```001// Exercise 3.2.6 3.2.32 3.2.33 (Solution published at http://algs4.cs.princeton.edu/)
002package algs32;
003import stdlib.*;
004import algs13.Queue;
005/* ***********************************************************************
006 *  Compilation:  javac BST.java
007 *  Execution:    java BST
008 *  Dependencies: StdIn.java StdOut.java
009 *  Data files:   http://algs4.cs.princeton.edu/32bst/tinyST.txt
010 *
011 *  A symbol table implemented with a binary search tree.
012 *
013 *  % more tinyST.txt
014 *  S E A R C H E X A M P L E
015 *
016 *  % java BST < tinyST.txt
017 *  A 8
018 *  C 4
019 *  E 12
020 *  H 5
021 *  L 11
022 *  M 9
023 *  P 10
024 *  R 3
025 *  S 0
026 *  X 7
027 *
028 *************************************************************************/
029public class BST<K extends Comparable<? super K>, V> {
030        private Node<K,V> root;             // root of BST
031
032        private static class Node<K extends Comparable<? super K>,V> {
033                public final K key;       // sorted by key
034                public V val;             // associated data
035                public Node<K,V> left, right;  // left and right subtrees
036                public int N;             // number of nodes in subtree
037
038                public Node(K key, V val, int N) {
039                        this.key = key;
040                        this.val = val;
041                        this.N = N;
042                }
043        }
044
045        // is the symbol table empty?
046        public boolean isEmpty() { return size() == 0; }
047
048        // return number of key-value pairs in BST
049        public int size() { return size(root); }
050
051        // return number of key-value pairs in BST rooted at x
052        private int size(Node<K,V> x) {
053                if (x == null) return 0;
054                else return x.N;
055        }
056
057        /* *********************************************************************
058         *  Search BST for given key, and return associated value if found,
060         ***********************************************************************/
061        // does there exist a key-value pair with given key?
062        public boolean contains(K key) {
063                return get(key) != null;
064        }
065
066        // return value associated with the given key, or null if no such key exists
067        public V get(K key) { return get(root, key); }
068        private V get(Node<K,V> x, K key) {
069                if (x == null) return null;
070                int cmp = key.compareTo(x.key);
071                if      (cmp < 0) return get(x.left, key);
072                else if (cmp > 0) return get(x.right, key);
073                else              return x.val;
074        }
075
076        /* *********************************************************************
077         *  Insert key-value pair into BST
078         *  If key already exists, update with new value
079         ***********************************************************************/
080        public void put(K key, V val) {
081                if (val == null) { delete(key); return; }
082                root = put(root, key, val);
083                //assert check();
084        }
085
086        private Node<K,V> put(Node<K,V> x, K key, V val) {
087                if (x == null) return new Node<>(key, val, 1);
088                int cmp = key.compareTo(x.key);
089                if      (cmp < 0)
090                        x.left  = put(x.left,  key, val);
091                else if (cmp > 0)
092                        x.right = put(x.right, key, val);
093                else
094                        x.val   = val;
095                x.N = 1 + size(x.left) + size(x.right);
096                return x;
097        }
098
099        /* *********************************************************************
100         *  Delete
101         ***********************************************************************/
102
103        public void deleteMin() {
104                if (isEmpty()) throw new Error("Symbol table underflow");
105                root = deleteMin(root);
106                //assert check();
107        }
108
109        private Node<K,V> deleteMin(Node<K,V> x) {
110                if (x.left == null) return x.right;
111                x.left = deleteMin(x.left);
112                x.N = size(x.left) + size(x.right) + 1;
113                return x;
114        }
115
116        public void deleteMax() {
117                if (isEmpty()) throw new Error("Symbol table underflow");
118                root = deleteMax(root);
119                //assert check();
120        }
121
122        private Node<K,V> deleteMax(Node<K,V> x) {
123                if (x.right == null) return x.left;
124                x.right = deleteMax(x.right);
125                x.N = size(x.left) + size(x.right) + 1;
126                return x;
127        }
128
129        public void delete(K key) {
130                root = delete(root, key);
131                //assert check();
132        }
133
134        private Node<K,V> delete(Node<K,V> x, K key) {
135                if (x == null) return null;
136                int cmp = key.compareTo(x.key);
137                if      (cmp < 0) x.left  = delete(x.left,  key);
138                else if (cmp > 0) x.right = delete(x.right, key);
139                else {
140                        if (x.right == null) return x.left;
141                        if (x.left  == null) return x.right;
142                        Node<K,V> t = x;
143                        x = min(t.right);
144                        x.right = deleteMin(t.right);
145                        x.left = t.left;
146                }
147                x.N = size(x.left) + size(x.right) + 1;
148                return x;
149        }
150
151
152        /* *********************************************************************
153         *  Min, max, floor, and ceiling
154         ***********************************************************************/
155        public K min() {
156                if (isEmpty()) return null;
157                return min(root).key;
158        }
159
160        private Node<K,V> min(Node<K,V> x) {
161                if (x.left == null) return x;
162                else                return min(x.left);
163        }
164
165        public K max() {
166                if (isEmpty()) return null;
167                return max(root).key;
168        }
169
170        private Node<K,V> max(Node<K,V> x) {
171                if (x.right == null) return x;
172                else                 return max(x.right);
173        }
174
175        public K floor(K key) {
176                Node<K,V> x = floor(root, key);
177                if (x == null) return null;
178                else return x.key;
179        }
180
181        private Node<K,V> floor(Node<K,V> x, K key) {
182                if (x == null) return null;
183                int cmp = key.compareTo(x.key);
184                if (cmp == 0) return x;
185                if (cmp <  0) return floor(x.left, key);
186                Node<K,V> t = floor(x.right, key);
187                if (t != null) return t;
188                else return x;
189        }
190
191        public K ceiling(K key) {
192                Node<K,V> x = ceiling(root, key);
193                if (x == null) return null;
194                else return x.key;
195        }
196
197        private Node<K,V> ceiling(Node<K,V> x, K key) {
198                if (x == null) return null;
199                int cmp = key.compareTo(x.key);
200                if (cmp == 0) return x;
201                if (cmp < 0) {
202                        Node<K,V> t = ceiling(x.left, key);
203                        if (t != null) return t;
204                        else return x;
205                }
206                return ceiling(x.right, key);
207        }
208
209        /* *********************************************************************
210         *  Rank and selection
211         ***********************************************************************/
212        public K select(int k) {
213                if (k < 0 || k >= size())  return null;
214                Node<K,V> x = select(root, k);
215                return x.key;
216        }
217
218        // Return key of rank k.
219        private Node<K,V> select(Node<K,V> x, int k) {
220                if (x == null) return null;
221                int t = size(x.left);
222                if      (t > k) return select(x.left,  k);
223                else if (t < k) return select(x.right, k-t-1);
224                else            return x;
225        }
226
227        public int rank(K key) {
228                return rank(key, root);
229        }
230
231        // Number of keys in the subtree less than x.key.
232        private int rank(K key, Node<K,V> x) {
233                if (x == null) return 0;
234                int cmp = key.compareTo(x.key);
235                if      (cmp < 0) return rank(key, x.left);
236                else if (cmp > 0) return 1 + size(x.left) + rank(key, x.right);
237                else              return size(x.left);
238        }
239
240        /* *********************************************************************
241         *  Range count and range search.
242         ***********************************************************************/
243        public Iterable<K> keys() {
244                Queue<K> q = new Queue<>();
245                inOrder(root, q);
246                return q;
247        }
248
249        private void inOrder(Node<K,V> x, Queue<K> q) {
250                if (x == null) return;
251                inOrder(x.left, q);
252                inOrder(x.right, q);
253                q.enqueue(x.key);
254        }
255
256        public Iterable<K> keys(K lo, K hi) {
257                Queue<K> queue = new Queue<>();
258                inOrder(root, queue, lo, hi);
259                return queue;
260        }
261
262        private void inOrder(Node<K,V> x, Queue<K> queue, K lo, K hi) {
263                if (x == null) return;
264                int cmplo = lo.compareTo(x.key);
265                int cmphi = hi.compareTo(x.key);
266                if (cmplo < 0) inOrder(x.left, queue, lo, hi);
267                if (cmplo <= 0 && cmphi >= 0) queue.enqueue(x.key);
268                if (cmphi > 0) inOrder(x.right, queue, lo, hi);
269        }
270
271        public int size(K lo, K hi) {
272                if (lo.compareTo(hi) > 0) return 0;
273                if (contains(hi)) return rank(hi) - rank(lo) + 1;
274                else              return rank(hi) - rank(lo);
275        }
276
277
278        // height of this BST (one-node tree has height 0)
279        public int height() { return height(root); }
280        private int height(Node<K,V> x) {
281                if (x == null) return -1;
282                return 1 + Math.max(height(x.left), height(x.right));
283        }
284
285        // level order traversal
286        public Iterable<K> levelOrder() {
287                Queue<K> keys = new Queue<>();
288                Queue<Node<K,V>> queue = new Queue<>();
289                queue.enqueue(root);
290                while (!queue.isEmpty()) {
291                        Node<K,V> x = queue.dequeue();
292                        if (x == null) continue;
293                        keys.enqueue(x.key);
294                        queue.enqueue(x.left);
295                        queue.enqueue(x.right);
296                }
297                return keys;
298        }
299
300        /* ***********************************************************************
301         *  Check integrity of BST data structure
302         *************************************************************************/
303        private boolean check() {
304                if (!isBST())            StdOut.println("Not in symmetric order");
305                if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent");
306                if (!isRankConsistent()) StdOut.println("Ranks not consistent");
307                return isBST() && isSizeConsistent() && isRankConsistent();
308        }
309
310        // does this binary tree satisfy symmetric order?
311        // Note: this test also ensures that data structure is a binary tree since order is strict
312        private boolean isBST() {
313                return isBST(root, null, null);
314        }
315
316        // is the tree rooted at x a BST with all keys strictly between min and max
317        // (if min or max is null, treat as empty constraint)
318        // Credit: Bob Dondero's elegant solution
319        private boolean isBST(Node<K,V> x, K min, K max) {
320                if (x == null) return true;
321                if (min != null && x.key.compareTo(min) <= 0) return false;
322                if (max != null && x.key.compareTo(max) >= 0) return false;
323                return isBST(x.left, min, x.key) && isBST(x.right, x.key, max);
324        }
325
326        // are the size fields correct?
327        private boolean isSizeConsistent() { return isSizeConsistent(root); }
328        private boolean isSizeConsistent(Node<K,V> x) {
329                if (x == null) return true;
330                if (x.N != size(x.left) + size(x.right) + 1) return false;
331                return isSizeConsistent(x.left) && isSizeConsistent(x.right);
332        }
333
334        // check that ranks are consistent
335        private boolean isRankConsistent() {
336                for (int i = 0; i < size(); i++)
337                        if (i != rank(select(i))) return false;
338                for (K key : keys())
339                        if (key.compareTo(select(rank(key))) != 0) return false;
340                return true;
341        }
342
343        /* ***************************************************************************
344         *  Visualization
345         *****************************************************************************/
346        public String toString() {
347                StringBuilder sb = new StringBuilder();
348                for (K key: levelOrder())
349                        sb.append (key + " ");
350                return sb.toString ();
351        }
352
353        public void toGraphviz(String filename) {
354                GraphvizBuilder gb = new GraphvizBuilder ();
355                toGraphviz (gb, null, root);
356                gb.toFileUndirected (filename, "ordering=\"out\"");
357        }
358        private void toGraphviz (GraphvizBuilder gb, Node<K,V> parent, Node<K,V> n) {
359                if (n == null) { gb.addNullEdge (parent); return; }
361                if (parent != null) gb.addEdge (parent, n);
362                toGraphviz (gb, n, n.left);
363                toGraphviz (gb, n, n.right);
364        }
365
366        // You may modify "drawTree" if you wish
367        public void drawTree() {
368                if (root != null) {
369                        StdDraw.setPenColor (StdDraw.BLACK);
370                        StdDraw.setCanvasSize(1200,700);
371                        drawTree(root, .5, 1, .25, 0);
372                }
373        }
374        private void drawTree (Node<K,V> n, double x, double y, double range, int depth) {
375                int CUTOFF = 10;
376                StdDraw.text (x, y, n.key.toString ());
378                if (n.left != null && depth != CUTOFF) {
379                        StdDraw.line (x-range, y-.08, x-.01, y-.01);
380                        drawTree (n.left, x-range, y-.1, range*.5, depth+1);
381                }
382                if (n.right != null && depth != CUTOFF) {
383                        StdDraw.line (x+range, y-.08, x+.01, y-.01);
384                        drawTree (n.right, x+range, y-.1, range*.5, depth+1);
385                }
386        }
387
388        /* ***************************************************************************
389         *  Test client
390         *****************************************************************************/
391        public static void main(String[] args) {
392                //StdIn.fromString ("S E A R C H E X A M P L E");
393                //StdIn.fromString ("D F B  G E A C");
394                StdIn.fromString ("C A B E D");
395
396                BST<String, Integer> st = new BST<>();
397                for (int i = 0; !StdIn.isEmpty(); i++) {
399                        st.put(key, i);
400                }
401                //GraphvizBuilder.nodesToFile (st.root);
402                st.toGraphviz ("g.png");
403                //        st.drawTree ();
404                Iterable<String> keys = st.levelOrder();
405                for (String s : keys)
406                        StdOut.println(s + " " + st.get(s));
407                //        StdOut.println();
408                //        for (String s : st.keys())
409                //            StdOut.println(s + " " + st.get(s));
410        }
411}

```