339 lines
9.2 KiB
Java
339 lines
9.2 KiB
Java
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/*This is a Java Program to implement 2D KD Tree and print the various traversals. In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. k-d trees are a useful data structure for several applications, such as searches involving a multidimensional search key (e.g. range searches and nearest neighbor searches). k-d trees are a special case of binary space partitioning trees.*/
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//This is a java program to construct a KD tree for two dimensional static data
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import java.io.IOException;
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class KD2DNode
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{
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int axis;
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double[] x;
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int id;
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boolean checked;
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boolean orientation;
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KD2DNode Parent;
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KD2DNode Left;
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KD2DNode Right;
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public KD2DNode(double[] x0, int axis0)
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{
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x = new double[2];
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axis = axis0;
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for (int k = 0; k < 2; k++)
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x[k] = x0[k];
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Left = Right = Parent = null;
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checked = false;
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id = 0;
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}
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public KD2DNode FindParent(double[] x0)
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{
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KD2DNode parent = null;
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KD2DNode next = this;
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int split;
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while (next != null)
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{
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split = next.axis;
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parent = next;
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if (x0[split] > next.x[split])
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next = next.Right;
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else
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next = next.Left;
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}
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return parent;
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}
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public KD2DNode Insert(double[] p)
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{
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x = new double[2];
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KD2DNode parent = FindParent(p);
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if (equal(p, parent.x, 2) == true)
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return null;
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KD2DNode newNode = new KD2DNode(p,
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parent.axis + 1 < 2 ? parent.axis + 1 : 0);
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newNode.Parent = parent;
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if (p[parent.axis] > parent.x[parent.axis])
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{
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parent.Right = newNode;
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newNode.orientation = true; //
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}
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else
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{
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parent.Left = newNode;
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newNode.orientation = false; //
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}
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return newNode;
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}
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boolean equal(double[] x1, double[] x2, int dim)
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{
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for (int k = 0; k < dim; k++)
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{
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if (x1[k] != x2[k])
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return false;
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}
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return true;
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}
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double distance2(double[] x1, double[] x2, int dim)
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{
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double S = 0;
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for (int k = 0; k < dim; k++)
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S += (x1[k] - x2[k]) * (x1[k] - x2[k]);
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return S;
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}
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}
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class KD2DTree
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{
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KD2DNode Root;
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int TimeStart, TimeFinish;
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int CounterFreq;
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double d_min;
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KD2DNode nearest_neighbour;
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int KD_id;
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int nList;
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KD2DNode CheckedNodes[];
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int checked_nodes;
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KD2DNode List[];
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double x_min[], x_max[];
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boolean max_boundary[], min_boundary[];
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int n_boundary;
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public KD2DTree(int i)
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{
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Root = null;
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KD_id = 1;
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nList = 0;
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List = new KD2DNode[i];
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CheckedNodes = new KD2DNode[i];
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max_boundary = new boolean[2];
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min_boundary = new boolean[2];
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x_min = new double[2];
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x_max = new double[2];
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}
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public boolean add(double[] x)
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{
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if (nList >= 2000000 - 1)
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return false; // can't add more points
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if (Root == null)
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{
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Root = new KD2DNode(x, 0);
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Root.id = KD_id++;
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List[nList++] = Root;
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}
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else
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{
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KD2DNode pNode;
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if ((pNode = Root.Insert(x)) != null)
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{
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pNode.id = KD_id++;
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List[nList++] = pNode;
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}
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}
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return true;
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}
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public KD2DNode find_nearest(double[] x)
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{
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if (Root == null)
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return null;
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checked_nodes = 0;
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KD2DNode parent = Root.FindParent(x);
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nearest_neighbour = parent;
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d_min = Root.distance2(x, parent.x, 2);
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;
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if (parent.equal(x, parent.x, 2) == true)
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return nearest_neighbour;
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search_parent(parent, x);
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uncheck();
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return nearest_neighbour;
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}
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public void check_subtree(KD2DNode node, double[] x)
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{
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if ((node == null) || node.checked)
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return;
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CheckedNodes[checked_nodes++] = node;
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node.checked = true;
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set_bounding_cube(node, x);
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int dim = node.axis;
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double d = node.x[dim] - x[dim];
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if (d * d > d_min)
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{
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if (node.x[dim] > x[dim])
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check_subtree(node.Left, x);
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else
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check_subtree(node.Right, x);
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}
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else
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{
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check_subtree(node.Left, x);
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check_subtree(node.Right, x);
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}
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}
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public void set_bounding_cube(KD2DNode node, double[] x)
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{
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if (node == null)
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return;
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int d = 0;
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double dx;
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for (int k = 0; k < 2; k++)
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{
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dx = node.x[k] - x[k];
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if (dx > 0)
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{
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dx *= dx;
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if (!max_boundary[k])
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{
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if (dx > x_max[k])
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x_max[k] = dx;
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if (x_max[k] > d_min)
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{
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max_boundary[k] = true;
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n_boundary++;
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}
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}
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}
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else
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{
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dx *= dx;
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if (!min_boundary[k])
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{
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if (dx > x_min[k])
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x_min[k] = dx;
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if (x_min[k] > d_min)
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{
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min_boundary[k] = true;
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n_boundary++;
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}
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}
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}
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d += dx;
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if (d > d_min)
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return;
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}
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if (d < d_min)
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{
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d_min = d;
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nearest_neighbour = node;
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}
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}
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public KD2DNode search_parent(KD2DNode parent, double[] x)
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{
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for (int k = 0; k < 2; k++)
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{
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x_min[k] = x_max[k] = 0;
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max_boundary[k] = min_boundary[k] = false; //
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}
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n_boundary = 0;
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KD2DNode search_root = parent;
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while (parent != null && (n_boundary != 2 * 2))
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{
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check_subtree(parent, x);
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search_root = parent;
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parent = parent.Parent;
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}
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return search_root;
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}
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public void uncheck()
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{
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for (int n = 0; n < checked_nodes; n++)
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CheckedNodes[n].checked = false;
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}
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public void inorder()
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{
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inorder(Root);
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}
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private void inorder(KD2DNode root)
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{
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if (root != null)
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{
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inorder(root.Left);
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System.out.print("(" + root.x[0] + ", " + root.x[1] + ") ");
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inorder(root.Right);
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}
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}
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public void preorder()
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{
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preorder(Root);
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}
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private void preorder(KD2DNode root)
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{
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if (root != null)
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{
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System.out.print("(" + root.x[0] + ", " + root.x[1] + ") ");
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inorder(root.Left);
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inorder(root.Right);
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}
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}
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public void postorder()
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{
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postorder(Root);
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}
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private void postorder(KD2DNode root)
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{
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if (root != null)
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{
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inorder(root.Left);
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inorder(root.Right);
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System.out.print("(" + root.x[0] + ", " + root.x[1] + ") ");
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}
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}
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}
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public class KDTree_TwoD_Data
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{
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public static void main(String args[]) throws IOException
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{
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int numpoints = 5;
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KD2DTree kdt = new KD2DTree(numpoints);
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double x[] = new double[2];
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x[0] = 0.0;
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x[1] = 0.0;
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kdt.add(x);
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x[0] = 3.3;
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x[1] = 1.5;
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kdt.add(x);
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x[0] = 4.7;
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x[1] = 11.1;
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kdt.add(x);
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x[0] = 5.0;
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x[1] = 12.3;
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kdt.add(x);
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x[0] = 5.1;
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x[1] = 1.2;
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kdt.add(x);
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System.out.println("Inorder of 2D Kd tree: ");
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kdt.inorder();
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System.out.println("\nPreorder of 2D Kd tree: ");
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kdt.preorder();
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System.out.println("\nPostorder of 2D Kd tree: ");
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kdt.postorder();
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}
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}
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/*
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Inorder of 2D Kd tree:
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(0.0, 0.0) (5.1, 1.2) (3.3, 1.5) (4.7, 11.1) (5.0, 12.3)
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Preorder of 2D Kd tree:
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(0.0, 0.0) (5.1, 1.2) (3.3, 1.5) (4.7, 11.1) (5.0, 12.3)
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Postorder of 2D Kd tree:
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(5.1, 1.2) (3.3, 1.5) (4.7, 11.1) (5.0, 12.3) (0.0, 0.0)
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