给定平面上的N个点，寻找距离最远的两个点

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; }