Ben Murdoch | 3ef787d | 2012-04-12 10:51:47 +0100 | [diff] [blame] | 1 | // Copyright 2011 the V8 project authors. All rights reserved. |
| 2 | // Redistribution and use in source and binary forms, with or without |
| 3 | // modification, are permitted provided that the following conditions are |
| 4 | // met: |
| 5 | // |
| 6 | // * Redistributions of source code must retain the above copyright |
| 7 | // notice, this list of conditions and the following disclaimer. |
| 8 | // * Redistributions in binary form must reproduce the above |
| 9 | // copyright notice, this list of conditions and the following |
| 10 | // disclaimer in the documentation and/or other materials provided |
| 11 | // with the distribution. |
| 12 | // * Neither the name of Google Inc. nor the names of its |
| 13 | // contributors may be used to endorse or promote products derived |
| 14 | // from this software without specific prior written permission. |
| 15 | // |
| 16 | // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| 17 | // "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| 18 | // LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR |
| 19 | // A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT |
| 20 | // OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 21 | // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT |
| 22 | // LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, |
| 23 | // DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY |
| 24 | // THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT |
| 25 | // (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE |
| 26 | // OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. |
| 27 | |
| 28 | /** |
| 29 | * Constructs a Splay tree. A splay tree is a self-balancing binary |
| 30 | * search tree with the additional property that recently accessed |
| 31 | * elements are quick to access again. It performs basic operations |
| 32 | * such as insertion, look-up and removal in O(log(n)) amortized time. |
| 33 | * |
| 34 | * @constructor |
| 35 | */ |
| 36 | function SplayTree() { |
| 37 | }; |
| 38 | |
| 39 | |
| 40 | /** |
| 41 | * Pointer to the root node of the tree. |
| 42 | * |
| 43 | * @type {SplayTree.Node} |
| 44 | * @private |
| 45 | */ |
| 46 | SplayTree.prototype.root_ = null; |
| 47 | |
| 48 | |
| 49 | /** |
| 50 | * @return {boolean} Whether the tree is empty. |
| 51 | */ |
| 52 | SplayTree.prototype.isEmpty = function() { |
| 53 | return !this.root_; |
| 54 | }; |
| 55 | |
| 56 | |
| 57 | /** |
| 58 | * Inserts a node into the tree with the specified key and value if |
| 59 | * the tree does not already contain a node with the specified key. If |
| 60 | * the value is inserted, it becomes the root of the tree. |
| 61 | * |
| 62 | * @param {number} key Key to insert into the tree. |
| 63 | * @param {*} value Value to insert into the tree. |
| 64 | */ |
| 65 | SplayTree.prototype.insert = function(key, value) { |
| 66 | if (this.isEmpty()) { |
| 67 | this.root_ = new SplayTree.Node(key, value); |
| 68 | return; |
| 69 | } |
| 70 | // Splay on the key to move the last node on the search path for |
| 71 | // the key to the root of the tree. |
| 72 | this.splay_(key); |
| 73 | if (this.root_.key == key) { |
| 74 | return; |
| 75 | } |
| 76 | var node = new SplayTree.Node(key, value); |
| 77 | if (key > this.root_.key) { |
| 78 | node.left = this.root_; |
| 79 | node.right = this.root_.right; |
| 80 | this.root_.right = null; |
| 81 | } else { |
| 82 | node.right = this.root_; |
| 83 | node.left = this.root_.left; |
| 84 | this.root_.left = null; |
| 85 | } |
| 86 | this.root_ = node; |
| 87 | }; |
| 88 | |
| 89 | |
| 90 | /** |
| 91 | * Removes a node with the specified key from the tree if the tree |
| 92 | * contains a node with this key. The removed node is returned. If the |
| 93 | * key is not found, an exception is thrown. |
| 94 | * |
| 95 | * @param {number} key Key to find and remove from the tree. |
| 96 | * @return {SplayTree.Node} The removed node. |
| 97 | */ |
| 98 | SplayTree.prototype.remove = function(key) { |
| 99 | if (this.isEmpty()) { |
| 100 | throw Error('Key not found: ' + key); |
| 101 | } |
| 102 | this.splay_(key); |
| 103 | if (this.root_.key != key) { |
| 104 | throw Error('Key not found: ' + key); |
| 105 | } |
| 106 | var removed = this.root_; |
| 107 | if (!this.root_.left) { |
| 108 | this.root_ = this.root_.right; |
| 109 | } else { |
| 110 | var right = this.root_.right; |
| 111 | this.root_ = this.root_.left; |
| 112 | // Splay to make sure that the new root has an empty right child. |
| 113 | this.splay_(key); |
| 114 | // Insert the original right child as the right child of the new |
| 115 | // root. |
| 116 | this.root_.right = right; |
| 117 | } |
| 118 | return removed; |
| 119 | }; |
| 120 | |
| 121 | |
| 122 | /** |
| 123 | * Returns the node having the specified key or null if the tree doesn't contain |
| 124 | * a node with the specified key. |
| 125 | * |
| 126 | * @param {number} key Key to find in the tree. |
| 127 | * @return {SplayTree.Node} Node having the specified key. |
| 128 | */ |
| 129 | SplayTree.prototype.find = function(key) { |
| 130 | if (this.isEmpty()) { |
| 131 | return null; |
| 132 | } |
| 133 | this.splay_(key); |
| 134 | return this.root_.key == key ? this.root_ : null; |
| 135 | }; |
| 136 | |
| 137 | |
| 138 | /** |
| 139 | * @return {SplayTree.Node} Node having the maximum key value. |
| 140 | */ |
| 141 | SplayTree.prototype.findMax = function(opt_startNode) { |
| 142 | if (this.isEmpty()) { |
| 143 | return null; |
| 144 | } |
| 145 | var current = opt_startNode || this.root_; |
| 146 | while (current.right) { |
| 147 | current = current.right; |
| 148 | } |
| 149 | return current; |
| 150 | }; |
| 151 | |
| 152 | |
| 153 | /** |
| 154 | * @return {SplayTree.Node} Node having the maximum key value that |
| 155 | * is less than the specified key value. |
| 156 | */ |
| 157 | SplayTree.prototype.findGreatestLessThan = function(key) { |
| 158 | if (this.isEmpty()) { |
| 159 | return null; |
| 160 | } |
| 161 | // Splay on the key to move the node with the given key or the last |
| 162 | // node on the search path to the top of the tree. |
| 163 | this.splay_(key); |
| 164 | // Now the result is either the root node or the greatest node in |
| 165 | // the left subtree. |
| 166 | if (this.root_.key < key) { |
| 167 | return this.root_; |
| 168 | } else if (this.root_.left) { |
| 169 | return this.findMax(this.root_.left); |
| 170 | } else { |
| 171 | return null; |
| 172 | } |
| 173 | }; |
| 174 | |
| 175 | |
| 176 | /** |
| 177 | * @return {Array<*>} An array containing all the keys of tree's nodes. |
| 178 | */ |
| 179 | SplayTree.prototype.exportKeys = function() { |
| 180 | var result = []; |
| 181 | if (!this.isEmpty()) { |
| 182 | this.root_.traverse_(function(node) { result.push(node.key); }); |
| 183 | } |
| 184 | return result; |
| 185 | }; |
| 186 | |
| 187 | |
| 188 | /** |
| 189 | * Perform the splay operation for the given key. Moves the node with |
| 190 | * the given key to the top of the tree. If no node has the given |
| 191 | * key, the last node on the search path is moved to the top of the |
| 192 | * tree. This is the simplified top-down splaying algorithm from: |
| 193 | * "Self-adjusting Binary Search Trees" by Sleator and Tarjan |
| 194 | * |
| 195 | * @param {number} key Key to splay the tree on. |
| 196 | * @private |
| 197 | */ |
| 198 | SplayTree.prototype.splay_ = function(key) { |
| 199 | if (this.isEmpty()) { |
| 200 | return; |
| 201 | } |
| 202 | // Create a dummy node. The use of the dummy node is a bit |
| 203 | // counter-intuitive: The right child of the dummy node will hold |
| 204 | // the L tree of the algorithm. The left child of the dummy node |
| 205 | // will hold the R tree of the algorithm. Using a dummy node, left |
| 206 | // and right will always be nodes and we avoid special cases. |
| 207 | var dummy, left, right; |
| 208 | dummy = left = right = new SplayTree.Node(null, null); |
| 209 | var current = this.root_; |
| 210 | while (true) { |
| 211 | if (key < current.key) { |
| 212 | if (!current.left) { |
| 213 | break; |
| 214 | } |
| 215 | if (key < current.left.key) { |
| 216 | // Rotate right. |
| 217 | var tmp = current.left; |
| 218 | current.left = tmp.right; |
| 219 | tmp.right = current; |
| 220 | current = tmp; |
| 221 | if (!current.left) { |
| 222 | break; |
| 223 | } |
| 224 | } |
| 225 | // Link right. |
| 226 | right.left = current; |
| 227 | right = current; |
| 228 | current = current.left; |
| 229 | } else if (key > current.key) { |
| 230 | if (!current.right) { |
| 231 | break; |
| 232 | } |
| 233 | if (key > current.right.key) { |
| 234 | // Rotate left. |
| 235 | var tmp = current.right; |
| 236 | current.right = tmp.left; |
| 237 | tmp.left = current; |
| 238 | current = tmp; |
| 239 | if (!current.right) { |
| 240 | break; |
| 241 | } |
| 242 | } |
| 243 | // Link left. |
| 244 | left.right = current; |
| 245 | left = current; |
| 246 | current = current.right; |
| 247 | } else { |
| 248 | break; |
| 249 | } |
| 250 | } |
| 251 | // Assemble. |
| 252 | left.right = current.left; |
| 253 | right.left = current.right; |
| 254 | current.left = dummy.right; |
| 255 | current.right = dummy.left; |
| 256 | this.root_ = current; |
| 257 | }; |
| 258 | |
| 259 | |
| 260 | /** |
| 261 | * Constructs a Splay tree node. |
| 262 | * |
| 263 | * @param {number} key Key. |
| 264 | * @param {*} value Value. |
| 265 | */ |
| 266 | SplayTree.Node = function(key, value) { |
| 267 | this.key = key; |
| 268 | this.value = value; |
| 269 | }; |
| 270 | |
| 271 | |
| 272 | /** |
| 273 | * @type {SplayTree.Node} |
| 274 | */ |
| 275 | SplayTree.Node.prototype.left = null; |
| 276 | |
| 277 | |
| 278 | /** |
| 279 | * @type {SplayTree.Node} |
| 280 | */ |
| 281 | SplayTree.Node.prototype.right = null; |
| 282 | |
| 283 | |
| 284 | /** |
| 285 | * Performs an ordered traversal of the subtree starting at |
| 286 | * this SplayTree.Node. |
| 287 | * |
| 288 | * @param {function(SplayTree.Node)} f Visitor function. |
| 289 | * @private |
| 290 | */ |
| 291 | SplayTree.Node.prototype.traverse_ = function(f) { |
| 292 | var current = this; |
| 293 | while (current) { |
| 294 | var left = current.left; |
| 295 | if (left) left.traverse_(f); |
| 296 | f(current); |
| 297 | current = current.right; |
| 298 | } |
| 299 | }; |
| 300 | |
| 301 | SplayTree.prototype.traverseBreadthFirst = function (f) { |
| 302 | if (f(this.root_.value)) return; |
| 303 | |
| 304 | var stack = [this.root_]; |
| 305 | var length = 1; |
| 306 | |
| 307 | while (length > 0) { |
| 308 | var new_stack = new Array(stack.length * 2); |
| 309 | var new_length = 0; |
| 310 | for (var i = 0; i < length; i++) { |
| 311 | var n = stack[i]; |
| 312 | var l = n.left; |
| 313 | var r = n.right; |
| 314 | if (l) { |
| 315 | if (f(l.value)) return; |
| 316 | new_stack[new_length++] = l; |
| 317 | } |
| 318 | if (r) { |
| 319 | if (f(r.value)) return; |
| 320 | new_stack[new_length++] = r; |
| 321 | } |
| 322 | } |
| 323 | stack = new_stack; |
| 324 | length = new_length; |
| 325 | } |
| 326 | }; |