Geeks - AVL Tree Insertion 平衡二叉树

AVL可以保证搜索达到O(lgn)的时间效率，因为两边的树高都差不多。不会出现搜索是线性的最坏情况。

但是AVL在插入和删除节点的时候需要做较多的旋转操作，所以如果修改节点多的时候，最好使用红黑树，但是如果搜索多的时候，就最好使用AVL了。

参考：http://www.geeksforgeeks.org/avl-tree-set-1-insertion/

注意点：

1 判断关键字和节点的孩子节点的大小判断应该是左转还是右转

2 利用递归就不需要记录父母节点了

3 注意更新balance和判断balance的顺序

#pragma once
#include <stdio.h>
#include <algorithm>

using std::max;

class AVL
{
	struct Node
	{
		int key;
		Node *left, *right;
		int h;
		Node(int k) : key(k)
		{
			left = right = NULL;
			h = 1;
		}
		~Node()
		{
			if (left) delete left;
			if (right) delete right;
		}
	};

	inline int getHeight(Node *n)
	{
		if (!n) return 0;
		return n->h;
	}

	inline void updateHeight(Node *y)
	{
		y->h = max(getHeight(y->left), getHeight(y->right)) + 1;
	}

	Node *rightRotate(Node *y)
	{
		Node *x = y->left;
		y->left = x->right;
		x->right = y;

		updateHeight(y);
		updateHeight(x);

		return x;
	}

	Node *leftRotate(Node *y)
	{
		Node *x = y->right;
		y->right = x->left;
		x->left = y;

		updateHeight(y);
		updateHeight(x);

		return x;
	}

	inline int getBalance(Node *n)
	{
		if (!n) return 0;
		return getHeight(n->left) - getHeight(n->right);
	}

	Node *insert(Node *node, int key)
	{
		if (!node) return new Node(key);

		if (key < node->key) node->left = insert(node->left, key);
		else node->right = insert(node->right, key);

		updateHeight(node);

		int balance = getBalance(node);

		if (balance > 1 && key < node->left->key)
			return rightRotate(node);

		else if (balance < -1 && node->right->key < key)
			return leftRotate(node);

		else if (balance > 1 && node->left->key < key)
		{
			node->left = leftRotate(node->left);
			return rightRotate(node);
		}

		else if (balance < -1 && key < node->right->key)
		{
			node->right = rightRotate(node->right);
			return leftRotate(node);
		}

		//unchanged node pointer
		return node;
	}

	void preOrder(Node *root)
	{
		if(root != NULL)
		{
			printf("%d ", root->key);
			preOrder(root->left);
			preOrder(root->right);
		}
	}
public:
	AVL()
	{
		Node *root = NULL;

		/* Constructing tree given in the above figure */
		root = insert(root, 10);
		root = insert(root, 20);
		root = insert(root, 30);
		root = insert(root, 40);
		root = insert(root, 50);
		root = insert(root, 25);

		/* The constructed AVL Tree would be
		30
		/  		20   40
		/  \     		10  25    50
		*/

		printf("Pre order traversal of the constructed AVL tree is \n");
		preOrder(root);
	}
};

Geeks - AVL Tree Insertion 平衡二叉树