544 lines
14 KiB
JavaScript
544 lines
14 KiB
JavaScript
/**
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* Simple binary search tree
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*/
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var customUtils = require('./customUtils');
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/**
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* Constructor
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* @param {Object} options Optional
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* @param {Boolean} options.unique Whether to enforce a 'unique' constraint on the key or not
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* @param {Key} options.key Initialize this BST's key with key
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* @param {Value} options.value Initialize this BST's data with [value]
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* @param {Function} options.compareKeys Initialize this BST's compareKeys
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*/
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function BinarySearchTree (options) {
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options = options || {};
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this.left = null;
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this.right = null;
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this.parent = options.parent !== undefined ? options.parent : null;
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if (options.hasOwnProperty('key')) { this.key = options.key; }
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this.data = options.hasOwnProperty('value') ? [options.value] : [];
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this.unique = options.unique || false;
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this.compareKeys = options.compareKeys || customUtils.defaultCompareKeysFunction;
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this.checkValueEquality = options.checkValueEquality || customUtils.defaultCheckValueEquality;
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}
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// ================================
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// Methods used to test the tree
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// ================================
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/**
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* Get the descendant with max key
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*/
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BinarySearchTree.prototype.getMaxKeyDescendant = function () {
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if (this.right) {
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return this.right.getMaxKeyDescendant();
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} else {
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return this;
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}
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};
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/**
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* Get the maximum key
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*/
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BinarySearchTree.prototype.getMaxKey = function () {
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return this.getMaxKeyDescendant().key;
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};
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/**
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* Get the descendant with min key
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*/
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BinarySearchTree.prototype.getMinKeyDescendant = function () {
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if (this.left) {
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return this.left.getMinKeyDescendant()
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} else {
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return this;
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}
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};
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/**
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* Get the minimum key
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*/
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BinarySearchTree.prototype.getMinKey = function () {
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return this.getMinKeyDescendant().key;
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};
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/**
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* Check that all nodes (incl. leaves) fullfil condition given by fn
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* test is a function passed every (key, data) and which throws if the condition is not met
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*/
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BinarySearchTree.prototype.checkAllNodesFullfillCondition = function (test) {
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if (!this.hasOwnProperty('key')) { return; }
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test(this.key, this.data);
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if (this.left) { this.left.checkAllNodesFullfillCondition(test); }
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if (this.right) { this.right.checkAllNodesFullfillCondition(test); }
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};
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/**
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* Check that the core BST properties on node ordering are verified
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* Throw if they aren't
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*/
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BinarySearchTree.prototype.checkNodeOrdering = function () {
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var self = this;
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if (!this.hasOwnProperty('key')) { return; }
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if (this.left) {
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this.left.checkAllNodesFullfillCondition(function (k) {
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if (self.compareKeys(k, self.key) >= 0) {
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throw new Error('Tree with root ' + self.key + ' is not a binary search tree');
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}
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});
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this.left.checkNodeOrdering();
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}
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if (this.right) {
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this.right.checkAllNodesFullfillCondition(function (k) {
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if (self.compareKeys(k, self.key) <= 0) {
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throw new Error('Tree with root ' + self.key + ' is not a binary search tree');
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}
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});
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this.right.checkNodeOrdering();
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}
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};
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/**
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* Check that all pointers are coherent in this tree
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*/
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BinarySearchTree.prototype.checkInternalPointers = function () {
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if (this.left) {
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if (this.left.parent !== this) { throw new Error('Parent pointer broken for key ' + this.key); }
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this.left.checkInternalPointers();
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}
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if (this.right) {
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if (this.right.parent !== this) { throw new Error('Parent pointer broken for key ' + this.key); }
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this.right.checkInternalPointers();
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}
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};
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/**
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* Check that a tree is a BST as defined here (node ordering and pointer references)
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*/
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BinarySearchTree.prototype.checkIsBST = function () {
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this.checkNodeOrdering();
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this.checkInternalPointers();
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if (this.parent) { throw new Error("The root shouldn't have a parent"); }
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};
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/**
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* Get number of keys inserted
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*/
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BinarySearchTree.prototype.getNumberOfKeys = function () {
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var res;
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if (!this.hasOwnProperty('key')) { return 0; }
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res = 1;
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if (this.left) { res += this.left.getNumberOfKeys(); }
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if (this.right) { res += this.right.getNumberOfKeys(); }
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return res;
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};
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// ============================================
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// Methods used to actually work on the tree
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// ============================================
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/**
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* Create a BST similar (i.e. same options except for key and value) to the current one
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* Use the same constructor (i.e. BinarySearchTree, AVLTree etc)
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* @param {Object} options see constructor
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*/
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BinarySearchTree.prototype.createSimilar = function (options) {
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options = options || {};
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options.unique = this.unique;
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options.compareKeys = this.compareKeys;
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options.checkValueEquality = this.checkValueEquality;
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return new this.constructor(options);
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};
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/**
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* Create the left child of this BST and return it
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*/
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BinarySearchTree.prototype.createLeftChild = function (options) {
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var leftChild = this.createSimilar(options);
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leftChild.parent = this;
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this.left = leftChild;
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return leftChild;
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};
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/**
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* Create the right child of this BST and return it
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*/
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BinarySearchTree.prototype.createRightChild = function (options) {
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var rightChild = this.createSimilar(options);
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rightChild.parent = this;
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this.right = rightChild;
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return rightChild;
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};
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/**
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* Insert a new element
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*/
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BinarySearchTree.prototype.insert = function (key, value) {
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// Empty tree, insert as root
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if (!this.hasOwnProperty('key')) {
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this.key = key;
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this.data.push(value);
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return;
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}
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// Same key as root
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if (this.compareKeys(this.key, key) === 0) {
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if (this.unique) {
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var err = new Error("Can't insert key " + key + ", it violates the unique constraint");
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err.key = key;
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err.errorType = 'uniqueViolated';
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throw err;
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} else {
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this.data.push(value);
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}
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return;
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}
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if (this.compareKeys(key, this.key) < 0) {
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// Insert in left subtree
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if (this.left) {
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this.left.insert(key, value);
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} else {
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this.createLeftChild({ key: key, value: value });
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}
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} else {
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// Insert in right subtree
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if (this.right) {
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this.right.insert(key, value);
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} else {
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this.createRightChild({ key: key, value: value });
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}
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}
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};
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/**
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* Search for all data corresponding to a key
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*/
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BinarySearchTree.prototype.search = function (key) {
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if (!this.hasOwnProperty('key')) { return []; }
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if (this.compareKeys(this.key, key) === 0) { return this.data; }
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if (this.compareKeys(key, this.key) < 0) {
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if (this.left) {
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return this.left.search(key);
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} else {
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return [];
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}
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} else {
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if (this.right) {
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return this.right.search(key);
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} else {
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return [];
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}
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}
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};
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/**
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* Return a function that tells whether a given key matches a lower bound
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*/
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BinarySearchTree.prototype.getLowerBoundMatcher = function (query) {
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var self = this;
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// No lower bound
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if (!query.hasOwnProperty('$gt') && !query.hasOwnProperty('$gte')) {
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return function () { return true; };
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}
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if (query.hasOwnProperty('$gt') && query.hasOwnProperty('$gte')) {
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if (self.compareKeys(query.$gte, query.$gt) === 0) {
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return function (key) { return self.compareKeys(key, query.$gt) > 0; };
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}
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if (self.compareKeys(query.$gte, query.$gt) > 0) {
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return function (key) { return self.compareKeys(key, query.$gte) >= 0; };
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} else {
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return function (key) { return self.compareKeys(key, query.$gt) > 0; };
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}
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}
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if (query.hasOwnProperty('$gt')) {
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return function (key) { return self.compareKeys(key, query.$gt) > 0; };
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} else {
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return function (key) { return self.compareKeys(key, query.$gte) >= 0; };
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}
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};
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/**
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* Return a function that tells whether a given key matches an upper bound
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*/
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BinarySearchTree.prototype.getUpperBoundMatcher = function (query) {
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var self = this;
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// No lower bound
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if (!query.hasOwnProperty('$lt') && !query.hasOwnProperty('$lte')) {
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return function () { return true; };
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}
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if (query.hasOwnProperty('$lt') && query.hasOwnProperty('$lte')) {
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if (self.compareKeys(query.$lte, query.$lt) === 0) {
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return function (key) { return self.compareKeys(key, query.$lt) < 0; };
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}
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if (self.compareKeys(query.$lte, query.$lt) < 0) {
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return function (key) { return self.compareKeys(key, query.$lte) <= 0; };
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} else {
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return function (key) { return self.compareKeys(key, query.$lt) < 0; };
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}
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}
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if (query.hasOwnProperty('$lt')) {
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return function (key) { return self.compareKeys(key, query.$lt) < 0; };
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} else {
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return function (key) { return self.compareKeys(key, query.$lte) <= 0; };
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}
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};
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// Append all elements in toAppend to array
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function append (array, toAppend) {
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var i;
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for (i = 0; i < toAppend.length; i += 1) {
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array.push(toAppend[i]);
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}
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}
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/**
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* Get all data for a key between bounds
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* Return it in key order
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* @param {Object} query Mongo-style query where keys are $lt, $lte, $gt or $gte (other keys are not considered)
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* @param {Functions} lbm/ubm matching functions calculated at the first recursive step
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*/
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BinarySearchTree.prototype.betweenBounds = function (query, lbm, ubm) {
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var res = [];
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if (!this.hasOwnProperty('key')) { return []; } // Empty tree
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lbm = lbm || this.getLowerBoundMatcher(query);
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ubm = ubm || this.getUpperBoundMatcher(query);
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if (lbm(this.key) && this.left) { append(res, this.left.betweenBounds(query, lbm, ubm)); }
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if (lbm(this.key) && ubm(this.key)) { append(res, this.data); }
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if (ubm(this.key) && this.right) { append(res, this.right.betweenBounds(query, lbm, ubm)); }
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return res;
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};
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/**
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* Delete the current node if it is a leaf
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* Return true if it was deleted
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*/
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BinarySearchTree.prototype.deleteIfLeaf = function () {
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if (this.left || this.right) { return false; }
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// The leaf is itself a root
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if (!this.parent) {
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delete this.key;
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this.data = [];
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return true;
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}
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if (this.parent.left === this) {
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this.parent.left = null;
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} else {
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this.parent.right = null;
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}
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return true;
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};
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/**
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* Delete the current node if it has only one child
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* Return true if it was deleted
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*/
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BinarySearchTree.prototype.deleteIfOnlyOneChild = function () {
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var child;
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if (this.left && !this.right) { child = this.left; }
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if (!this.left && this.right) { child = this.right; }
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if (!child) { return false; }
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// Root
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if (!this.parent) {
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this.key = child.key;
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this.data = child.data;
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this.left = null;
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if (child.left) {
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this.left = child.left;
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child.left.parent = this;
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}
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this.right = null;
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if (child.right) {
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this.right = child.right;
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child.right.parent = this;
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}
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return true;
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}
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if (this.parent.left === this) {
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this.parent.left = child;
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child.parent = this.parent;
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} else {
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this.parent.right = child;
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child.parent = this.parent;
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}
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return true;
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};
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/**
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* Delete a key or just a value
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* @param {Key} key
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* @param {Value} value Optional. If not set, the whole key is deleted. If set, only this value is deleted
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*/
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BinarySearchTree.prototype.delete = function (key, value) {
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var newData = [], replaceWith
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, self = this
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;
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if (!this.hasOwnProperty('key')) { return; }
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if (this.compareKeys(key, this.key) < 0) {
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if (this.left) { this.left.delete(key, value); }
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return;
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}
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if (this.compareKeys(key, this.key) > 0) {
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if (this.right) { this.right.delete(key, value); }
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return;
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}
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if (!this.compareKeys(key, this.key) === 0) { return; }
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// Delete only a value
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if (this.data.length > 1 && value !== undefined) {
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this.data.forEach(function (d) {
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if (!self.checkValueEquality(d, value)) { newData.push(d); }
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});
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self.data = newData;
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return;
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}
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// Delete the whole node
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if (this.deleteIfLeaf()) {
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return;
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}
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if (this.deleteIfOnlyOneChild()) {
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return;
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}
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// We are in the case where the node to delete has two children
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if (Math.random() >= 0.5) { // Randomize replacement to avoid unbalancing the tree too much
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// Use the in-order predecessor
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replaceWith = this.left.getMaxKeyDescendant();
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this.key = replaceWith.key;
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this.data = replaceWith.data;
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if (this === replaceWith.parent) { // Special case
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this.left = replaceWith.left;
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if (replaceWith.left) { replaceWith.left.parent = replaceWith.parent; }
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} else {
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replaceWith.parent.right = replaceWith.left;
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if (replaceWith.left) { replaceWith.left.parent = replaceWith.parent; }
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}
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} else {
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// Use the in-order successor
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replaceWith = this.right.getMinKeyDescendant();
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this.key = replaceWith.key;
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this.data = replaceWith.data;
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if (this === replaceWith.parent) { // Special case
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this.right = replaceWith.right;
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if (replaceWith.right) { replaceWith.right.parent = replaceWith.parent; }
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} else {
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replaceWith.parent.left = replaceWith.right;
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if (replaceWith.right) { replaceWith.right.parent = replaceWith.parent; }
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}
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}
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};
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/**
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* Execute a function on every node of the tree, in key order
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* @param {Function} fn Signature: node. Most useful will probably be node.key and node.data
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*/
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BinarySearchTree.prototype.executeOnEveryNode = function (fn) {
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if (this.left) { this.left.executeOnEveryNode(fn); }
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fn(this);
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if (this.right) { this.right.executeOnEveryNode(fn); }
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};
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/**
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* Pretty print a tree
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* @param {Boolean} printData To print the nodes' data along with the key
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*/
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BinarySearchTree.prototype.prettyPrint = function (printData, spacing) {
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spacing = spacing || "";
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console.log(spacing + "* " + this.key);
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if (printData) { console.log(spacing + "* " + this.data); }
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if (!this.left && !this.right) { return; }
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if (this.left) {
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this.left.prettyPrint(printData, spacing + " ");
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} else {
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console.log(spacing + " *");
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}
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if (this.right) {
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this.right.prettyPrint(printData, spacing + " ");
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} else {
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console.log(spacing + " *");
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}
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};
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// Interface
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module.exports = BinarySearchTree;
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