// Copyright 2011 the V8 project authors. All rights reserved.
// Redistribution and use in source and binary forms, with or without
// modification, are permitted provided that the following conditions are
// met:
//
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above
// copyright notice, this list of conditions and the following
// disclaimer in the documentation and/or other materials provided
// with the distribution.
// * Neither the name of Google Inc. nor the names of its
// contributors may be used to endorse or promote products derived
// from this software without specific prior written permission.
//
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
// "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
// LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
// A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
// OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
// SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
// LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
// DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
// THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
// (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
// OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
/**
* Constructs a Splay tree. A splay tree is a self-balancing binary
* search tree with the additional property that recently accessed
* elements are quick to access again. It performs basic operations
* such as insertion, look-up and removal in O(log(n)) amortized time.
*
* @constructor
*/
function SplayTree() {
};
/**
* Pointer to the root node of the tree.
*
* @type {SplayTree.Node}
* @private
*/
SplayTree.prototype.root_ = null;
/**
* @return {boolean} Whether the tree is empty.
*/
SplayTree.prototype.isEmpty = function() {
return !this.root_;
};
/**
* Inserts a node into the tree with the specified key and value if
* the tree does not already contain a node with the specified key. If
* the value is inserted, it becomes the root of the tree.
*
* @param {number} key Key to insert into the tree.
* @param {*} value Value to insert into the tree.
*/
SplayTree.prototype.insert = function(key, value) {
if (this.isEmpty()) {
this.root_ = new SplayTree.Node(key, value);
return;
}
// Splay on the key to move the last node on the search path for
// the key to the root of the tree.
this.splay_(key);
if (this.root_.key == key) {
return;
}
var node = new SplayTree.Node(key, value);
if (key > this.root_.key) {
node.left = this.root_;
node.right = this.root_.right;
this.root_.right = null;
} else {
node.right = this.root_;
node.left = this.root_.left;
this.root_.left = null;
}
this.root_ = node;
};
/**
* Removes a node with the specified key from the tree if the tree
* contains a node with this key. The removed node is returned. If the
* key is not found, an exception is thrown.
*
* @param {number} key Key to find and remove from the tree.
* @return {SplayTree.Node} The removed node.
*/
SplayTree.prototype.remove = function(key) {
if (this.isEmpty()) {
throw Error('Key not found: ' + key);
}
this.splay_(key);
if (this.root_.key != key) {
throw Error('Key not found: ' + key);
}
var removed = this.root_;
if (!this.root_.left) {
this.root_ = this.root_.right;
} else {
var right = this.root_.right;
this.root_ = this.root_.left;
// Splay to make sure that the new root has an empty right child.
this.splay_(key);
// Insert the original right child as the right child of the new
// root.
this.root_.right = right;
}
return removed;
};
/**
* Returns the node having the specified key or null if the tree doesn't contain
* a node with the specified key.
*
* @param {number} key Key to find in the tree.
* @return {SplayTree.Node} Node having the specified key.
*/
SplayTree.prototype.find = function(key) {
if (this.isEmpty()) {
return null;
}
this.splay_(key);
return this.root_.key == key ? this.root_ : null;
};
/**
* @return {SplayTree.Node} Node having the maximum key value.
*/
SplayTree.prototype.findMax = function(opt_startNode) {
if (this.isEmpty()) {
return null;
}
var current = opt_startNode || this.root_;
while (current.right) {
current = current.right;
}
return current;
};
/**
* @return {SplayTree.Node} Node having the maximum key value that
* is less than the specified key value.
*/
SplayTree.prototype.findGreatestLessThan = function(key) {
if (this.isEmpty()) {
return null;
}
// Splay on the key to move the node with the given key or the last
// node on the search path to the top of the tree.
this.splay_(key);
// Now the result is either the root node or the greatest node in
// the left subtree.
if (this.root_.key < key) {
return this.root_;
} else if (this.root_.left) {
return this.findMax(this.root_.left);
} else {
return null;
}
};
/**
* @return {Array<*>} An array containing all the keys of tree's nodes.
*/
SplayTree.prototype.exportKeys = function() {
var result = [];
if (!this.isEmpty()) {
this.root_.traverse_(function(node) { result.push(node.key); });
}
return result;
};
/**
* Perform the splay operation for the given key. Moves the node with
* the given key to the top of the tree. If no node has the given
* key, the last node on the search path is moved to the top of the
* tree. This is the simplified top-down splaying algorithm from:
* "Self-adjusting Binary Search Trees" by Sleator and Tarjan
*
* @param {number} key Key to splay the tree on.
* @private
*/
SplayTree.prototype.splay_ = function(key) {
if (this.isEmpty()) {
return;
}
// Create a dummy node. The use of the dummy node is a bit
// counter-intuitive: The right child of the dummy node will hold
// the L tree of the algorithm. The left child of the dummy node
// will hold the R tree of the algorithm. Using a dummy node, left
// and right will always be nodes and we avoid special cases.
var dummy, left, right;
dummy = left = right = new SplayTree.Node(null, null);
var current = this.root_;
while (true) {
if (key < current.key) {
if (!current.left) {
break;
}
if (key < current.left.key) {
// Rotate right.
var tmp = current.left;
current.left = tmp.right;
tmp.right = current;
current = tmp;
if (!current.left) {
break;
}
}
// Link right.
right.left = current;
right = current;
current = current.left;
} else if (key > current.key) {
if (!current.right) {
break;
}
if (key > current.right.key) {
// Rotate left.
var tmp = current.right;
current.right = tmp.left;
tmp.left = current;
current = tmp;
if (!current.right) {
break;
}
}
// Link left.
left.right = current;
left = current;
current = current.right;
} else {
break;
}
}
// Assemble.
left.right = current.left;
right.left = current.right;
current.left = dummy.right;
current.right = dummy.left;
this.root_ = current;
};
/**
* Constructs a Splay tree node.
*
* @param {number} key Key.
* @param {*} value Value.
*/
SplayTree.Node = function(key, value) {
this.key = key;
this.value = value;
};
/**
* @type {SplayTree.Node}
*/
SplayTree.Node.prototype.left = null;
/**
* @type {SplayTree.Node}
*/
SplayTree.Node.prototype.right = null;
/**
* Performs an ordered traversal of the subtree starting at
* this SplayTree.Node.
*
* @param {function(SplayTree.Node)} f Visitor function.
* @private
*/
SplayTree.Node.prototype.traverse_ = function(f) {
var current = this;
while (current) {
var left = current.left;
if (left) left.traverse_(f);
f(current);
current = current.right;
}
};
SplayTree.prototype.traverseBreadthFirst = function (f) {
if (f(this.root_.value)) return;
var stack = [this.root_];
var length = 1;
while (length > 0) {
var new_stack = new Array(stack.length * 2);
var new_length = 0;
for (var i = 0; i < length; i++) {
var n = stack[i];
var l = n.left;
var r = n.right;
if (l) {
if (f(l.value)) return;
new_stack[new_length++] = l;
}
if (r) {
if (f(r.value)) return;
new_stack[new_length++] = r;
}
}
stack = new_stack;
length = new_length;
}
};