【2d-Tree】Kd-tree的特例

最近在学习coursera上的算法4，讲的确实很精彩，2d-tree的实现是基于二叉查找树（BST)，但是其中有有很多小的tricks需要与大家分享。

需要注意的是在node数据结构的选取上：

private Point2D point;private Node left;private Node right;private boolean flag;private RectHV rect;

前三个理所当然是链表必备要素，后面flag和rect则是为了方便实现range search和nearest point search所添加，rect为node节点所占据的空间，flag表明当前节点是以x还是y划分。

range search的实现基于以下原理：

首先判断需要搜索的矩形rect是否与root所占据的空间有交集，如果有，判断root是否在rect中，然后向下搜索。

nearest point 的实现

nearest的实现比较好玩，利用二叉树的深度优先搜索配合剪枝！

首先判断目标节点与root所占据空间的最短距离dist是否比best大，如果dist>best，则剪枝。贴出伪代码供大家学习

再给出java实现的代码

package kdtree;import java.util.Set;import java.util.TreeSet;import edu.princeton.cs.algs4.Point2D;import edu.princeton.cs.algs4.RectHV;import edu.princeton.cs.algs4.StdDraw;public class KdTree {private class Node implements Comparable<Node> {private Point2D point;private Node left;private Node right;private boolean flag;private RectHV rect;public Node(Point2D point, boolean flag,RectHV rect){this.point = point;this.flag = flag;this.rect = rect;}public int compareTo(Node that){if(flag){return Double.compare(this.point.x(), that.point.x());}else{return Double.compare(this.point.y(), that.point.y());}}}private Node root;private int size = 0;   public KdTree(){   // construct an empty set of points    root = null;   size = 0;   }   public boolean isEmpty(){   // is the set empty?   return size == 0;   }   public int size(){   // number of points in the set   return size;   }   public void insert(Point2D p){   // add the point to the set (if it is not already in the set)if(this.size==0) {this.root = new Node(p,true,new RectHV(0,0,1,1));this.size ++;}else if(put (root, p)) this.size ++;   }   private boolean put(Node root, Point2D p){   Node tmp = new Node(p,!root.flag,null);   if(root.point.x() == p.x() && root.point.y() == p.y()) return false;   int cmp = root.compareTo(tmp);   RectHV newrect = null;   if(cmp > 0){   if(root.left == null){   if(root.flag){   newrect = new RectHV(root.rect.xmin(), root.rect.ymin(), root.point.x(), root.rect.ymax());   }else{   newrect = new RectHV(root.rect.xmin(), root.rect.ymin(), root.rect.xmax(), root.point.y());   }   tmp.rect = newrect;   root.left = tmp;   return true;   }  return put(root.left, p);   }else{   if(root.right == null){   if(root.flag){   newrect = new RectHV(root.point.x(), root.rect.ymin(), root.rect.xmax(), root.rect.ymax());   }else{   newrect = new RectHV(root.rect.xmin(),  root.point.y(), root.rect.xmax(), root.rect.ymax());   }   tmp.rect = newrect;   root.right = tmp;   return true;   }  return put(root.right, p);   }   }   public boolean contains(Point2D p){   // does the set contain point p?    if(isEmpty()) return false;   Node tmp = new Node(p,!root.flag,null);   Node x = root;   while(x !=null){   int cmp = x.compareTo(tmp);   if(cmp > 0) x = x.left;   else if((x.point.x() == p.x() && x.point.y() == p.y())) return true;    else x = x.right;   }   return false;   }   public void draw(){   // draw all points to standard drawif (isEmpty()) return;drawRec(root, 0, 1, 0, 1);   }   public Iterable<Point2D> range(RectHV rect){   // all points that are inside the rectangle   Set<Point2D> pointList = new TreeSet<Point2D>();   rangeRec(root, rect, pointList);   return pointList;      }private void rangeRec(Node root, RectHV rect, Set<Point2D> set) {if (root == null) return;if (root.rect.intersects(rect)) {if (rect.contains(root.point)) set.add(root.point);rangeRec(root.left, rect, set);rangeRec(root.right, rect, set);}}public Point2D nearest(Point2D p){   // a nearest neighbor in the set to point p; null if the set is emptyif(isEmpty()) return null;   return nearest(root, root.point, p);   }   private Point2D nearest(Node root, Point2D champion, Point2D aim){   //Point2D closest = champion;   if(root == null || root.rect.distanceSquaredTo(aim) > champion.distanceSquaredTo(aim)) return champion;double dist = root.point.distanceSquaredTo(aim);if (dist < champion.distanceSquaredTo(aim)){champion = root.point;}Node near, far;if((root.flag && (aim.x() < root.point.x())) || (!root.flag && (aim.y() < root.point.y()))){            near = root.left;            far = root.right;        }        else {            near = root.right;            far = root.left;        }        champion = nearest(near, champion,aim);        champion = nearest(far, champion,aim);return champion;      }      /* public Point2D nearest(Point2D p) {        if (root == null) return null;        Point2D retp = null;        double mindis = Double.MAX_VALUE;        Queue<Node> queue = new Queue<Node>();        queue.enqueue(root);        while (!queue.isEmpty()) {            Node x = queue.dequeue();            double dis = p.distanceSquaredTo(x.point);            if (dis < mindis) {                retp = x.point;                mindis = dis;             }            if (x.left != null && x.left.rect.distanceSquaredTo(p) < mindis)                 queue.enqueue(x.left);            if (x.right != null && x.right.rect.distanceSquaredTo(p) < mindis)                 queue.enqueue(x.right);        }        return retp;    }*/      private void drawRec(Node root, double minX, double maxX, double minY, double maxY) {if (root == null) return;StdDraw.setPenRadius(.001);if (root.flag) {StdDraw.setPenColor(StdDraw.RED);StdDraw.line(root.point.x(), minY, root.point.x(), maxY);drawRec(root.left, minX, root.point.x(), minY, maxY);drawRec(root.right, root.point.x(), maxX, minY, maxY);} else {StdDraw.setPenColor(StdDraw.BLUE);StdDraw.line(minX, root.point.y(), maxX, root.point.y());drawRec(root.left, minX, maxX, minY, root.point.y());drawRec(root.right, minX, maxX, root.point.y(), maxY);}StdDraw.setPenColor(StdDraw.BLACK);StdDraw.setPenRadius(.01);root.point.draw();}   public static void main(String[] args){   // unit testing of the methods (optional)    }}