    for(int i=0; i<N; i++)
    {
        vec.push_back(Point(rand()%30, rand()%30));
    }
    cout<<"平面上的点："<<endl;
    copy(vec.begin(), vec.end(), ostream_iterator<Point>(cout, "/n"));
    cout<<endl;
    vector<Point> result;
    GetConvexHull(vec, result);

    cout<<"凸包上的点："<<endl;
    copy(result.begin(), result.end(), ostream_iterator<Point>(cout, " "));
    cout<<endl;
    int distace = RotatingCalipers(result, result.size()-1);
    cout<<sqrt(double(distace))<<endl;
}