给定平面上的N个点，寻找距离最远的两个点(转载)

转载自:http://blog.csdn.net/wangyangkobe/archive/2010/12/17/6081975.aspx

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;   
}

 

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