无需存储高度的java AVL树实现
我现在处于AVL树插入实现的中间,在插入和回溯树的过程中,我在维护平衡因素方面挣扎。
实际上,我能找到的每一个AVL实现都使用一个节点的两个子树的高度来计算平衡因子,这与
node.balance = node.right.height - node.left.height
如果你的节点类看起来像
class Node {
int value, height;
Node left, right;
}
尽管问题在于,对于这个特定的实现,跟踪节点的高度是“违反规则的”,相反,我们只能跟踪平衡因子。所以Node类看起来像
class Node {
int value, balance;
Node left, right;
}
我知道,维护节点的平衡因子在概念上类似于维护树中每个插入的高度,但在我的一生中,我无法计算出特定节点的平衡因子应该改变的所有情况
目前,我已经通过递归调用每个节点的高度函数来设置平衡因子(不是最优的!)以确保我的旋转和一般插入是正确的
node.balance = height(node.right) - height(node.left)
其中height()
递归地遍历树,以找到到叶子的最长路径
我已经验证了旋转逻辑确实是正确的,但是当我开始编写代码以+-1的增量回溯树时,代码立即变成了意大利面条,因为我显然不理解节点平衡因子的一些基本原理
如果你想看到代码,我已经在下面发布了(有点长)。下面的实现也是一个字符串AVL树,但思想是一样的
任何意见都将不胜感激,谢谢
class StringAVLNode {
private String item;
private int balance;
private StringAVLNode left, right;
// just one constructor, please
public StringAVLNode(String str) {
item = str;
balance = 0;
left = null; right = null;
}
public int getBalance () {
return balance;
}
public void setBalance ( int bal){
balance = bal;
}
public String getItem () {
return item;
}
public StringAVLNode getLeft () {
return left;
}
public void setLeft (StringAVLNode pt){
left = pt;
}
public StringAVLNode getRight () {
return right;
}
public void setRight (StringAVLNode pt){
right = pt;
}
public void insert(String str) {
root = insert(str, root);
}
private StringAVLNode insert(String str, StringAVLNode t) {
// Base case - Just insert the node
if (t == null)
t = new StringAVLNode(str);
else {
int balance, leftChildBalance, rightChildBalance;
leftChildBalance = t.getLeft() != null ? t.getLeft().getBalance() : -99;
rightChildBalance = t.getRight() != null ? t.getRight().getBalance() : -99;
// Perform string comparisons to determine left/right insert
int compareResult = str.compareToIgnoreCase(t.getItem());
if (compareResult < 0) {
t.setLeft(insert(str, t.getLeft()));
if (t.getRight() == null)
t.setBalance(t.getBalance()-1);
else if (leftChildBalance == 0 && t.getLeft().getBalance() != 0)
t.setBalance(t.getBalance()-1);
else if (leftChildBalance == -99 && t.getLeft() != null)
t.setBalance(t.getBalance()-1);
}
else if (compareResult > 0) {
t.setRight(insert(str, t.getRight()));
if (t.getLeft() == null)
t.setBalance(t.getBalance()+1);
else if (rightChildBalance == 0 && t.getRight().getBalance() != 0)
t.setBalance(t.getBalance()+1);
else if (rightChildBalance == -99 && t.getRight() != null)
t.setBalance(t.getBalance()+1);
}
balance = t.getBalance();
// Verbosify booleans
boolean rightImbalance = balance > 1; boolean leftImbalance = balance < -1;
// Imbalance tree situation calls balanceTrees() to handle the rotation logic
// ( Keeps insert() succinct )
if (rightImbalance || leftImbalance)
t = balanceTrees(balance, t);
}
return t;
}
// Rotation Handler
private StringAVLNode balanceTrees(int balance, StringAVLNode t) {
// Verbosify boolean values
boolean rightHeavy = balance > 1; boolean leftHeavy = balance < -1;
boolean requiresDoubleLeft = t.getRight() != null && t.getRight().getBalance() <= -1;
boolean requiresDoubleRight = t.getLeft() != null && t.getLeft().getBalance() >= 1;
if (rightHeavy) {
/** Do double left rotation by right rotating the right child subtree, then
* rotate left
*/
if (requiresDoubleLeft) {
t.setRight(rotateRight(t.getRight()));
t.getRight().setBalance(0);
t = rotateLeft(t);
t.setBalance(0);
}
else {
t = rotateLeft(t);
t.setBalance(0);
if (t.getLeft() != null) t.getLeft().setBalance(0);
if (t.getRight() != null) t.getRight().setBalance(0);
}
}
/** Do double right rotation by left rotating the left child subtree, then
* rotate right
*/
else if (leftHeavy) {
if (requiresDoubleRight) {
t.setLeft(rotateLeft(t.getLeft()));
t.getLeft().setBalance(0);
t = rotateRight(t);
t.setBalance(0);
}
else {
t = rotateRight(t);
t.setBalance(0);
if (t.getLeft() != null) t.getLeft().setBalance(0);
if (t.getRight() != null) t.getRight().setBalance(0);
}
}
if (t.getLeft() != null) {
if (t.getLeft().getRight() != null && t.getLeft().getLeft() == null)
t.getLeft().setBalance(1);
else if (t.getLeft().getLeft() != null && t.getLeft().getRight() == null)
t.getLeft().setBalance(-1);
else if ((t.getLeft().getLeft() != null && t.getLeft().getRight() != null)
|| (t.getLeft().getLeft() == null && t.getLeft().getRight() == null))
t.getLeft().setBalance(0);
}
if (t.getRight() != null) {
if (t.getRight().getRight() != null && t.getRight().getLeft() == null)
t.getRight().setBalance(1);
else if (t.getRight().getLeft() != null && t.getRight().getRight() == null)
t.getRight().setBalance(-1);
else if ((t.getRight().getLeft() != null && t.getRight().getRight() != null)
|| (t.getRight().getLeft() == null && t.getRight().getRight() == null))
t.getRight().setBalance(0);
}
return t;
}
}
# 1 楼答案
查看我在Java writeup中的AVL树,网址为:
https://debugnotes.wordpress.com/2015/01/07/implementing-an-avl-tree-in-java-part-2
您的实现似乎不包含任何类型的基于堆栈的元素(递归或基于数组),以跟踪您在树中的深度。这是能够导航自平衡树数据结构的一个关键部分——能够向下搜索,找到目标节点并对其执行操作,然后追溯到它开始导航的树的根节点,并在向上操作它。使用递归是一种方法(即使用程序堆栈),或者您需要实现自己的堆栈(例如使用队列或链接列表),但除非您的代码有一个内存结构记录它所在的位置,否则不幸的是,它总是会丢失