题目正文：
http://coursera.cs.princeton.edu/algs4/assignments/kdtree.html
作业难点：
如何组织自己的数据结构是本道题的最难点，基本上有思路就肯定可以完成。题目一定要看仔细，基本上2dtree部分已经把实现原理说清楚了。
作业技巧：
1、逐步实现，实现完成后用insert、contain测试下，没问题再写draw，测试没问题再写其余的。
2、重复输入的问题不要忘了
3、range虽然api里写的是all point inside the rectangle，但是你必须把边界上的点也算进去
4、java不像C#可以传参数前面加ref或out，所以必须在递归的时候返回Point
5、比较容易疏忽的是子节点在分界线上部或者下部的处理是不一样的，你认为左边是右子树，上边是左子树都没关系。最后结果不会有问题
代码参考：
（这是我自己亲测100分的答案，不代表写得最好，请在自己实在完成不了的时候再看，不然的话做这个题目的意义一点都没有）
1 import edu.princeton.cs.algs4.Point2D;
2 import edu.princeton.cs.algs4.RectHV;
3 import edu.princeton.cs.algs4.SET;
4
5 import java.util.Stack;
6
7
8 public class PointSET {
9 private SET<Point2D> pointSet;
10
11 public PointSET() // construct an empty set of points
12 {
13 pointSet = new SET<Point2D>();
14 }
15
16 private void checkNull(Object obj) {
17 if (obj == null) {
18 throw new NullPointerException();
19 }
20 }
21
22 public boolean isEmpty() // is the set empty?
23 {
24 return pointSet.isEmpty();
25 }
26
27 public int size() // number of points in the set
28 {
29 return pointSet.size();
30 }
31
32 public void insert(Point2D p) // add the point to the set (if it is not already in the set)
33 {
34 checkNull(p);
35 pointSet.add(p);
36 }
37
38 public boolean contains(Point2D p) // does the set contain point p?
39 {
40 checkNull(p);
41
42 return pointSet.contains(p);
43 }
44
45 public void draw() // draw all points to standard draw
46 {
47 for (Point2D p : pointSet) {
48 p.draw();
49 }
50 }
51
52 public Iterable<Point2D> range(RectHV rect) // all points that are inside the rectangle
53 {
54 checkNull(rect);
55
56 Stack<Point2D> stack = new Stack<Point2D>();
57
58 for (Point2D p : pointSet) {
59 if ((p.x() >= rect.xmin()) && (p.x() <= rect.xmax()) &&
60 (p.y() >= rect.ymin()) && (p.y() <= rect.ymax())) {
61 stack.push(p);
62 }
63 }
64
65 return stack;
66 }
67
68 public Point2D nearest(Point2D p) // a nearest neighbor in the set to point p; null if the set is empty
69 {
70 checkNull(p);
71
72 Point2D point = null;
73
74 for (Point2D setp : pointSet) {
75 if ((point == null) ||
76 (p.distanceSquaredTo(point) > p.distanceSquaredTo(setp))) {
77 point = setp;
78 }
79 }
80
81 return point;
82 }
83
84 public static void main(String[] args) // unit testing of the methods (optional)
85 {
86 }
87 }
PointSET
1 import edu.princeton.cs.algs4.In;
2 import edu.princeton.cs.algs4.Point2D;
3 import edu.princeton.cs.algs4.RectHV;
4 import edu.princeton.cs.algs4.StdDraw;
5 import edu.princeton.cs.algs4.StdOut;
6
7 import java.util.Stack;
8
9
10 public class KdTree {
11 private PointNode root;
12 private int pointCount;
13
14 public KdTree() // construct an empty set of points
15 {
16 root = null;
17 pointCount = 0;
18 }
19
20 private void checkNull(Object obj) {
21 if (obj == null) {
22 throw new NullPointerException();
23 }
24 }
25
26 public boolean isEmpty() // is the set empty?
27 {
28 return root == null;
29 }
30
31 public int size() // number of points in the set
32 {
33 return pointCount;
34 }
35
36 public void insert(Point2D p) // add the point to the set (if it is not already in the set)
37 {
38 checkNull(p);
39
40 if (root == null) {
41 root = new PointNode(p, null, false);
42 pointCount++;
43 } else {
44 PointNode current = root;
45
46 while (true) {
47 if (current.value.compareTo(p) == 0) {
48 return;
49 }
50 if (current.isAtLeftSideOfNode(p)) {
51 if (current.left == null) {
52 current.left = new PointNode(p, current, true);
53 pointCount++;
54 break;
55 } else {
56 current = current.left;
57 }
58 } else {
59 if (current.right == null) {
60 current.right = new PointNode(p, current, false);
61 pointCount++;
62 break;
63 } else {
64 current = current.right;
65 }
66 }
67 }
68 }
69 }
70
71 public boolean contains(Point2D p) // does the set contain point p?
72 {
73 checkNull(p);
74
75 PointNode current = root;
76
77 while (current != null) {
78 if (current.value.compareTo(p) == 0) {
79 return true;
80 } else if (current.isAtLeftSideOfNode(p)) {
81 current = current.left;
82 } else {
83 current = current.right;
84 }
85 }
86
87 return false;
88 }
89
90 public void draw() // draw all points to standard draw
91 {
92 if (root != null) {
93 root.draw(null, false);
94 }
95 }
96
97 private void addToStack(Stack<Point2D> stack, PointNode current, RectHV rect) {
98
99 if (!rect.intersects(current.rect)) {
100 return;
101 }
102
103 if ((current.value.x() >= rect.xmin()) &&
104 (current.value.x() <= rect.xmax()) &&
105 (current.value.y() >= rect.ymin()) &&
106 (current.value.y() <= rect.ymax())) {
107 stack.push(current.value);
108 }
109
110 if (current.left != null) {
111 addToStack(stack, current.left, rect);
112 }
113
114 if (current.right != null) {
115 addToStack(stack, current.right, rect);
116 }
117 }
118
119 private Point2D searchNode(Point2D toSearch, PointNode current,
120 Point2D nearestPoint) {
121 if (nearestPoint == null) {
122 nearestPoint = current.value;
123 }
124
125 double distance = nearestPoint.distanceSquaredTo(toSearch);
126 double newdistance = current.value.distanceSquaredTo(toSearch);
127
128 if ((distance >= current.rect.distanceSquaredTo(toSearch)) ||
129 (distance >= newdistance)) {
130 if (distance > newdistance) {
131 nearestPoint = current.value;
132 }
133
134 if ((current.isH && (toSearch.y() > current.value.y())) ||
135 (!current.isH && (toSearch.x() < current.value.x()))) {
136 if (current.left != null) {
137 nearestPoint = searchNode(toSearch, current.left,
138 nearestPoint);
139 }
140
141 if (current.right != null) {
142 nearestPoint = searchNode(toSearch, current.right,
143 nearestPoint);
144 }
145 } else {
146 if (current.right != null) {
147 nearestPoint = searchNode(toSearch, current.right,
148 nearestPoint);
149 }
150
151 if (current.left != null) {
152 nearestPoint = searchNode(toSearch, current.left,
153 nearestPoint);
154 }
155 }
156 }
157
158 return nearestPoint;
159 }
160
161 public Iterable<Point2D> range(RectHV rect) // all points that are inside the rectangle
162 {
163 checkNull(rect);
164
165 Stack<Point2D> stack = new Stack<Point2D>();
166 if (root != null)
167 addToStack(stack, root, rect);
168
169 return stack;
170 }
171
172 public Point2D nearest(Point2D p) // a nearest neighbor in the set to point p; null if the set is empty
173 {
174 checkNull(p);
175
176 Point2D point = null;
177 if (root != null)
178 point = searchNode(p, root, point);
179
180 return point;
181 }
182
183 public static void main(String[] args) // unit testing of the methods (optional)
184 {
185 String filename = args[0];
186 In in = new In(filename);
187
188 KdTree kdtree = new KdTree();
189
190 while (!in.isEmpty()) {
191 double x = in.readDouble();
192 double y = in.readDouble();
193 Point2D p = new Point2D(x, y);
194 kdtree.insert(p);
195 }
196
197 kdtree.draw();
198 }
199
200 private static class PointNode {
201 private PointNode left;
202 private PointNode right;
203 private RectHV rect;
204 private Point2D value;
205 private boolean isH;
206
207 public PointNode(Point2D p, PointNode parent, boolean isLeftUp) {
208 value = p;
209 left = null;
210 right = null;
211 if (parent == null) {
212 isH = false;
213 rect = new RectHV(0, 0, 1, 1);
214 } else {
215 isH = !parent.isH;
216
217 if (isH) {
218 if (isLeftUp) {
219 rect = new RectHV(parent.rect.xmin(),
220 parent.rect.ymin(), parent.value.x(),
221 parent.rect.ymax());
222 } else {
223 rect = new RectHV(parent.value.x(), parent.rect.ymin(),
224 parent.rect.xmax(), parent.rect.ymax());
225 }
226 } else {
227 if (isLeftUp) {
228 rect = new RectHV(parent.rect.xmin(), parent.value.y(),
229 parent.rect.xmax(), parent.rect.ymax());
230 } else {
231 rect = new RectHV(parent.rect.xmin(),
232 parent.rect.ymin(), parent.rect.xmax(),
233 parent.value.y());
234 }
235 }
236 }
237 }
238
239 public void draw(PointNode parent, boolean isLeftUp) {
240 StdOut.println(isLeftUp ? "leftup" : "rightdown");
241 StdDraw.setPenColor(StdDraw.BLACK);
242 StdDraw.setPenRadius(0.01);
243 value.draw();
244 StdDraw.setPenRadius();
245
246 if (parent == null) {
247 StdDraw.setPenColor(StdDraw.RED);
248 new Point2D(value.x(), 1).drawTo(new Point2D(value.x(), 0));
249 } else {
250 StdOut.println(value);
251 StdOut.println(parent.rect);
252
253 if (parent.isH) {
254 StdDraw.setPenColor(StdDraw.RED);
255 new Point2D(value.x(), rect.ymin()).drawTo(new Point2D(
256 value.x(), rect.ymax()));
257 } else {
258 StdDraw.setPenColor(StdDraw.BLUE);
259 new Point2D(rect.xmax(), value.y()).drawTo(new Point2D(
260 rect.xmin(), value.y()));
261 }
262 }
263
264 StdDraw.pause(100);
265
266 if (left != null) {
267 left.draw(this, true);
268 }
269
270 if (right != null) {
271 right.draw(this, false);
272 }
273 }
274
275 public boolean isAtLeftSideOfNode(Point2D p) {
276 if (isH) {
277 return p.y() > value.y();
278 } else {
279 return p.x() < value.x();
280 }
281 }
282 }
283 }
KdTree
时间： 2024-10-19 21:15:09