15c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Copyright 2009 the V8 project authors. All rights reserved.
25c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Redistribution and use in source and binary forms, with or without
35c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// modification, are permitted provided that the following conditions are
45c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// met:
55c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//
65c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//     * Redistributions of source code must retain the above copyright
75c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//       notice, this list of conditions and the following disclaimer.
85c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//     * Redistributions in binary form must reproduce the above
95c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//       copyright notice, this list of conditions and the following
105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//       disclaimer in the documentation and/or other materials provided
115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//       with the distribution.
125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//     * Neither the name of Google Inc. nor the names of its
135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//       contributors may be used to endorse or promote products derived
145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//       from this software without specific prior written permission.
155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)//
165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// This benchmark is based on a JavaScript log processing module used
295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// by the V8 profiler to generate execution time profiles for runs of
305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// JavaScript applications, and it effectively measures how fast the
315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// JavaScript engine is at allocating nodes and reclaiming the memory
325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// used for old nodes. Because of the way splay trees work, the engine
335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// also has to deal with a lot of changes to the large tree object
345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// graph.
355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)// Configuration.
375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var kSplayTreeSize = 8000;
385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var kSplayTreeModifications = 80;
395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var kSplayTreePayloadDepth = 5;
405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)var splayTree = null;
425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function GeneratePayloadTree(depth, key) {
455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (depth == 0) {
465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return {
475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      array  : [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ],
485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      string : 'String for key ' + key + ' in leaf node'
495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    };
505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  } else {
515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return {
525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      left:  GeneratePayloadTree(depth - 1, key),
535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      right: GeneratePayloadTree(depth - 1, key)
545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    };
555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)}
575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function GenerateKey() {
605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // The benchmark framework guarantees that Math.random is
615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // deterministic; see base.js.
625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  return Math.random();
635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)}
645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function InsertNewNode() {
675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Insert new node with a unique key.
685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var key;
695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  do {
705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    key = GenerateKey();
715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  } while (splayTree.find(key) != null);
725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  splayTree.insert(key, GeneratePayloadTree(kSplayTreePayloadDepth, key));
735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  return key;
745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)}
755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function SplaySetup() {
795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  splayTree = new SplayTree();
805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  for (var i = 0; i < kSplayTreeSize; i++) InsertNewNode();
815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)}
825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function SplayTearDown() {
855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Allow the garbage collector to reclaim the memory
865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // used by the splay tree no matter how we exit the
875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // tear down function.
885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var keys = splayTree.exportKeys();
895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  splayTree = null;
905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Verify that the splay tree has the right size.
925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var length = keys.length;
935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (length != kSplayTreeSize) {
945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    throw new Error("Splay tree has wrong size");
955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Verify that the splay tree has sorted, unique keys.
985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  for (var i = 0; i < length - 1; i++) {
995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    if (keys[i] >= keys[i + 1]) {
1005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      throw new Error("Splay tree not sorted");
1015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    }
1025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
1035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)}
1045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function SplayRun() {
1075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Replace a few nodes in the splay tree.
1085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  for (var i = 0; i < kSplayTreeModifications; i++) {
1095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    var key = InsertNewNode();
1105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    var greatest = splayTree.findGreatestLessThan(key);
1115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    if (greatest == null) splayTree.remove(key);
1125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    else splayTree.remove(greatest.key);
1135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
1145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)}
1155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
1185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Constructs a Splay tree.  A splay tree is a self-balancing binary
1195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * search tree with the additional property that recently accessed
1205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * elements are quick to access again. It performs basic operations
1215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * such as insertion, look-up and removal in O(log(n)) amortized time.
1225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
1235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @constructor
1245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
1255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)function SplayTree() {
1265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
1275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
1305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Pointer to the root node of the tree.
1315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
1325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @type {SplayTree.Node}
1335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @private
1345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
1355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.root_ = null;
1365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
1395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @return {boolean} Whether the tree is empty.
1405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
1415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.isEmpty = function() {
1425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  return !this.root_;
1435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
1445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
1475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Inserts a node into the tree with the specified key and value if
1485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * the tree does not already contain a node with the specified key. If
1495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * the value is inserted, it becomes the root of the tree.
1505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
1515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {number} key Key to insert into the tree.
1525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {*} value Value to insert into the tree.
1535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
1545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.insert = function(key, value) {
1555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.isEmpty()) {
1565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.root_ = new SplayTree.Node(key, value);
1575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return;
1585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
1595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Splay on the key to move the last node on the search path for
1605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // the key to the root of the tree.
1615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.splay_(key);
1625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.root_.key == key) {
1635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return;
1645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
1655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var node = new SplayTree.Node(key, value);
1665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (key > this.root_.key) {
1675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    node.left = this.root_;
1685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    node.right = this.root_.right;
1695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.root_.right = null;
1705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  } else {
1715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    node.right = this.root_;
1725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    node.left = this.root_.left;
1735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.root_.left = null;
1745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
1755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.root_ = node;
1765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
1775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
1795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
1805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Removes a node with the specified key from the tree if the tree
1815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * contains a node with this key. The removed node is returned. If the
1825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * key is not found, an exception is thrown.
1835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
1845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {number} key Key to find and remove from the tree.
1855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @return {SplayTree.Node} The removed node.
1865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
1875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.remove = function(key) {
1885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.isEmpty()) {
1895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    throw Error('Key not found: ' + key);
1905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
1915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.splay_(key);
1925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.root_.key != key) {
1935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    throw Error('Key not found: ' + key);
1945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
1955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var removed = this.root_;
1965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (!this.root_.left) {
1975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.root_ = this.root_.right;
1985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  } else {
1995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    var right = this.root_.right;
2005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.root_ = this.root_.left;
2015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    // Splay to make sure that the new root has an empty right child.
2025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.splay_(key);
2035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    // Insert the original right child as the right child of the new
2045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    // root.
2055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.root_.right = right;
2065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
2075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  return removed;
2085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
2095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
2125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Returns the node having the specified key or null if the tree doesn't contain
2135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * a node with the specified key.
2145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
2155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {number} key Key to find in the tree.
2165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @return {SplayTree.Node} Node having the specified key.
2175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
2185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.find = function(key) {
2195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.isEmpty()) {
2205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return null;
2215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
2225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.splay_(key);
2235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  return this.root_.key == key ? this.root_ : null;
2245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
2255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
2285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @return {SplayTree.Node} Node having the maximum key value that
2295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *     is less or equal to the specified key value.
2305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
2315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.findGreatestLessThan = function(key) {
2325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.isEmpty()) {
2335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return null;
2345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
2355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Splay on the key to move the node with the given key or the last
2365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // node on the search path to the top of the tree.
2375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.splay_(key);
2385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Now the result is either the root node or the greatest node in
2395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // the left subtree.
2405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.root_.key <= key) {
2415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return this.root_;
2425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  } else if (this.root_.left) {
2435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return this.findMax(this.root_.left);
2445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  } else {
2455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return null;
2465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
2475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
2485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
2515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @return {Array<*>} An array containing all the keys of tree's nodes.
2525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
2535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.exportKeys = function() {
2545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var result = [];
2555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (!this.isEmpty()) {
2565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    this.root_.traverse_(function(node) { result.push(node.key); });
2575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
2585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  return result;
2595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
2605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
2625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
2635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Perform the splay operation for the given key. Moves the node with
2645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * the given key to the top of the tree.  If no node has the given
2655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * key, the last node on the search path is moved to the top of the
2665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * tree. This is the simplified top-down splaying algorithm from:
2675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * "Self-adjusting Binary Search Trees" by Sleator and Tarjan
2685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
2695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {number} key Key to splay the tree on.
2705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @private
2715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
2725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.prototype.splay_ = function(key) {
2735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  if (this.isEmpty()) {
2745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    return;
2755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
2765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Create a dummy node.  The use of the dummy node is a bit
2775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // counter-intuitive: The right child of the dummy node will hold
2785c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // the L tree of the algorithm.  The left child of the dummy node
2795c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // will hold the R tree of the algorithm.  Using a dummy node, left
2805c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // and right will always be nodes and we avoid special cases.
2815c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var dummy, left, right;
2825c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  dummy = left = right = new SplayTree.Node(null, null);
2835c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var current = this.root_;
2845c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  while (true) {
2855c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    if (key < current.key) {
2865c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      if (!current.left) {
2875c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        break;
2885c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      }
2895c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      if (key < current.left.key) {
2905c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        // Rotate right.
2915c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        var tmp = current.left;
2925c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        current.left = tmp.right;
2935c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        tmp.right = current;
2945c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        current = tmp;
2955c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        if (!current.left) {
2965c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)          break;
2975c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        }
2985c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      }
2995c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      // Link right.
3005c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      right.left = current;
3015c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      right = current;
3025c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      current = current.left;
3035c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    } else if (key > current.key) {
3045c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      if (!current.right) {
3055c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        break;
3065c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      }
3075c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      if (key > current.right.key) {
3085c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        // Rotate left.
3095c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        var tmp = current.right;
3105c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        current.right = tmp.left;
3115c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        tmp.left = current;
3125c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        current = tmp;
3135c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        if (!current.right) {
3145c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)          break;
3155c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)        }
3165c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      }
3175c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      // Link left.
3185c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      left.right = current;
3195c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      left = current;
3205c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      current = current.right;
3215c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    } else {
3225c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)      break;
3235c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    }
3245c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
3255c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  // Assemble.
3265c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  left.right = current.left;
3275c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  right.left = current.right;
3285c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  current.left = dummy.right;
3295c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  current.right = dummy.left;
3305c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.root_ = current;
3315c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
3325c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3335c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3345c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
3355c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Constructs a Splay tree node.
3365c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
3375c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {number} key Key.
3385c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {*} value Value.
3395c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
3405c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.Node = function(key, value) {
3415c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.key = key;
3425c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  this.value = value;
3435c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
3445c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3455c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3465c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
3475c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @type {SplayTree.Node}
3485c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
3495c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.Node.prototype.left = null;
3505c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3515c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3525c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
3535c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @type {SplayTree.Node}
3545c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
3555c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.Node.prototype.right = null;
3565c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3575c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3585c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)/**
3595c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * Performs an ordered traversal of the subtree starting at
3605c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * this SplayTree.Node.
3615c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) *
3625c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @param {function(SplayTree.Node)} f Visitor function.
3635c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) * @private
3645c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles) */
3655c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTree.Node.prototype.traverse_ = function(f) {
3665c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  var current = this;
3675c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  while (current) {
3685c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    var left = current.left;
3695c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    if (left) left.traverse_(f);
3705c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    f(current);
3715c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)    current = current.right;
3725c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)  }
3735c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)};
3745c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)
3755c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplaySetup();
3765c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayRun();
3775c87bf8b86a7c82ef50fb7a89697d8e02e2553beTorne (Richard Coles)SplayTearDown();
378