// ----------------------------------------------------------------------
// dyoo: the following code comes from the Google Closure Library. I've done
// edits to flatten the namespace from goog.structs to just
// AvlTree, commented out inorderTraverse and reverseOrderTraverse.
//
// I'm considering changing the code to work with CPSed control flow.
//
// ----------------------------------------------------------------------
// Original license follows:
// ----------------------------------------------------------------------
// Copyright 2007 The Closure Library Authors. All Rights Reserved.
//
// Licensed under the Apache License, Version 2.0 (the "License");
// you may not use this file except in compliance with the License.
// You may obtain a copy of the License at
//
// http://www.apache.org/licenses/LICENSE-2.0
//
// Unless required by applicable law or agreed to in writing, software
// distributed under the License is distributed on an "AS-IS" BASIS,
// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
// See the License for the specific language governing permissions and
// limitations under the License.
/**
* @fileoverview Datastructure: AvlTree.
*
*
* This file provides the implementation of an AVL-Tree datastructure. The tree
* maintains a set of unique values in a sorted order. The values can be
* accessed efficiently in their sorted order since the tree enforces an O(logn)
* maximum height. See http://en.wikipedia.org/wiki/Avl_tree for more detail.
*
* The big-O notation for all operations are below:
* <pre>
* Method big-O
* ----------------------------------------------------------------------------
* - add O(logn)
* - remove O(logn)
* - clear O(1)
* - contains O(logn)
* - getCount O(1)
* - getMinimum O(1), or O(logn) when optional root is specified
* - getMaximum O(1), or O(logn) when optional root is specified
* - getHeight O(1)
* - getValues O(n)
* - inOrderTraverse O(logn + k), where k is number of traversed nodes
* - reverseOrderTraverse O(logn + k), where k is number of traversed nodes
* </pre>
*/
/**
* Constructs an AVL-Tree, which uses the specified comparator to order its
* values. The values can be accessed efficiently in their sorted order since
* the tree enforces a O(logn) maximum height.
*
* @param {Function=} opt_comparator Function used to order the tree's nodes.
* @constructor
* @implements {Collection}
*/
var AvlTree = function(opt_comparator) {
this.comparator_ = opt_comparator ||
AvlTree.DEFAULT_COMPARATOR_;
};
/**
* String comparison function used to compare values in the tree. This function
* is used by default if no comparator is specified in the tree's constructor.
*
* @param {string} a The first string.
* @param {string} b The second string.
* @return {number} -1 if a < b, 1 if a > b, 0 if a = b.
* @private
*/
AvlTree.DEFAULT_COMPARATOR_ = function(a, b) {
if (String(a) < String(b)) {
return -1;
} else if (String(a) > String(b)) {
return 1;
}
return 0;
};
/**
* Pointer to the root node of the tree.
*
* @type {AvlTree.Node}
* @private
*/
AvlTree.prototype.root_ = null;
/**
* Comparison function used to compare values in the tree. This function should
* take two values, a and b, and return x where:
* <pre>
* x < 0 if a < b,
* x > 0 if a > b,
* x = 0 otherwise
* </pre>
*
* @type {Function}
* @private
*/
AvlTree.prototype.comparator_ = null;
/**
* Pointer to the node with the smallest value in the tree.
*
* @type {AvlTree.Node}
* @private
*/
AvlTree.prototype.minNode_ = null;
/**
* Pointer to the node with the largest value in the tree.
*
* @type {AvlTree.Node}
* @private
*/
AvlTree.prototype.maxNode_ = null;
/**
* Keeps track of the number of nodes in the tree.
*
* @type {number}
* @private
*/
AvlTree.prototype.count_ = 0;
/**
* Inserts a node into the tree with the specified value if the tree does
* not already contain a node with the specified value. If the value is
* inserted, the tree is balanced to enforce the AVL-Tree height property.
*
* @param {*} value Value to insert into the tree.
* @return {boolean} Whether value was inserted into the tree.
*/
AvlTree.prototype.add = function(value) {
// If the tree is empty, create a root node with the specified value
if (this.root_ == null) {
this.root_ = new AvlTree.Node(value);
this.minNode_ = this.root_;
this.maxNode_ = this.root_;
this.count_ = 1;
return true;
}
// Assume a node is not added and change status when one is
var retStatus = false;
// Depth traverse the tree and insert the value if we reach a null node
this.traverse_(function(node) {
var retNode = null;
if (this.comparator_(node.value, value) > 0) {
retNode = node.left;
if (node.left == null) {
var newNode = new AvlTree.Node(value, node);
node.left = newNode;
if (node == this.minNode_) {
this.minNode_ = newNode;
}
retStatus = true; // Value was added to tree
this.balance_(node); // Maintain the AVL-tree balance
}
} else if (this.comparator_(node.value, value) < 0) {
retNode = node.right;
if (node.right == null) {
var newNode = new AvlTree.Node(value, node);
node.right = newNode;
if (node == this.maxNode_) {
this.maxNode_ = newNode;
}
retStatus = true; // Value was added to tree
this.balance_(node); // Maintain the AVL-tree balance
}
}
return retNode; // If null, we'll stop traversing the tree
});
// If a node was added, increment count
if (retStatus) {
this.count_ += 1;
}
// Return true if a node was added, false otherwise
return retStatus;
};
/**
* Removes a node from the tree with the specified value if the tree contains a
* node with this value. If a node is removed the tree is balanced to enforce
* the AVL-Tree height property. The value of the removed node is returned.
*
* @param {*} value Value to find and remove from the tree.
* @return {*} The value of the removed node or null if the value was not in
* the tree.
*/
AvlTree.prototype.remove = function(value) {
// Assume the value is not removed and set the value when it is removed
var retValue = null;
// Depth traverse the tree and remove the value if we find it
this.traverse_(function(node) {
var retNode = null;
if (this.comparator_(node.value, value) > 0) {
retNode = node.left;
} else if (this.comparator_(node.value, value) < 0) {
retNode = node.right;
} else {
retValue = node.value;
this.removeNode_(node);
}
return retNode; // If null, we'll stop traversing the tree
});
// If a node was removed, decrement count.
if (retValue) {
// Had traverse_() cleared the tree, set to 0.
this.count_ = this.root_ ? this.count_ - 1 : 0;
}
// Return the value that was removed, null if the value was not in the tree
return retValue;
};
/**
* Removes all nodes from the tree.
*/
AvlTree.prototype.clear = function() {
this.root_ = null;
this.minNode_ = null;
this.maxNode_ = null;
this.count_ = 0;
};
/**
* Returns true if the tree contains a node with the specified value, false
* otherwise.
*
* @param {*} value Value to find in the tree.
* @return {boolean} Whether the tree contains a node with the specified value.
*/
AvlTree.prototype.contains = function(value) {
// Assume the value is not in the tree and set this value if it is found
var isContained = false;
// Depth traverse the tree and set isContained if we find the node
this.traverse_(function(node) {
var retNode = null;
if (this.comparator_(node.value, value) > 0) {
retNode = node.left;
} else if (this.comparator_(node.value, value) < 0) {
retNode = node.right;
} else {
isContained = true;
}
return retNode; // If null, we'll stop traversing the tree
});
// Return true if the value is contained in the tree, false otherwise
return isContained;
};
/**
* Returns the number of values stored in the tree.
*
* @return {number} The number of values stored in the tree.
*/
AvlTree.prototype.getCount = function() {
return this.count_;
};
/**
* Returns the value u, such that u is contained in the tree and u < v, for all
* values v in the tree where v != u.
*
* @return {*} The minimum value contained in the tree.
*/
AvlTree.prototype.getMinimum = function() {
return this.getMinNode_().value;
};
/**
* Returns the value u, such that u is contained in the tree and u > v, for all
* values v in the tree where v != u.
*
* @return {*} The maximum value contained in the tree.
*/
AvlTree.prototype.getMaximum = function() {
return this.getMaxNode_().value;
};
/**
* Returns the height of the tree (the maximum depth). This height should
* always be <= 1.4405*(Math.log(n+2)/Math.log(2))-1.3277, where n is the
* number of nodes in the tree.
*
* @return {number} The height of the tree.
*/
AvlTree.prototype.getHeight = function() {
return this.root_ ? this.root_.height : 0;
};
/**
* Inserts the values stored in the tree into a new Array and returns the Array.
*
* @return {Array} An array containing all of the trees values in sorted order.
*/
AvlTree.prototype.getValues = function() {
var ret = [];
this.inOrderTraverse(function(value) {
ret.push(value);
});
return ret;
};
/**
* Performs an in-order traversal of the tree and calls {@code func} with each
* traversed node, optionally starting from the smallest node with a value >= to
* the specified start value. The traversal ends after traversing the tree's
* maximum node or when {@code func} returns a value that evaluates to true.
*
* @param {Function} func Function to call on each traversed node.
* @param {Object=} opt_startValue If specified, traversal will begin on the
* node with the smallest value >= opt_startValue.
*/
AvlTree.prototype.inOrderTraverse =
function(func, opt_startValue) {
// If our tree is empty, return immediately
if (!this.root_) {
return;
}
// Depth traverse the tree to find node to begin in-order traversal from
var startNode;
if (opt_startValue) {
this.traverse_(function(node) {
var retNode = null;
if (this.comparator_(node.value, opt_startValue) > 0) {
retNode = node.left;
startNode = node;
} else if (this.comparator_(node.value, opt_startValue) < 0) {
retNode = node.right;
} else {
startNode = node;
}
return retNode; // If null, we'll stop traversing the tree
});
} else {
startNode = this.getMinNode_();
}
// Traverse the tree and call func on each traversed node's value
var node = startNode, prev = startNode.left ? startNode.left : startNode;
while (node != null) {
if (node.left != null && node.left != prev && node.right != prev) {
node = node.left;
} else {
if (node.right != prev) {
if (func(node.value)) {
return;
}
}
var temp = node;
node = node.right != null && node.right != prev ?
node.right :
node.parent;
prev = temp;
}
}
};
// /**
// * Performs a reverse-order traversal of the tree and calls {@code func} with
// * each traversed node, optionally starting from the largest node with a value
// * <= to the specified start value. The traversal ends after traversing the
// * tree's minimum node or when func returns a value that evaluates to true.
// *
// * @param {Function} func Function to call on each traversed node.
// * @param {Object=} opt_startValue If specified, traversal will begin on the
// * node with the largest value <= opt_startValue.
// */
// AvlTree.prototype.reverseOrderTraverse =
// function(func, opt_startValue) {
// // If our tree is empty, return immediately
// if (!this.root_) {
// return;
// }
// // Depth traverse the tree to find node to begin reverse-order traversal from
// var startNode;
// if (opt_startValue) {
// this.traverse_(goog.bind(function(node) {
// var retNode = null;
// if (this.comparator_(node.value, opt_startValue) > 0) {
// retNode = node.left;
// } else if (this.comparator_(node.value, opt_startValue) < 0) {
// retNode = node.right;
// startNode = node;
// } else {
// startNode = node;
// }
// return retNode; // If null, we'll stop traversing the tree
// }, this));
// } else {
// startNode = this.getMaxNode_();
// }
// // Traverse the tree and call func on each traversed node's value
// var node = startNode, prev = startNode.right ? startNode.right : startNode;
// while (node != null) {
// if (node.right != null && node.right != prev && node.left != prev) {
// node = node.right;
// } else {
// if (node.left != prev) {
// if (func(node.value)) {
// return;
// }
// }
// var temp = node;
// node = node.left != null && node.left != prev ?
// node.left :
// node.parent;
// prev = temp;
// }
// }
// };
/**
* Performs a traversal defined by the supplied {@code traversalFunc}. The first
* call to {@code traversalFunc} is passed the root or the optionally specified
* startNode. After that, calls {@code traversalFunc} with the node returned
* by the previous call to {@code traversalFunc} until {@code traversalFunc}
* returns null or the optionally specified endNode. The first call to
* traversalFunc is passed the root or the optionally specified startNode.
*
* @param {Function} traversalFunc Function used to traverse the tree. Takes a
* node as a parameter and returns a node.
* @param {AvlTree.Node=} opt_startNode The node at which the
* traversal begins.
* @param {AvlTree.Node=} opt_endNode The node at which the
* traversal ends.
* @private
*/
AvlTree.prototype.traverse_ =
function(traversalFunc, opt_startNode, opt_endNode) {
var node = opt_startNode ? opt_startNode : this.root_;
var endNode = opt_endNode ? opt_endNode : null;
while (node && node != endNode) {
node = traversalFunc.call(this, node);
}
};
// CPS'ed version of the traverse function
AvlTree.prototype.traverse_k_ =
function(traversalFunc_k, opt_startNode, opt_endNode, k) {
var node = opt_startNode ? opt_startNode : this.root_;
var endNode = opt_endNode ? opt_endNode : null;
var loop = function(node) {
if (node && node != endNode) {
traversalFunc_k.call(this, node, loop);
} else {
k();
}
}
return loop(node);
};
/**
* Ensures that the specified node and all its ancestors are balanced. If they
* are not, performs left and right tree rotations to achieve a balanced
* tree. This method assumes that at most 2 rotations are necessary to balance
* the tree (which is true for AVL-trees that are balanced after each node is
* added or removed).
*
* @param {AvlTree.Node} node Node to begin balance from.
* @private
*/
AvlTree.prototype.balance_ = function(node) {
this.traverse_(function(node) {
// Calculate the left and right node's heights
var lh = node.left ? node.left.height : 0;
var rh = node.right ? node.right.height : 0;
// Rotate tree rooted at this node if it is not AVL-tree balanced
if (lh - rh > 1) {
if (node.left.right && (!node.left.left ||
node.left.left.height < node.left.right.height)) {
this.leftRotate_(node.left);
}
this.rightRotate_(node);
} else if (rh - lh > 1) {
if (node.right.left && (!node.right.right ||
node.right.right.height < node.right.left.height)) {
this.rightRotate_(node.right);
}
this.leftRotate_(node);
}
// Recalculate the left and right node's heights
lh = node.left ? node.left.height : 0;
rh = node.right ? node.right.height : 0;
// Set this node's height
node.height = Math.max(lh, rh) + 1;
// Traverse up tree and balance parent
return node.parent;
}, node);
};
/**
* Performs a left tree rotation on the specified node.
*
* @param {AvlTree.Node} node Pivot node to rotate from.
* @private
*/
AvlTree.prototype.leftRotate_ = function(node) {
// Re-assign parent-child references for the parent of the node being removed
if (node.isLeftChild()) {
node.parent.left = node.right;
node.right.parent = node.parent;
} else if (node.isRightChild()) {
node.parent.right = node.right;
node.right.parent = node.parent;
} else {
this.root_ = node.right;
this.root_.parent = null;
}
// Re-assign parent-child references for the child of the node being removed
var temp = node.right;
node.right = node.right.left;
if (node.right != null) node.right.parent = node;
temp.left = node;
node.parent = temp;
};
/**
* Performs a right tree rotation on the specified node.
*
* @param {AvlTree.Node} node Pivot node to rotate from.
* @private
*/
AvlTree.prototype.rightRotate_ = function(node) {
// Re-assign parent-child references for the parent of the node being removed
if (node.isLeftChild()) {
node.parent.left = node.left;
node.left.parent = node.parent;
} else if (node.isRightChild()) {
node.parent.right = node.left;
node.left.parent = node.parent;
} else {
this.root_ = node.left;
this.root_.parent = null;
}
// Re-assign parent-child references for the child of the node being removed
var temp = node.left;
node.left = node.left.right;
if (node.left != null) node.left.parent = node;
temp.right = node;
node.parent = temp;
};
/**
* Removes the specified node from the tree and ensures the tree still
* maintains the AVL-tree balance.
*
* @param {AvlTree.Node} node The node to be removed.
* @private
*/
AvlTree.prototype.removeNode_ = function(node) {
// Perform normal binary tree node removal, but balance the tree, starting
// from where we removed the node
if (node.left != null || node.right != null) {
var b = null; // Node to begin balance from
var r; // Node to replace the node being removed
if (node.left != null) {
r = this.getMaxNode_(node.left);
if (r != node.left) {
r.parent.right = r.left;
if (r.left) r.left.parent = r.parent;
r.left = node.left;
r.left.parent = r;
b = r.parent;
}
r.parent = node.parent;
r.right = node.right;
if (r.right) r.right.parent = r;
if (node == this.maxNode_) this.maxNode_ = r;
} else {
r = this.getMinNode_(node.right);
if (r != node.right) {
r.parent.left = r.right;
if (r.right) r.right.parent = r.parent;
r.right = node.right;
r.right.parent = r;
b = r.parent;
}
r.parent = node.parent;
r.left = node.left;
if (r.left) r.left.parent = r;
if (node == this.minNode_) this.minNode_ = r;
}
// Update the parent of the node being removed to point to its replace
if (node.isLeftChild()) {
node.parent.left = r;
} else if (node.isRightChild()) {
node.parent.right = r;
} else {
this.root_ = r;
}
// Balance the tree
this.balance_(b ? b : r);
} else {
// If the node is a leaf, remove it and balance starting from its parent
if (node.isLeftChild()) {
this.special = 1;
node.parent.left = null;
if (node == this.minNode_) this.minNode_ = node.parent;
this.balance_(node.parent);
} else if (node.isRightChild()) {
node.parent.right = null;
if (node == this.maxNode_) this.maxNode_ = node.parent;
this.balance_(node.parent);
} else {
this.clear();
}
}
};
/**
* Returns the node with the smallest value in tree, optionally rooted at
* {@code opt_rootNode}.
*
* @param {AvlTree.Node=} opt_rootNode Optional root node.
* @return {AvlTree.Node} The node with the smallest value in
* the tree.
* @private
*/
AvlTree.prototype.getMinNode_ = function(opt_rootNode) {
if (!opt_rootNode) {
return this.minNode_;
}
var minNode = opt_rootNode;
this.traverse_(function(node) {
var retNode = null;
if (node.left) {
minNode = node.left;
retNode = node.left;
}
return retNode; // If null, we'll stop traversing the tree
}, opt_rootNode);
return minNode;
};
/**
* Returns the node with the largest value in tree, optionally rooted at
* opt_rootNode.
*
* @param {AvlTree.Node=} opt_rootNode Optional root node.
* @return {AvlTree.Node} The node with the largest value in
* the tree.
* @private
*/
AvlTree.prototype.getMaxNode_ = function(opt_rootNode) {
if (!opt_rootNode) {
return this.maxNode_;
}
var maxNode = opt_rootNode;
this.traverse_(function(node) {
var retNode = null;
if (node.right) {
maxNode = node.right;
retNode = node.right;
}
return retNode; // If null, we'll stop traversing the tree
}, opt_rootNode);
return maxNode;
};
/**
* Constructs an AVL-Tree node with the specified value. If no parent is
* specified, the node's parent is assumed to be null. The node's height
* defaults to 1 and its children default to null.
*
* @param {*} value Value to store in the node.
* @param {AvlTree.Node=} opt_parent Optional parent node.
* @constructor
*/
AvlTree.Node = function(value, opt_parent) {
/**
* The value stored by the node.
*
* @type {*}
*/
this.value = value;
/**
* The node's parent. Null if the node is the root.
*
* @type {AvlTree.Node}
*/
this.parent = opt_parent ? opt_parent : null;
};
/**
* The node's left child. Null if the node does not have a left child.
*
* @type {AvlTree.Node?}
*/
AvlTree.Node.prototype.left = null;
/**
* The node's right child. Null if the node does not have a right child.
*
* @type {AvlTree.Node?}
*/
AvlTree.Node.prototype.right = null;
/**
* The height of the tree rooted at this node.
*
* @type {number}
*/
AvlTree.Node.prototype.height = 1;
/**
* Returns true iff the specified node has a parent and is the right child of
* its parent.
*
* @return {boolean} Whether the specified node has a parent and is the right
* child of its parent.
*/
AvlTree.Node.prototype.isRightChild = function() {
return !!this.parent && this.parent.right == this;
};
/**
* Returns true iff the specified node has a parent and is the left child of
* its parent.
*
* @return {boolean} Whether the specified node has a parent and is the left
* child of its parent.
*/
AvlTree.Node.prototype.isLeftChild = function() {
return !!this.parent && this.parent.left == this;
};