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/**
* Splay Tree.
*
* @example
* var STree = require('path-to-algorithms/src/data-structures'+
* '/splay-tree');
* var sTree = new STree.SplayTree();
* sTree.insert(10);
* sTree.insert(5);
* sTree.insert(15);
* sTree.insert(7);
* sTree.insert(12);
* sTree.search(10);
* console.log(sTree._root);
* sTree.remove(10);
* console.log(sTree._root);
* sTree.search(15);
* console.log(sTree._root);
*
* @module data-structures/splay-tree
*/
(function (exports) {
'use strict';
/**
* Node of the tree.
*
* @public
* @constructor
* @param {Number|String} value Value of the node.
* @param {Node} left Left sibling.
* @param {Node} right Right sibling.
* @param {Node} parent Parent of the node.
*/
exports.Node = function (value, left, right, parent) {
/**
* @member {Number|String}
*/
this.value = value;
this._left = left;
this._right = right;
this._parent = parent;
};
/**
* Splay tree.
* {@link http://en.wikipedia.org/wiki/Splay_tree}
* @public
* @constructor
*/
exports.SplayTree = function () {
this._root = null;
};
/**
* Splays a node to the root.<br><br>
*
* @private
* @method
* @param {Node} node Node to be splayed.
* @returns {Node} The same node from the parameter, post splayed.
*/
exports.SplayTree.prototype._splay = function (node) {
while (this._root !== node) {
var hasParent = node._parent !== null;
var hasGrandparent = (hasParent && node._parent._parent !== null);
if (hasParent && hasGrandparent) {
var isLeftChild = node._parent._left === node;
var isParentLeftChild = node._parent._parent._left === node._parent;
if (
(isLeftChild && isParentLeftChild) ||
(!isLeftChild && !isParentLeftChild)
) {
node = this._zigZig(node);
} else {
node = this._zigZag(node);
}
} else {
node = this._zig(node);
}
}
return node;
};
/**
* Performs a zig-zig splay pattern<br><br>
*
* @private
* @method
* @param {Node} node Node to be zig-zig'd.
* @returns {Node} The same node from the parameter, post splayed.
*/
exports.SplayTree.prototype._zigZig = function (node) {
var parent = node._parent;
var grandParent = node._parent._parent;
var greatGrandParent = grandParent._parent !== undefined ?
grandParent._parent : null;
var orientation = (parent._right === node) ? '_right' : '_left';
var oppositeOrientation = (orientation === '_left') ? '_right' : '_left';
var grandParentOrientation = (greatGrandParent !== null &&
greatGrandParent._left === grandParent) ? '_left' : '_right';
// Fix grandparent & great if it exists/not root
if (this._root === grandParent) {
this._root = node;
} else {
greatGrandParent[grandParentOrientation] = node;
}
grandParent._parent = parent;
// Fix grandparent subtree
grandParent[orientation] = parent[oppositeOrientation];
if (grandParent[orientation] !== null) {
grandParent[orientation]._parent = grandParent;
}
// Fix Parent
parent[oppositeOrientation] = grandParent;
parent[orientation] = node[oppositeOrientation];
if (parent[orientation] !== null) {
parent[orientation]._parent = parent;
}
parent._parent = node;
// Fix Curr Node
node[oppositeOrientation] = parent;
if (node === this._root) {
node._parent = null;
} else if (greatGrandParent !== null) {
node._parent = greatGrandParent;
}
return node;
};
/**
* Performs a zig-zag splay pattern<br><br>
*
* @private
* @method
* @param {Node} node Node to be zig-zag'd.
* @returns {Node} The same node from the parameter, post splayed.
*/
exports.SplayTree.prototype._zigZag = function (node) {
var parent = node._parent;
var grandParent = parent._parent;
var greatGrandParent = grandParent._parent !== undefined ?
grandParent._parent : null;
var orientation = (parent._left === node) ? '_left' : '_right';
var oppositeOrientation = (orientation === '_right') ? '_left' : '_right';
var grandParentOrientation = (greatGrandParent !== null &&
greatGrandParent._left === grandParent) ? '_left' : '_right';
// Fix GrandParent
if (this._root === grandParent) {
this._root = node;
} else {
greatGrandParent[grandParentOrientation] = node;
}
grandParent._parent = node;
// Fix GrandParent subtree
grandParent[oppositeOrientation] = node[orientation];
if (grandParent[oppositeOrientation] !== null) {
grandParent[oppositeOrientation]._parent = grandParent;
}
// Fix Parent
parent[orientation] = node[oppositeOrientation];
if (parent[orientation] !== null) {
parent[orientation]._parent = parent;
}
parent._parent = node;
// Fix Curr Node
node[orientation] = grandParent;
node[oppositeOrientation] = parent;
if (this._root === node) {
node._parent = null;
} else if (greatGrandParent !== null) {
node._parent = greatGrandParent;
}
return node;
};
/**
* Performs a zig splay pattern<br><br>
*
* @private
* @method
* @param {Node} node Node to be zig'd.
* @returns {Node} The same node from the parameter, post splayed.
*/
exports.SplayTree.prototype._zig = function (node) {
var parent = node._parent;
var orientation = (parent._right === node) ? '_right' : '_left';
var oppositeOrientation = (orientation === '_right') ? '_left' : '_right';
if (this._root === parent) {
this._root = node;
}
// Fix Parent
parent[orientation] = node[oppositeOrientation];
if (parent[orientation] !== null) {
parent[orientation]._parent = parent;
}
parent._parent = node;
// Fix Curr Node
node[oppositeOrientation] = parent;
node._parent = null;
return node;
};
/**
* Inserts a node into the splay tree.<br><br>
* Time complexity: O(log N) in the average case
* and amortized O(log n) in the worst case.
*
* @public
* @method
* @param {Number|String} value Node value.
* @param {Node} current Current node.
*/
exports.SplayTree.prototype.insert = function (value, current) {
if (this._root === null) {
this._root = new exports.Node(value, null, null, null);
return;
}
var insertKey;
current = current || this._root;
if (current.value > value) {
insertKey = '_left';
} else {
insertKey = '_right';
}
if (!current[insertKey]) {
current[insertKey] = new exports.Node(value, null, null, current);
this._splay(current[insertKey]);
} else {
this.insert(value, current[insertKey]);
}
};
/**
* In-order traversal from the given node.
*
* @private
* @param {Node} current Node from which to start the traversal.
* @param {Function} callback Callback which
* will be called for each traversed node.
*/
exports.SplayTree.prototype._inorder = function (current, callback) {
if (!current) {
return;
}
this._inorder(current._left, callback);
if (typeof callback === 'function') {
callback(current);
}
this._inorder(current._right, callback);
};
/**
* In-order traversal of the whole Splay Tree.
*
* @public
* @method
* @param {Function} callback Callback which will be
* called for each traversed node.
*/
exports.SplayTree.prototype.inorder = function (callback) {
return this._inorder(this._root, callback);
};
/**
* Post-order traversal from given node.
*
* @private
* @param {Node} current Node from which to start the traversal.
* @param {Function} callback Callback which will
* be called for each traversed node
*/
exports.SplayTree.prototype._postorder = function (current, callback) {
if (!current) {
return;
}
if (typeof callback === 'function') {
callback(current);
}
this._postorder(current._left, callback);
this._postorder(current._right, callback);
};
/**
* Post-order traversal of the whole tree.
*
* @public
* @param {Function} callback Callback which
* will be called for each traversed node.
*/
exports.SplayTree.prototype.postorder = function (callback) {
return this._postorder(this._root, callback);
};
/**
* Pre-order traversal of the tree from given node.
*
* @private
* @param {Node} current Node from which to start the traversal.
* @param {Function} callback Callback which
* will be called for each traversed node.
*/
exports.SplayTree.prototype._preorder = function (current, callback) {
if (!current) {
return;
}
if (typeof callback === 'function') {
callback(current);
}
this._preorder(current._left, callback);
this._preorder(current._right, callback);
};
/**
* Pre-order preorder traversal of the whole tree.
*
* @public
* @param {Function} callback Callback which will
* be called for each traversed node.
*/
exports.SplayTree.prototype.preorder = function (callback) {
return this._preorder(this._root, callback);
};
/**
* Finds a node by it's value.<br><br>
* Average time complexity: O(log N).
*
* @public
* @param {Number|String} value of the node which should be found.
*/
exports.SplayTree.prototype.search = function (value) {
var node = this._search(value, this._root);
return this._splay(node);
};
/**
* Finds a node by it's value.<br><br>
* Average time complexity: O(log N).
*
* @public
* @param {Number|String} value of the node which should be found.
*/
exports.SplayTree.prototype._splaylessSearch = function (value) {
return this._search(value, this._root);
};
/**
* Finds a node by it's value in a given sub-tree.
* Average time complexity: O(log N).
*
* @private
* @param {Number|String} value of the node which should be found.
* @param {Node} current node to be checked.
*/
exports.SplayTree.prototype._search = function (value, current) {
if (!current) {
return null;
}
if (current.value === value) {
return current;
}
if (current.value > value) {
return this._search(value, current._left);
}
if (current.value < value) {
return this._search(value, current._right);
}
};
/**
* Replaces given child with new one, for given parent.
*
* @private
* @param {Node} parent Parent node.
* @param {Node} oldChild Child to be replaced.
* @param {Node} newChild Child replacement.
*/
exports.SplayTree.prototype._replaceChild =
function (parent, oldChild, newChild) {
if (!parent) {
this._root = newChild;
this._root._parent = null;
} else {
if (parent._left === oldChild) {
parent._left = newChild;
} else {
parent._right = newChild;
}
if (newChild) {
newChild._parent = parent;
}
}
};
/**
* Removes node with given value from the tree. <br><br>
* Average runtime complexity: O(log N).
*
* @public
* @param {Number|String} value Value to be removed
* @returns {Boolean} True/false depending
* on whether the given node is removed.
*/
exports.SplayTree.prototype.remove = function (value) {
var node = this._splaylessSearch(value);
if (!node) {
return false;
}
if (node._left && node._right) {
var min = this._findMin(node._right);
var temp = node.value;
node.value = min.value;
min.value = temp;
return this.remove(min);
} else {
if (node._parent !== null) {
if (node._left) {
this._replaceChild(node._parent, node, node._left);
} else if (node._right) {
this._replaceChild(node._parent, node, node._right);
} else {
this._replaceChild(node._parent, node, null);
}
this._splay(node._parent);
} else {
this._root = null;
}
return true;
}
};
/**
* Finds the node with minimum value in given sub-tree.
*
* @private
* @param {Node} node Root of the sub-tree.
* @param {Number|String} current Current minimum value of the sub-tree.
* @returns {Node} Node with the minimum value in the sub-tree.
*/
exports.SplayTree.prototype._findMin = function (node, current) {
current = current || {
value: Infinity
};
if (!node) {
return current;
}
if (current.value > node.value) {
current = node;
}
return this._findMin(node._left, current);
};
exports.SplayTree.prototype._isBalanced = function (current) {
if (!current) {
return true;
}
return this._isBalanced(current._left) &&
this._isBalanced(current._right) &&
Math.abs(this._getHeight(current._left) -
this._getHeight(current._right)) <= 1;
};
/**
* Returns whether the Splay Tree is balanced.
*
* @public
* @returns {Boolean} Whether the tree is balanced or not.
*/
exports.SplayTree.prototype.isBalanced = function () {
return this._isBalanced(this._root);
};
/**
* Finds the diameter of the Splay Tree.
*
* @public
* @returns {Number} The longest path in the tree.
*/
exports.SplayTree.prototype.getDiameter = function () {
var getDiameter = function (root) {
if (!root) {
return 0;
}
var leftHeight = this._getHeight(root._left);
var rightHeight = this._getHeight(root._right);
var path = leftHeight + rightHeight + 1;
return Math.max(path, getDiameter(root._left), getDiameter(root._right));
}.bind(this);
return getDiameter(this._root);
};
/**
* Returns the height of the tree.
*
* @public
* @returns {Number} The height of the tree.
*/
exports.SplayTree.prototype.getHeight = function () {
return this._getHeight(this._root);
};
/**
* Recursive worker function for getHeight()
*
* @public
* @param {Node} node The node of the current recursive frame.
* @returns {Number} The height of the tree.
*/
exports.SplayTree.prototype._getHeight = function (node) {
if (!node) {
return 0;
}
return 1 + Math.max(this._getHeight(node._left),
this._getHeight(node._right));
};
/**
* Finds the lowest common ancestor of two nodes.
*
* @public
* @returns {Node} The lowest common ancestor of the two nodes or null.
*/
exports.SplayTree.prototype.lowestCommonAncestor =
function (firstNode, secondNode) {
return this._lowestCommonAncestor(firstNode, secondNode, this._root);
};
/**
* Obtains the lowest common ancestor for the given nodes.
*
* @private
* @param {Node} firstNode First node to be considered when checking
* for ancestor.
* @param {Node} secondNode Second node to be considered when checking
* for ancestor.
* @param {Node} current Current node.
* @returns {Node} The lowest common ancestor of the two nodes or null.
*/
exports.SplayTree.prototype._lowestCommonAncestor =
function (firstNode, secondNode, current) {
var firstNodeInLeft = this._existsInSubtree(firstNode, current._left);
var secondNodeInLeft = this._existsInSubtree(secondNode, current._left);
var firstNodeInRight = this._existsInSubtree(firstNode, current._right);
var secondNodeInRight = this._existsInSubtree(secondNode, current._right);
if ((firstNodeInLeft && secondNodeInRight) ||
(firstNodeInRight && secondNodeInLeft)) {
return current;
}
if (secondNodeInLeft && firstNodeInLeft) {
return this._lowestCommonAncestor(firstNode, secondNode, current._left);
}
if (secondNodeInRight && secondNodeInLeft) {
return this._lowestCommonAncestor(firstNode, secondNode,
current._right);
}
return null;
};
/**
* Checks if a given node exists in a subtree.
*
* @private
* @param {Node} node Node to check for.
* @param {Node} root Root node of a given subtree.
* @returns {Node} The lowest common ancestor of the two nodes or null.
*/
exports.SplayTree.prototype._existsInSubtree = function (node, root) {
if (!root) {
return false;
}
if (node === root.value) {
return true;
}
return this._existsInSubtree(node, root._left) ||
this._existsInSubtree(node, root._right);
};
})(typeof window === 'undefined' ? module.exports : window);