A complete Java implementation:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 | /************************************************************************* * Compilation: javac BST.java * Execution: java BST * Dependencies: StdIn.java StdOut.java Queue.java * Data files: http://algs4.cs.princeton.edu/32bst/tinyST.txt * * A symbol table implemented with a binary search tree. * * % more tinyST.txt * S E A R C H E X A M P L E * * % java BST < tinyST.txt * A 8 * C 4 * E 12 * H 5 * L 11 * M 9 * P 10 * R 3 * S 0 * X 7 * *************************************************************************/import java.util.NoSuchElementException;public class BST<Key extends Comparable<Key>, Value> { private Node root; // root of BST private class Node { private Key key; // sorted by key private Value val; // associated data private Node left, right; // left and right subtrees private int N; // number of nodes in subtree public Node(Key key, Value val, int N) { this.key = key; this.val = val; this.N = N; } } // is the symbol table empty? public boolean isEmpty() { return size() == 0; } // return number of key-value pairs in BST public int size() { return size(root); } // return number of key-value pairs in BST rooted at x private int size(Node x) { if (x == null) return 0; else return x.N; } /*********************************************************************** * Search BST for given key, and return associated value if found, * return null if not found ***********************************************************************/ // does there exist a key-value pair with given key? public boolean contains(Key key) { return get(key) != null; } // return value associated with the given key, or null if no such key exists public Value get(Key key) { return get(root, key); } private Value get(Node x, Key key) { if (x == null) return null; int cmp = key.compareTo(x.key); if (cmp < 0) return get(x.left, key); else if (cmp > 0) return get(x.right, key); else return x.val; } /*********************************************************************** * Insert key-value pair into BST * If key already exists, update with new value ***********************************************************************/ public void put(Key key, Value val) { if (val == null) { delete(key); return; } root = put(root, key, val); assert check(); } private Node put(Node x, Key key, Value val) { if (x == null) return new Node(key, val, 1); int cmp = key.compareTo(x.key); if (cmp < 0) x.left = put(x.left, key, val); else if (cmp > 0) x.right = put(x.right, key, val); else x.val = val; x.N = 1 + size(x.left) + size(x.right); return x; } /*********************************************************************** * Delete ***********************************************************************/ public void deleteMin() { if (isEmpty()) throw new NoSuchElementException("Symbol table underflow"); root = deleteMin(root); assert check(); } private Node deleteMin(Node x) { if (x.left == null) return x.right; x.left = deleteMin(x.left); x.N = size(x.left) + size(x.right) + 1; return x; } public void deleteMax() { if (isEmpty()) throw new NoSuchElementException("Symbol table underflow"); root = deleteMax(root); assert check(); } private Node deleteMax(Node x) { if (x.right == null) return x.left; x.right = deleteMax(x.right); x.N = size(x.left) + size(x.right) + 1; return x; } public void delete(Key key) { root = delete(root, key); assert check(); } private Node delete(Node x, Key key) { if (x == null) return null; int cmp = key.compareTo(x.key); if (cmp < 0) x.left = delete(x.left, key); else if (cmp > 0) x.right = delete(x.right, key); else { if (x.right == null) return x.left; if (x.left == null) return x.right; Node t = x; x = min(t.right); x.right = deleteMin(t.right); x.left = t.left; } x.N = size(x.left) + size(x.right) + 1; return x; } /*********************************************************************** * Min, max, floor, and ceiling ***********************************************************************/ public Key min() { if (isEmpty()) return null; return min(root).key; } private Node min(Node x) { if (x.left == null) return x; else return min(x.left); } public Key max() { if (isEmpty()) return null; return max(root).key; } private Node max(Node x) { if (x.right == null) return x; else return max(x.right); } public Key floor(Key key) { Node x = floor(root, key); if (x == null) return null; else return x.key; } private Node floor(Node x, Key key) { if (x == null) return null; int cmp = key.compareTo(x.key); if (cmp == 0) return x; if (cmp < 0) return floor(x.left, key); Node t = floor(x.right, key); if (t != null) return t; else return x; } public Key ceiling(Key key) { Node x = ceiling(root, key); if (x == null) return null; else return x.key; } private Node ceiling(Node x, Key key) { if (x == null) return null; int cmp = key.compareTo(x.key); if (cmp == 0) return x; if (cmp < 0) { Node t = ceiling(x.left, key); if (t != null) return t; else return x; } return ceiling(x.right, key); } /*********************************************************************** * Rank and selection ***********************************************************************/ public Key select(int k) { if (k < 0 || k >= size()) return null; Node x = select(root, k); return x.key; } // Return key of rank k. private Node select(Node x, int k) { if (x == null) return null; int t = size(x.left); if (t > k) return select(x.left, k); else if (t < k) return select(x.right, k-t-1); else return x; } public int rank(Key key) { return rank(key, root); } // Number of keys in the subtree less than key. private int rank(Key key, Node x) { if (x == null) return 0; int cmp = key.compareTo(x.key); if (cmp < 0) return rank(key, x.left); else if (cmp > 0) return 1 + size(x.left) + rank(key, x.right); else return size(x.left); } /*********************************************************************** * Range count and range search. ***********************************************************************/ public Iterable<Key> keys() { return keys(min(), max()); } public Iterable<Key> keys(Key lo, Key hi) { Queue<key> queue = new Queue<key>(); keys(root, queue, lo, hi); return queue; } private void keys(Node x, Queue<Key> queue, Key lo, Key hi) { if (x == null) return; int cmplo = lo.compareTo(x.key); int cmphi = hi.compareTo(x.key); if (cmplo < 0) keys(x.left, queue, lo, hi); if (cmplo <= 0 && cmphi >= 0) queue.enqueue(x.key); if (cmphi > 0) keys(x.right, queue, lo, hi); } public int size(Key lo, Key hi) { if (lo.compareTo(hi) > 0) return 0; if (contains(hi)) return rank(hi) - rank(lo) + 1; else return rank(hi) - rank(lo); } // height of this BST (one-node tree has height 0) public int height() { return height(root); } private int height(Node x) { if (x == null) return -1; return 1 + Math.max(height(x.left), height(x.right)); } // level order traversal public Iterable<Key> levelOrder() { Queue<Key> keys = new Queue<Key>(); Queue<Node> queue = new Queue<Node>(); queue.enqueue(root); while (!queue.isEmpty()) { Node x = queue.dequeue(); if (x == null) continue; keys.enqueue(x.key); queue.enqueue(x.left); queue.enqueue(x.right); } return keys; } /************************************************************************* * Check integrity of BST data structure *************************************************************************/ private boolean check() { if (!isBST()) StdOut.println("Not in symmetric order"); if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent"); if (!isRankConsistent()) StdOut.println("Ranks not consistent"); return isBST() && isSizeConsistent() && isRankConsistent(); } // does this binary tree satisfy symmetric order? // Note: this test also ensures that data structure is a binary tree since order is strict private boolean isBST() { return isBST(root, null, null); } // is the tree rooted at x a BST with all keys strictly between min and max // (if min or max is null, treat as empty constraint) // Credit: Bob Dondero's elegant solution private boolean isBST(Node x, Key min, Key max) { if (x == null) return true; if (min != null && x.key.compareTo(min) <= 0) return false; if (max != null && x.key.compareTo(max) >= 0) return false; return isBST(x.left, min, x.key) && isBST(x.right, x.key, max); } // are the size fields correct? private boolean isSizeConsistent() { return isSizeConsistent(root); } private boolean isSizeConsistent(Node x) { if (x == null) return true; if (x.N != size(x.left) + size(x.right) + 1) return false; return isSizeConsistent(x.left) && isSizeConsistent(x.right); } // check that ranks are consistent private boolean isRankConsistent() { for (int i = 0; i < size(); i++) if (i != rank(select(i))) return false; for (Key key : keys()) if (key.compareTo(select(rank(key))) != 0) return false; return true; } /***************************************************************************** * Test client *****************************************************************************/ public static void main(String[] args) { BST<String, Integer> st = new BST<String, Integer>(); for (int i = 0; !StdIn.isEmpty(); i++) { String key = StdIn.readString(); st.put(key, i); } for (String s : st.levelOrder()) StdOut.println(s + " " + st.get(s)); StdOut.println(); for (String s : st.keys()) StdOut.println(s + " " + st.get(s)); }}</key></key> |
Another BST deletion:
http://buttercola.blogspot.com/2014/12/data-structure-algorithms-binary-search.html
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