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; }