求平面上N个点间最短距离(分治法的经典问题)

#include <iostream>#include <ctime>#include <iterator>#include <functional>#include <algorithm>#include <cmath>#include <vector>using namespace std;struct Point{int x;int y;Point(){}Point(int m_x, int m_y):x(m_x), y(m_y){}};/************************************************************************//* 函数功能：按点的X坐标排序 *//************************************************************************/struct CmpX : public binary_function<bool, Point, Point>{bool operator() (const Point& lhs, const Point& rhs){return (lhs.x < rhs.x);}};/************************************************************************//* 函数功能：按点的Y坐标排序 *//************************************************************************/struct CmpY : public binary_function<bool, Point, Point>{bool operator() (const Point& lhs, const Point& rhs){return (lhs.y < rhs.y);}};/************************************************************************//* 类功能：产生无重复的随机数类成员：num 表示要产生的随机数的个数bound 表示每个随机数的范围[0, bound-1). *//************************************************************************/class Random{public:explicit Random(int m_num, int m_bound):num(m_num), bound(m_bound){arr = new int[m_bound];for(int i = 0; i < bound; i++)arr[i] = i;}int* GetResult(){int temp = 0;srand((unsigned)time(0));for (int i = 0; i < num; i++){temp = rand() % (bound - i - 1) + i;swap(arr[i], arr[temp]);}return arr;}~Random(){delete []arr;}private:int *arr;int num;//随机数的个数int bound; //随机数的范围};/************************************************************************//* 函数功能：求两点间的距离 *//************************************************************************/inline double Distance(const Point& lhs, const Point& rhs){int x_diff = lhs.x - rhs.x;int y_diff = lhs.y - rhs.y;double res = x_diff * x_diff + y_diff *y_diff;return sqrt(res);}/************************************************************************//* 函数功能：求数组中两点间的最短距离 *//************************************************************************/double GetShortestDistace(Point arr[], int low, int high){double result = 0.;if (high - low < 3) //小于等于3个点时{if (high - low == 1) //2个点时{double distance = Distance(arr[low], arr[high]);return distance;}else //3个点{double distance1 = Distance(arr[low], arr[low + 1]);double distance2 = Distance(arr[low], arr[low + 2]);double distance3 = Distance(arr[low + 1], arr[low + 2]);return min(min(distance1, distance2), distance3);}}int middle = (low + high) / 2;double left_distance = GetShortestDistace(arr, low, middle);//求middle左边的最短距离double right_distance = GetShortestDistace(arr, middle + 1, high);//求middle右边的最短距离double delta = min(left_distance, right_distance); //中间区域的界限result = delta;vector<Point> midArea;//存放中间条带区域的点for (int k = low; k < high; k++){if(arr[k].x > arr[middle].x - delta && arr[k].x < arr[middle].x + delta)midArea.push_back(arr[k]);}sort(midArea.begin(), midArea.end(), CmpY()); //按Y坐标排序int size = midArea.size();for (int i = 0; i < size; i++){int k = (i + 7) > size ? size : (i+7);//只有选取出7个点(证明过程没看懂)for (int j = i+1; j < k; j++){if(Distance(midArea.at(i), midArea.at(j)) < result)result = Distance(midArea.at(i), midArea.at(j));}}return result;}#define N 100 //点的个数int main(){Point arr[N];Random random(2*N, 1000);int *result = random.GetResult();for (int i =0; i < N; i++)arr[i] = Point(result[i], result[i + N]);sort(arr, arr + N, CmpX());double res = GetShortestDistace(arr, 0, N);cout<<"The shortest distance is:"<<res<<endl;}