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平衡二叉树(图文)

第十三双眼睛2023-10-21【数据结构与算法】人已围观

简介平衡二叉树

平衡二叉树

package com.xingchen.day014;
public class AVLTreeDemo {
public static void main(String[] args) {
//int[] arr = {4,3,6,5,7,8};
int[] arr = {10,12,8,9,7,6};
AVLTree avlTree = new AVLTree();
for (int i=0;i<arr.length;i++) {
avlTree.add(new Node(arr[i]));
}
avlTree.infixOrder();
System.out.println(avlTree.root.height());
}
}
class AVLTree {
public Node root;
public void add(Node node) {
if (root == null) {
root = node;
} else {
root.add(node);
}
}
public void infixOrder() {
if (root != null) {
root.infixOrder();
} else {
System.out.println("二叉排序树为空");
}
}
public Node search(int value) {
if (root == null) {
return null;
}
return root.search(value);
}
public Node searchParent(int value) {
if (root == null) {
return null;
} else {
return root.searchParent(value);
}
}
//返回以node为根节点的二叉树中的最小值
public int deleteRightMin(Node node) {
Node target = node;
//循环查找左节点
while (target.left != null) {
target = target.left;
}
//这时target就指向了最小节点
delNode(target.value);
return target.value;
}
public void delNode(int value) {
if (root == null) {
return;
} else {
Node targetNode = search(value);
// 如果没有找到，直接返回
if (targetNode == null) {
return;
}
//如果只有一个节点
if (root.left == null && root.right == null) {
root = null;
return;
}
//
Node parent = searchParent(value);
if (targetNode.left == null && targetNode.right == null) {
//判断当前节点是父节点的左子节点还是右子节点
if (parent.left != null && parent.left.value == value) {
parent.left = null;
} else if (parent.right != null && parent.right.value == value) {
parent.right = null;
}
} else if (targetNode.left != null && targetNode.right != null) {
int minValue = deleteRightMin(targetNode.right);
targetNode.value = minValue;
} else {
if (targetNode.left != null) {
if (parent != null) {
if (parent.left.value == value) {
parent.left = targetNode.left;
} else {
parent.right = targetNode.left;
}
} else {
root = targetNode.left;
}
} else {
if (parent != null) {
if (parent.left.value == value) {
parent.left = targetNode.right;
} else {
parent.right = targetNode.right;
}
} else {
root = targetNode.right;
}
}
}
}
}
}
class Node {
public int value;
public Node left;
public Node right;
public Node(int value) {
this.value = value;
}
public void add(Node node) {
if (node == null) {
return;
}
if (node.value < this.value) {
if (this.left == null) {
this.left = node;
} else {
this.left.add(node);
}
} else {
if (this.right == null) {
this.right = node;
} else {
this.right.add(node);
}
}
//添加完一个节点后，如果右子树的高度比左子树的高度大于1
if(rightHeight() - leftHeight() > 1) {
if (right != null && right.leftHeight() > right.rightHeight()) {
right.rightRotate();
leftRotate();
} else {
leftRotate();
}
return;
}
if (leftHeight() - rightHeight() > 1) {
if (left != null && left.rightHeight() > left.leftHeight()) {
//先堆当前节点的左子树进行左旋
left.leftRotate();
rightRotate();
} else {
rightRotate();
}
}
}
public void infixOrder() {
if (this.left != null) {
this.left.infixOrder();
}
System.out.println(this);
if (this.right != null) {
this.right.infixOrder();
}
}
public int height() {
return Math.max(left == null?0:left.height(),right == null? 0 :right.height()) + 1;
}
public int leftHeight() {
if (left == null) {
return 0;
}
return left.height();
}
public int rightHeight() {
if (right == null) {
return 0;
}
return right.height();
}
public void leftRotate() {
Node newNode = new Node(value);
//新的节点的左子树设置成当前节点的左子树
newNode.left = this.left;
//新的节点的右子树设置成当前节点的右子树的左子树
newNode.right = this.right.left;
//当前节点的值替换成右子节点的值
value = right.value;
//把当前节点的右子树设置成右子树的右子树
this.right = this.right.right;
//把当前节点的左子树设置成新的节点
this.left = newNode;
}
public void rightRotate() {
Node newNode = new Node(value);
newNode.left = left.right;
value = left.value;
left = left.left;
right = newNode;

}
public Node search(int value) {
if (value == this.value) {
return this;
} else if(value < this.value) {
if (this.left != null) {
return this.left.search(value);
} else {
return null;
}
} else {
if (this.right != null) {
return this.right.search(value);
} else {
return null;
}
}
}
public Node searchParent(int value) {
//如果当前节点就是要删除的节点的父节点
if ((this.left != null && this.left.value == value) || (this.right != null && this.right.value == value)) {
return this;
} else {
//向左递归
if (value < this.value && this.left != null) {
return this.left.searchParent(value);
} else if (value >= this.value && this.right != null) {
return this.right.searchParent(value);
} else {
return null;
}
}
}
@Override
public String toString() {
return "Node{" +
"value=" + value +
'}';
}
}

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