java——平衡二叉树 AVLTree、AVLMap、AVLSet
2024-10-21 11:44:20
平衡二叉树：对于任意一个节点，左子树和右子树的高度差不能超过1
package Date_pacage;
import java.util.ArrayList; public class AVLTree<K extends Comparable<K>, V> { private 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;
} // 判断该二叉树是否是一棵二分搜索树
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);
} // 判断该二叉树是否是一棵平衡二叉树
public boolean isBalanced(){
return isBalanced(root);
} // 判断以Node为根的二叉树是否是一棵平衡二叉树，递归算法
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);
} // 获得节点node的高度
private 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
// y x
// / \ / \
// x T4 向右旋转 (y) z y
// / \ - - - - - - - -> / \ / \
// z T3 T1 T2 T3 T4
// / \
// T1 T2
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)) + 1;
x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1; return x;
} // 对节点y进行向左旋转操作，返回旋转后新的根节点x
// y x
// / \ / \
// T1 x 向左旋转 (y) y z
// / \ - - - - - - - -> / \ / \
// T2 z T1 T2 T3 T4
// / \
// T3 T4
private Node leftRotate(Node y) {
Node x = y.right;
Node T2 = x.left; // 向左旋转过程
x.left = y;
y.right = T2; // 更新height
y.height = Math.max(getHeight(y.left), getHeight(y.right)) + 1;
x.height = Math.max(getHeight(x.left), getHeight(x.right)) + 1; return x;
} // 向二分搜索树中添加新的元素(key, value)
public void add(K key, V value){
root = add(root, key, value);
} // 向以node为根的二分搜索树中插入元素(key, value)，递归算法
// 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 // key.compareTo(node.key) == 0
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); // 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);
} 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;
} // 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);
// return node;
retNode = node;
}
else if(key.compareTo(node.key) > 0 ){
node.right = remove(node.right, key);
// return node;
retNode = node;
}
else{ // key.compareTo(node.key) == 0 // 待删除节点左子树为空的情况
if(node.left == null){
Node rightNode = node.right;
node.right = null;
size --;
// return rightNode;
retNode = rightNode;
} // 待删除节点右子树为空的情况
else if(node.right == null){
Node leftNode = node.left;
node.left = null;
size --;
// return leftNode;
retNode = leftNode;
} // 待删除节点左右子树均不为空的情况
else{
// 找到比待删除节点大的最小节点, 即待删除节点右子树的最小节点
// 用这个节点顶替待删除节点的位置
Node successor = minimum(node.right);
//successor.right = removeMin(node.right);
successor.right = remove(node.right, successor.key);
successor.left = node.left; node.left = node.right = null; // return successor;
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); // 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;
} }
AVLMap
package Date_pacage;
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) {
// TODO Auto-generated method stub
avl.add(key, value);
}
@Override
public V remove(K key) {
// TODO Auto-generated method stub
return avl.remove(key);
}
@Override
public boolean contains(K key) {
// TODO Auto-generated method stub
return avl.contains(key);
}
@Override
public V get(K key) {
// TODO Auto-generated method stub
return avl.get(key);
}
@Override
public void set(K key, V newValue) {
// TODO Auto-generated method stub
avl.set(key, newValue);
}
@Override
public int getSize() {
// TODO Auto-generated method stub
return avl.getSize();
}
@Override
public boolean inEmpty() {
// TODO Auto-generated method stub
return avl.isEmpty();
}
}
AVLSet：
package Date_pacage;
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) {
// TODO Auto-generated method stub
avl.add(e, null);
}
@Override
public void remove(E e) {
// TODO Auto-generated method stub
avl.remove(e);
}
@Override
public boolean contains(E e) {
// TODO Auto-generated method stub
return avl.contains(e);
}
@Override
public int getSize() {
// TODO Auto-generated method stub
return avl.getSize();
}
@Override
public boolean isEmpty() {
// TODO Auto-generated method stub
return avl.isEmpty();
}
}
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