分治法求解最近对问题（c++）

#include"stdafx.h"

#include<iostream>

#include<cmath>

#define TRUE 1

#define FALSE 0

using namespace std;

typedef struct Node//坐标点

{

 double x;

 double y;

}Node;  

typedef struct List

{

 Node* data;      //点

 int count;      //点的个数

}List;

typedef struct CloseNode

{

 Node a;

 Node b;     //计算距离的两个点

 double space;     //距离平方

}CloseNode;

int n;     //点的数目

//输入各点到List中

void create(List &L)

{

 cout << "请输入平面上点的数目:\n";

 cin >> n;

 L.count = n;

 L.data = new Node[L.count];      //动态空间分配

 cout << "输入各点坐标 :x_y):" << endl;

 for (int i = 0; i<L.count; ++i)

  cin >> L.data[i].x >> L.data[i].y;

}

//求距离的平方

double square(Node a, Node b)

{

 return ((a.x - b.x)*(a.x - b.x)) + ((a.y - b.y)*(a.y - b.y));

}

//冒泡排序

void BubbleSort(Node r[], int length)

{

 int change, n;

 n = length; change = TRUE;

 double b, c;

 for (int i = 0; i<n - 1 && change; ++i)

 {

  change = FALSE;

  for (int j = 0; j<n - i - 1; ++j)

  {

   if (r[j].x>r[j + 1].x)

   {

    b = r[j].x; c = r[j].y;

    r[j].x = r[j + 1].x; r[j].y = r[j + 1].y;

    r[j + 1].x = b; r[j + 1].y = c;

    change = TRUE;

   }

  }

 }

}

//分治法中先将坐标按X轴从小到大的顺序排列

void paixu(List L)

{

 BubbleSort(L.data, L.count);   //调用冒泡排序

}

//左右各距中线d的区域的最近对算法

void middle(const List & L, CloseNode &cnode, int mid, double midX)

{

 int i, j;    //分别表示中线左边，右边的点

 double d = sqrt(cnode.space);

 i = mid;

 while (i >= 0 && L.data[i].x >= (midX - d))    //在左边的d区域内

 {

  j = mid;

  while (L.data[++j].x <= (midX + d) && j <= L.count)    //在右边的d区域内

  {

   if (L.data[j].y<(L.data[i].y - d) || L.data[j].y>(L.data[i].y + d))   //判断纵坐标是否在左边某固定点的2d区域内

    continue;

   double space = square(L.data[i], L.data[j]);

   if (cnode.space>space)    //在满足条件的区域内依次判断

   {

    cnode.a = L.data[i];

    cnode.b = L.data[j];

    cnode.space = space;

   }

  }

  --i;

 }

}

//分治法求最近对

void DivideConquer(const List &L, CloseNode &closenode, int begin, int end)

{

 if (begin != end)

 {

  int mid = (begin + end) / 2;     //排列后的中间的那个点

  double midX = L.data[mid].x;

  DivideConquer(L, closenode, begin, mid);      //继续在左半边用分治法求最近对

  DivideConquer(L, closenode, mid + 1, end);      //继续在右半边用分治法求最近对

  middle(L, closenode, mid, midX);               //判断左右各距中线d的区域，是否有最近对

 }

}

void main()

{

 //初始化

 List list;

 CloseNode closenode;

 closenode.space = 10000;    

 create(list);    

 cout << "各点坐标为:" << endl;

 for (int i = 0; i<list.count; ++i)

  cout << "X=" << list.data[i].x << "   Y=" << list.data[i].y << "\n";

 cout << "用分治法求最近对:" << endl;

 paixu(list);

 cout << "经过排序后的各点:" << endl;

 for (int j = 0; j<list.count; ++j)

  cout << "X=" << list.data[j].x << "   Y=" << list.data[j].y << "\n";

 DivideConquer(list, closenode, 0, list.count - 1);

 cout << "最近对为点 (" << closenode.a.x << "," << closenode.a.y << ")和点(" << closenode.b.x << "," << closenode.b.y << ")\n" << "最近距离为: " << sqrt(closenode.space) << endl;

}