377 lines
13 KiB
Java
377 lines
13 KiB
Java
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package com.jwetherell.algorithms.data_structures;
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import java.util.ArrayList;
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import java.util.List;
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/**
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* An AVL tree is a self-balancing binary search tree, and it was the first such
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* data structure to be invented. In an AVL tree, the heights of the two child
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* subtrees of any node differ by at most one. AVL trees are often compared with
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* red-black trees because they support the same set of operations and because
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* red-black trees also take O(log n) time for the basic operations. Because AVL
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* trees are more rigidly balanced, they are faster than red-black trees for
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* lookup intensive applications. However, red-black trees are faster for
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* insertion and removal.
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*
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* http://en.wikipedia.org/wiki/AVL_tree
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*
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* @author Justin Wetherell <phishman3579@gmail.com>
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*/
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public class AVLTree<T extends Comparable<T>> extends BinarySearchTree<T> {
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private enum Balance {
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LEFT_LEFT, LEFT_RIGHT, RIGHT_LEFT, RIGHT_RIGHT
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}
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/**
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* Default constructor.
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*/
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public AVLTree() {
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this.creator = new BinarySearchTree.INodeCreator<T>() {
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/**
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* {@inheritDoc}
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*/
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@Override
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public BinarySearchTree.Node<T> createNewNode(BinarySearchTree.Node<T> parent, T id) {
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return (new AVLNode<T>(parent, id));
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}
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};
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}
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/**
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* Constructor with external Node creator.
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*/
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public AVLTree(INodeCreator<T> creator) {
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super(creator);
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}
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/**
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* {@inheritDoc}
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*/
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@Override
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protected Node<T> addValue(T id) {
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Node<T> nodeToReturn = super.addValue(id);
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AVLNode<T> nodeAdded = (AVLNode<T>) nodeToReturn;
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nodeAdded.updateHeight();
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balanceAfterInsert(nodeAdded);
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nodeAdded = (AVLNode<T>) nodeAdded.parent;
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while (nodeAdded != null) {
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int h1 = nodeAdded.height;
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nodeAdded.updateHeight();
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balanceAfterInsert(nodeAdded);
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// If height before and after balance is the same, stop going up the tree
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int h2 = nodeAdded.height;
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if (h1==h2)
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break;
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nodeAdded = (AVLNode<T>) nodeAdded.parent;
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}
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return nodeToReturn;
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}
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/**
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* Balance the tree according to the AVL post-insert algorithm.
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*
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* @param node
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* Root of tree to balance.
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*/
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private void balanceAfterInsert(AVLNode<T> node) {
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int balanceFactor = node.getBalanceFactor();
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if (balanceFactor > 1 || balanceFactor < -1) {
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AVLNode<T> child = null;
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Balance balance = null;
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if (balanceFactor < 0) {
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child = (AVLNode<T>) node.lesser;
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balanceFactor = child.getBalanceFactor();
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if (balanceFactor < 0)
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balance = Balance.LEFT_LEFT;
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else
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balance = Balance.LEFT_RIGHT;
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} else {
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child = (AVLNode<T>) node.greater;
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balanceFactor = child.getBalanceFactor();
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if (balanceFactor < 0)
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balance = Balance.RIGHT_LEFT;
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else
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balance = Balance.RIGHT_RIGHT;
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}
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if (balance == Balance.LEFT_RIGHT) {
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// Left-Right (Left rotation, right rotation)
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rotateLeft(child);
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rotateRight(node);
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} else if (balance == Balance.RIGHT_LEFT) {
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// Right-Left (Right rotation, left rotation)
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rotateRight(child);
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rotateLeft(node);
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} else if (balance == Balance.LEFT_LEFT) {
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// Left-Left (Right rotation)
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rotateRight(node);
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} else {
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// Right-Right (Left rotation)
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rotateLeft(node);
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}
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child.updateHeight();
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node.updateHeight();
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}
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}
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/**
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* {@inheritDoc}
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*/
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@Override
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protected Node<T> removeValue(T value) {
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// Find node to remove
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Node<T> nodeToRemoved = this.getNode(value);
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if (nodeToRemoved==null)
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return null;
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// Find the replacement node
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Node<T> replacementNode = this.getReplacementNode(nodeToRemoved);
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// Find the parent of the replacement node to re-factor the height/balance of the tree
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AVLNode<T> nodeToRefactor = null;
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if (replacementNode != null)
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nodeToRefactor = (AVLNode<T>) replacementNode.parent;
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if (nodeToRefactor == null)
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nodeToRefactor = (AVLNode<T>) nodeToRemoved.parent;
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if (nodeToRefactor != null && nodeToRefactor == nodeToRemoved)
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nodeToRefactor = (AVLNode<T>) replacementNode;
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// Replace the node
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replaceNodeWithNode(nodeToRemoved, replacementNode);
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// Re-balance the tree all the way up the tree
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while (nodeToRefactor != null) {
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nodeToRefactor.updateHeight();
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balanceAfterDelete(nodeToRefactor);
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nodeToRefactor = (AVLNode<T>) nodeToRefactor.parent;
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}
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return nodeToRemoved;
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}
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/**
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* Balance the tree according to the AVL post-delete algorithm.
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*
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* @param node
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* Root of tree to balance.
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*/
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private void balanceAfterDelete(AVLNode<T> node) {
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int balanceFactor = node.getBalanceFactor();
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if (balanceFactor == -2 || balanceFactor == 2) {
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if (balanceFactor == -2) {
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AVLNode<T> ll = (AVLNode<T>) node.lesser.lesser;
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int lesser = (ll != null) ? ll.height : 0;
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AVLNode<T> lr = (AVLNode<T>) node.lesser.greater;
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int greater = (lr != null) ? lr.height : 0;
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if (lesser >= greater) {
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rotateRight(node);
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node.updateHeight();
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if (node.parent != null)
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((AVLNode<T>) node.parent).updateHeight();
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} else {
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rotateLeft(node.lesser);
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rotateRight(node);
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AVLNode<T> p = (AVLNode<T>) node.parent;
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if (p.lesser != null)
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((AVLNode<T>) p.lesser).updateHeight();
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if (p.greater != null)
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((AVLNode<T>) p.greater).updateHeight();
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p.updateHeight();
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}
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} else if (balanceFactor == 2) {
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AVLNode<T> rr = (AVLNode<T>) node.greater.greater;
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int greater = (rr != null) ? rr.height : 0;
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AVLNode<T> rl = (AVLNode<T>) node.greater.lesser;
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int lesser = (rl != null) ? rl.height : 0;
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if (greater >= lesser) {
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rotateLeft(node);
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node.updateHeight();
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if (node.parent != null)
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((AVLNode<T>) node.parent).updateHeight();
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} else {
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rotateRight(node.greater);
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rotateLeft(node);
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AVLNode<T> p = (AVLNode<T>) node.parent;
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if (p.lesser != null)
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((AVLNode<T>) p.lesser).updateHeight();
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if (p.greater != null)
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((AVLNode<T>) p.greater).updateHeight();
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p.updateHeight();
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}
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}
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}
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}
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/**
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* {@inheritDoc}
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*/
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@Override
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protected boolean validateNode(Node<T> node) {
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boolean bst = super.validateNode(node);
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if (!bst)
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return false;
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AVLNode<T> avlNode = (AVLNode<T>) node;
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int balanceFactor = avlNode.getBalanceFactor();
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if (balanceFactor > 1 || balanceFactor < -1) {
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return false;
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}
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if (avlNode.isLeaf()) {
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if (avlNode.height != 1)
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return false;
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} else {
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AVLNode<T> avlNodeLesser = (AVLNode<T>) avlNode.lesser;
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int lesserHeight = 1;
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if (avlNodeLesser != null)
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lesserHeight = avlNodeLesser.height;
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AVLNode<T> avlNodeGreater = (AVLNode<T>) avlNode.greater;
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int greaterHeight = 1;
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if (avlNodeGreater != null)
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greaterHeight = avlNodeGreater.height;
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if (avlNode.height == (lesserHeight + 1) || avlNode.height == (greaterHeight + 1))
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return true;
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return false;
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}
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return true;
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}
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/**
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* {@inheritDoc}
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*/
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@Override
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public String toString() {
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return AVLTreePrinter.getString(this);
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}
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protected static class AVLNode<T extends Comparable<T>> extends Node<T> {
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protected int height = 1;
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/**
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* Constructor for an AVL node
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*
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* @param parent
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* Parent of the node in the tree, can be NULL.
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* @param value
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* Value of the node in the tree.
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*/
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protected AVLNode(Node<T> parent, T value) {
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super(parent, value);
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}
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/**
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* Determines is this node is a leaf (has no children).
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*
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* @return True if this node is a leaf.
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*/
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protected boolean isLeaf() {
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return ((lesser == null) && (greater == null));
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}
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/**
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* Updates the height of this node based on it's children.
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*/
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protected int updateHeight() {
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int lesserHeight = 0;
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if (lesser != null) {
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AVLNode<T> lesserAVLNode = (AVLNode<T>) lesser;
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lesserHeight = lesserAVLNode.height;
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}
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int greaterHeight = 0;
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if (greater != null) {
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AVLNode<T> greaterAVLNode = (AVLNode<T>) greater;
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greaterHeight = greaterAVLNode.height;
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}
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if (lesserHeight > greaterHeight) {
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height = lesserHeight + 1;
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} else {
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height = greaterHeight + 1;
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}
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return height;
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}
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/**
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* Get the balance factor for this node.
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*
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* @return An integer representing the balance factor for this node. It
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* will be negative if the lesser branch is longer than the
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* greater branch.
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*/
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protected int getBalanceFactor() {
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int lesserHeight = 0;
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if (lesser != null) {
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AVLNode<T> lesserAVLNode = (AVLNode<T>) lesser;
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lesserHeight = lesserAVLNode.height;
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}
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int greaterHeight = 0;
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if (greater != null) {
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AVLNode<T> greaterAVLNode = (AVLNode<T>) greater;
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greaterHeight = greaterAVLNode.height;
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}
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return greaterHeight - lesserHeight;
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}
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/**
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* {@inheritDoc}
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*/
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@Override
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public String toString() {
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return "value=" + id + " height=" + height + " parent=" + ((parent != null) ? parent.id : "NULL")
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+ " lesser=" + ((lesser != null) ? lesser.id : "NULL") + " greater="
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+ ((greater != null) ? greater.id : "NULL");
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}
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}
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protected static class AVLTreePrinter {
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public static <T extends Comparable<T>> String getString(AVLTree<T> tree) {
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if (tree.root == null)
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return "Tree has no nodes.";
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return getString((AVLNode<T>) tree.root, "", true);
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}
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public static <T extends Comparable<T>> String getString(AVLNode<T> node) {
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if (node == null)
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return "Sub-tree has no nodes.";
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return getString(node, "", true);
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}
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private static <T extends Comparable<T>> String getString(AVLNode<T> node, String prefix, boolean isTail) {
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StringBuilder builder = new StringBuilder();
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builder.append(prefix + (isTail ? "└── " : "├── ") + "(" + node.height + ") " + node.id + "\n");
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List<Node<T>> children = null;
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if (node.lesser != null || node.greater != null) {
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children = new ArrayList<Node<T>>(2);
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if (node.lesser != null)
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children.add(node.lesser);
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if (node.greater != null)
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children.add(node.greater);
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}
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if (children != null) {
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for (int i = 0; i < children.size() - 1; i++) {
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builder.append(getString((AVLNode<T>) children.get(i), prefix + (isTail ? " " : "│ "), false));
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}
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if (children.size() >= 1) {
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builder.append(getString((AVLNode<T>) children.get(children.size() - 1), prefix + (isTail ? " " : "│ "), true));
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}
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}
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return builder.toString();
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}
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}
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}
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