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1 基于AVL树的集合和映射
Map.java
package tree;
public interface Map<K, V> {
void add(K key, V value);
V remove(K key);
boolean contains(K key);
V get(K key);
void set(K key, V newValue);
int getSize();
boolean isEmpty();
}
AVLTree.java
package avltree;
import java.util.ArrayList;
public class AVLTree<K extends Comparable<K>, V> {
public class Node {
public K key;
public V value;
public Node left, right;
public int height;
public Node(K key, V value) {
this.key = key;
this.value = value;
left = null;
right = null;
height = 1;
}
}
private Node root;
private int size;
public AVLTree() {
root = null;
size = 0;
}
public int getSize() {
return size;
}
public boolean isEmpty() {
return size == 0;
}
public boolean contains(K key){
return getNode(root, key) != null;
}
public V get(K key){
Node node = getNode(root, key);
return node == null ? null : node.value;
}
public void set(K key, V newValue){
Node node = getNode(root, key);
if(node == null)
throw new IllegalArgumentException(key + " doesn't exist!");
node.value = newValue;
}
// 判断该二叉树是否是一颗二分搜索树
public boolean isBST() {
ArrayList<K> keys = new ArrayList<>();
inOrder(root, keys);
for (int i = 1; i < keys.size(); i++) {
if (keys.get(i - 1).compareTo(keys.get(i)) > 0) {
return false;
}
}
return true;
}
private void inOrder(Node node, ArrayList<K> keys) {
if (node == null) {
return;
}
inOrder(node.left, keys);
keys.add(node.key);
inOrder(node.right, keys);
}
public boolean isBalanced() {
return isBalanced(root);
}
private boolean isBalanced(Node node) {
if (node == null) {
return true;
}
int balanceFactor = getBalanceFactor(node);
if (Math.abs(balanceFactor) > 1) {
return false;
}
return isBalanced(node.left) && isBalanced(node.right);
}
public int getHeight(Node node) {
if (node == null) {
return 0;
}
return node.height;
}
// 获得节点 node 的平衡因子
private int getBalanceFactor(Node node) {
if (node == null) {
return 0;
}
return getHeight(node.left) - getHeight(node.right);
}
// 对节点 y 进行向右旋转操作，返回旋转后新的根节点 x
private Node rightRotate(Node y) {
Node x = y.left;
Node T3 = x.right;
// 向右旋转过程
x.right = y;
y.left = T3;
// 更新 height
y.height = Math.max(getHeight(y.left), getHeight(y.right));
x.height = Math.max(getHeight(x.left), getHeight(x.right));
return x;
}
// 对 y 进行左旋转操作，返回旋转后新的根节点
// y x
// / \ / \
// T1 x y z
// / \ / \ / \
// T2 z T1 T2 T3 T4
// / \
// T3 T4
private Node leftRotate(Node y) {
Node x = y.right;
Node T2 = x.left;
// 向左旋转的过程
x.left = y;
y.right = T2;
y.height = Math.max(getHeight(y.left), getHeight(y.right));
x.height = Math.max(getHeight(x.left), getHeight(x.right));
return x;
}
public void add(K key, V value) {
root = add(root, key, value);
}
// 以 node 为根的二分搜索树中插入元素 (key,value)
// 返回插入新节点后二分搜索树的根
private Node add(Node node, K key, V value) {
if (node == null) {
size++;
return new Node(key, value);
}
if (key.compareTo(node.key) < 0) {
node.left = add(node.left, key, value);
} else if (key.compareTo(node.key) > 0) {
node.right = add(node.right, key, value);
} else {
node.value = value;
}
// 更新 height
node.height = 1 + Math.max(getHeight(node.left), getHeight(node.right));
// 计算平衡因子
int balanceFactor = getBalanceFactor(node);
if (Math.abs(balanceFactor) > 1) {
System.out.println("unbalanced: " + balanceFactor);
}
// 平衡维护
// LL
if (balanceFactor > 1 && getBalanceFactor(node.left) >= 0) {
return rightRotate(node);
}
// RR
if (balanceFactor < -1 && getBalanceFactor(node.right) <= 0) {
return leftRotate(node);
}
// LR
if (balanceFactor > 1 && getBalanceFactor(node.left) < 0) {
node.left = leftRotate(node.left);
return rightRotate(node);
}
// RL
if (balanceFactor < -1 && getBalanceFactor(node.right) > 0) {
node.right = rightRotate(node.right);
return leftRotate(node);
}
return node;
}
// 返回以node为根节点的二分搜索树中，key所在的节点
private Node getNode(Node node, K key) {
if (node == null)
return null;
if (key.equals(node.key))
return node;
else if (key.compareTo(node.key) < 0)
return getNode(node.left, key);
else // if(key.compareTo(node.key) > 0)
return getNode(node.right, key);
}
// 返回以node为根的二分搜索树的最小值所在的节点
private Node minimum(Node node) {
if (node.left == null) {
return node;
}
return minimum(node.left);
}
// 从二分搜索树中删除键为 key 的节点
public V remove(K key) {
Node node = getNode(root, key);
if (node != null) {
root = remove(root, key);
return node.value;
}
return null;
}
private Node remove(Node node, K key) {
if (node == null) {
return null;
}
Node retNode;
if (key.compareTo(node.key) < 0) {
node.left = remove(node.left, key);
retNode = node;
} else if (key.compareTo(node.key) > 0) {
node.right = remove(node.right, key);
retNode = node;
} else { // key.compareTo(node.key) == 0
// 待删除节点左子树为空
if (node.left == null) {
Node rightNode = node.right;
node.right = null;
size--;
retNode = rightNode;
}
if (node.right == null) {
Node leftNode = node.left;
node.left = null;
size--;
retNode = leftNode;
}
/*
* 待删除节点左右子树均不为空
*
* 找到比待删除节点大的最小节点，即到删除节点左子树的最小节点
* 用这个节点顶替待删除节点的位置
*
* */
Node successor = minimum(node.right);
successor.right = remove(node.right, successor.key);
successor.left = node.left;
node.left = node.right = null;
retNode = successor;
}
if (retNode == null) {
return null;
}
// 更新 height
retNode.height = 1 + Math.max(getHeight(retNode.left), getHeight(retNode.right));
// 计算平衡因子
int balanceFactor = getBalanceFactor(retNode);
if (Math.abs(balanceFactor) > 1) {
System.out.println("unbalanced: " + balanceFactor);
}
// 平衡维护
// LL
if (balanceFactor > 1 && getBalanceFactor(retNode.left) >= 0) {
return rightRotate(retNode);
}
// RR
if (balanceFactor < -1 && getBalanceFactor(retNode.right) <= 0) {
return leftRotate(retNode);
}
// LR
if (balanceFactor > 1 && getBalanceFactor(retNode.left) < 0) {
retNode.left = leftRotate(retNode.left);
return rightRotate(retNode);
}
// RL
if (balanceFactor < -1 && getBalanceFactor(retNode.right) > 0) {
retNode.right = rightRotate(retNode.right);
return leftRotate(retNode);
}
return retNode;
}
}
1.1 基于 AVL 树的映射
AVLMap.java
package tree;
import avltree.AVLTree;
public class AVLMap <K extends Comparable<K>,V> implements Map<K,V>{
private AVLTree<K,V> avl;
public AVLMap(){
avl = new AVLTree<>();
}
@Override
public void add(K key, V value) {
avl.add(key,value);
}
@Override
public V remove(K key) {
return avl.remove(key);
}
@Override
public boolean contains(K key) {
return avl.contains(key);
}
@Override
public V get(K key) {
return avl.get(key);
}
@Override
public void set(K key, V newValue) {
avl.set(key,newValue);
}
@Override
public int getSize() {
return 0;
}
@Override
public boolean isEmpty() {
return avl.isEmpty();
}
}
1.2 基于 AVL 树的集合
Set.java
package tree;
public interface Set<E> {
void add(E e);
void remove(E e);
boolean contains(E e);
int getSize();
boolean isEmpty();
}
AVLSet.java
package tree;
import avltree.AVLTree;
public class AVLSet<E extends Comparable<E>> implements Set<E> {
private AVLTree<E, Object> avl;
public AVLSet() {
avl = new AVLTree<>();
}
@Override
public void add(E e) {
avl.add(e, null);
}
@Override
public void remove(E e) {
avl.remove(e);
}
@Override
public boolean contains(E e) {
return avl.contains(e);
}
@Override
public int getSize() {
return avl.getSize();
}
@Override
public boolean isEmpty() {
return avl.isEmpty();
}
}