本篇随笔主要从以下三个方面介绍树的平衡: 1):BST不平衡问题 2):BST 旋转 3):AVL Tree 一:BST不平衡问题的解析 之前有提过普通BST的一些一些缺点,例如BST的高度是介于lgN和N之间的,如果是N的的话,显然效率很低,不是我们需要的:但是在实际情况中,BST的高度h = N的情况却经常出现,例如下图所示.在BST中search,insert的running time都等于BST的高度h,我们肯定希望高度h越小越好,best case就是lgN.下图的example 2的…

1. 定义 (15-1) [AVL tree]: 一棵空二叉树是 AVL tree; 若 T 是一棵非空二叉树, 则 T 满足以下两个条件时, T 是一棵 AVL tree: T_LeftSubtree 和 T_RightSubtree 是 AVL tree. \(| h_{Left} - h_{Right}| \leq 1\). [AVL search tree]: AVL tree + binary search tree. AVL tree 的高度 \(h=O(\log{n})\) [ba…

平衡二叉树 LL RR LR RL 注意画图理解法 An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this pr…

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illust…

An AVL tree is a self-balancing binary search tree.  In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property.  Figures 1-4 illu…

Overview AVL tree is a special binary search tree, by definition, any node, its left tree height and right tree height difference is not more than 1. The purpose of AVL tree is to try best to reduce the search time complexity. if the binary search tr…

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illust…

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illust…

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illust…

An AVL tree is a self-balancing binary search tree. In an AVL tree, the heights of the two child subtrees of any node differ by at most one; if at any time they differ by more than one, rebalancing is done to restore this property. Figures 1-4 illust…