AVL树（Java实现）
2024-06-13 18:52:46
文章目录
- 一、AVL树
- 二、代码实现（Java)
一、AVL树
二、代码实现（Java)
import java.nio.BufferUnderflowException;/*** @author LongRookie* @description: AVL ,满足平衡条件的二叉查找树* @date 2021/6/27 16:38*/
public class AVL<AnyType extends Comparable<? super AnyType>> {/*** The statement of node in AVL Tree** @param <AnyType>*/private static class AvlNode<AnyType> {//ConstructorsAvlNode(AnyType element) {this(element, null, null);}AvlNode(AnyType theElement, AvlNode<AnyType> lt, AvlNode<AnyType> rt) {element = theElement;left = lt;right = rt;height = 0;}AnyType element; //The data in the nodeAvlNode<AnyType> left; //Left childAvlNode<AnyType> right; //Right childint height; //Height}public AvlNode<AnyType> root;//Constructorpublic AVL() {root = null;}//findMaxpublic AnyType findMax() {if (isEmpty()) throw new BufferUnderflowException();return findMax(root).element;}//findMinpublic AnyType findMin() {if (isEmpty()) throw new BufferUnderflowException();return findMin(root).element;}//insertpublic void insert(AnyType x) {root = insert(x, root);}//removepublic void remove(AnyType x) {root = remove(x,root);}//containpublic boolean contains(AnyType x){return contains(x,root);}private boolean contains(AnyType x, AvlNode<AnyType> t) {if (t == null) {return false;}int compareResult = x.compareTo(t.element);if (compareResult < 0) {return contains(x, t.left);} else if (compareResult > 0) {return contains(x, t.right);} else {return true;}}private boolean isEmpty() {return root == null;}private AvlNode<AnyType> insert(AnyType x, AvlNode<AnyType> t) {if (t == null) {return new AvlNode<AnyType>(x);}int compareResult = x.compareTo(t.element);if (compareResult < 0) {t.left = insert(x, t.left);} else if (compareResult > 0) {t.right = insert(x, t.right);} else; //Duplicate; do nothingreturn t;}private static final int ALLOWED_IMBALANCE = 1;/*** Assume t is either balanced or within one of being balanced** @param t* @return*/private AvlNode<AnyType> balance(AvlNode<AnyType> t) {// useless in insert operation;if (t == null) {return t;}// if the height of subtree t is larger than that of right subtree;if (height(t.left) - height(t.right) > ALLOWED_IMBALANCE) {// notice the '=' calculation ,when only insert ,that is useless;// when remove,that is possibly useful;if (height(t.left.left) >= height(t.left.right)) {t = rotateWithLeftChild(t);} else {t = doubleWithLeftChild(t);}} else if (height(t.right) - height(t.left) > ALLOWED_IMBALANCE) {if (height(t.right.right) >= height(t.right.left)) {t = rotateWithRightChild(t);} else {t = doubleWithRightChild(t);}}//update the height, the operate is useful for the node that does not need to balance;t.height = Math.max(height(t.left), height(t.right)) + 1;return t;}/*** Rotate binary tree node with left child* For AVL trees ,this is a single rotation for case 1* Update heights ,then return new root** @param k2* @return*/private AvlNode<AnyType> rotateWithLeftChild(AvlNode<AnyType> k2) {AvlNode<AnyType> k1 = k2.left;k2.left = k1.right;k1.right = k2;k2.height = Math.max(height(k2.left), height(k2.right)) + 1;k1.height = Math.max(height(k1.left), height(k1.right)) + 1;return k1;}/*** Rotate binary tree node with right child* For AVL trees ,this is a single rotation for case 4* Update heights ,then return new root** @param k1* @return*/private AvlNode<AnyType> rotateWithRightChild(AvlNode<AnyType> k1) {AvlNode<AnyType> k2 = k1.right;k1.right = k2.left;k2.left = k1;k1.height = Math.max(height(k1.left), height(k1.right)) + 1;k2.height = Math.max(height(k2.left), height(k2.right)) + 1;return k2;}/*** Double rotate binary tree node;first left child* with its right child; then node k3 with new left child.* For AVL trees, this is a double rotation for case 2.* Update heights , then return new root.** @param k3* @return*/private AvlNode<AnyType> doubleWithLeftChild(AvlNode<AnyType> k3) {k3.left = rotateWithRightChild(k3.left);return rotateWithLeftChild(k3);}/*** Double rotate binary tree node;first right child* with its left child; then node k3 with new right child.* For AVL trees, this is a double rotation for case 3.* Update heights , then return new root.** @param k3* @return*/private AvlNode<AnyType> doubleWithRightChild(AvlNode<AnyType> k3) {k3.right = rotateWithLeftChild(k3.right);return rotateWithRightChild(k3);}/*** Return the height of node t, or -1, if null;** @param t node* @return*/private int height(AvlNode<AnyType> t) {return t == null ? -1 : t.height;}/*** Internal method to find the node containing the smallest item in a subtree** @param t the node that roots the subtree* @return the node containing the smallest item*/private AvlNode<AnyType> findMin(AvlNode<AnyType> t) {if (t == null) {return null;}if (t.left == null) {return t;}return findMin(t.left);}/*** Internal method to find the node containing the largest item in a subtree** @param t the node that roots the subtree* @return the node containing the largest item*/private AvlNode<AnyType> findMax(AvlNode<AnyType> t) {if (t == null) {return null;}if (t.right == null) {return t;}return findMax(t.right);}private AvlNode<AnyType> remove(AnyType x, AvlNode<AnyType> t) {if (t == null) {return t; // Item not found; do nothing}int compareResult = x.compareTo(t.element);if (compareResult < 0) {t.left = remove(x, t.left);} else if (compareResult > 0) {t.right = remove(x, t.right);} else if (t.left != null && t.right != null) {//Two childrent.element = findMin(t.right).element; //the smallest item in right subtreet.right = remove(t.element, t.right);} elset = (t.left != null) ? 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