04-树5 Root of AVL Tree

/*=====================================================================================
#       COPYRIGHT NOTICE
#       Copyright (c) 2016

#
#       @Author       :Zehao Wang
#       @Email         :zehaowang@163.com
#       @from            ：https://pta.patest.cn/pta/test/1342/exam/4/question/20492
#       @Last modified         :2016-12-3
#       @Description    :求平衡二叉树根节点（涉及到旋转）
========================================================================================*/

#include <stdio.h>
#include<stdlib.h>

typedef struct AvlNode* AvlTree;
struct AvlNode
{
    int data;
    AvlTree left;
    AvlTree right;
    int height;
};

//求两数最大值
int Max(int a, int b)
{
    int i = (a > b ? a : b);
    return i;
}

//求节点高度。节点为NULL则高度为-1，没有左右儿子的节点高度为0
int height(AvlTree Tree)
{
    if (!Tree)
        return -1;
    else
        return Tree->height;
}

//左单旋
AvlTree singleRotateWithLeft(AvlTree K1)
{
    AvlTree K2 = K1->left;
     K1->left=K2->right;
     K2->right = K1;
     K1->height = Max(height(K1->left), height(K1->right))+1;
     K2->height = Max(height(K2->left), height(K1))+1;

     return K2;

}

//右单旋
AvlTree singleRotateWithRight(AvlTree K1)
{
    AvlTree K2 = K1->right;
    K1->right = K2->left;
    K2->left = K1;
    K1->height=Max(height(K1->left), height(K1->right))+1;
    K2->height= Max(height(K1), height(K2->right))+1;
    return K2;
}

//左双旋
AvlTree doubleRotateWithLeft(AvlTree K1)
{
    K1->left = singleRotateWithRight(K1->left);
    return  singleRotateWithLeft(K1);

}

//右双旋
AvlTree doubleRotateWithRight(AvlTree K1)
{
    K1->right = singleRotateWithLeft(K1->right);
    return singleRotateWithRight(K1);

}

//插入函数，每插入一个节点，都要调整一次平衡
AvlTree Insert(int x, AvlTree Tree)
{
    if (Tree == NULL)
    {
        Tree = (AvlTree)malloc(sizeof(struct AvlNode));
        Tree->data = x;
        Tree->left = NULL;
        Tree->right = NULL;
        Tree->height = 0;
    }
    else
    {
        if (x < Tree->data)
        {
            Tree->left=Insert(x, Tree->left);
            if (height(Tree->left)- height(Tree->right) == 2)
            {
                if (x < Tree->left->data)
                    Tree = singleRotateWithLeft(Tree);
                else if (x > Tree->left->data)
                    Tree = doubleRotateWithLeft(Tree);
            }
        }
        else if (x > Tree->data)
        {
            Tree->right = Insert(x, Tree->right);
            if (height(Tree->right) - height(Tree->left) == 2)
            {
                if (x > Tree->right->data)
                    Tree = singleRotateWithRight(Tree);
                else if(x<Tree->right->data)
                    Tree= doubleRotateWithRight(Tree);
            }
        }

    }
    Tree->height = Max(height(Tree->left), height(Tree->right)) + 1;
    return Tree;
}

int main(void)
{
    int N;
    int x;
    scanf("%d", &N);
    AvlTree Tree;
    Tree = NULL;
    for (int i = 0; i < N; i++)
    {
        if (scanf("%d", &x) == 1)
        Tree = Insert(x, Tree);
    }
    printf("%d",Tree->data);
}
/*=======================================================================================
注：最开始学旋转的时候很难理解二叉树的旋转究竟是一个怎样的流程。后来偶然看到一篇讲解二叉树
插入旋转的文章之后，茅塞顿开。文章链接：
http://www.2cto.com/kf/201606/514183.html
文章很重视思考的过程。从一开始为什么要旋转二叉树讲起，不断深入，最后一步步引到二叉树的不同
旋转方式。其实，所有的知识产物都是为了解决问题而被人不断思考，改进出来的，绝非空穴来风。但
现在大多数的教科书都会把人的思考过程隐去，只告诉你结论，只告诉你要掌握住什么。而有意无意的
忽略了知识从无到有产生的过程。或许思考过程并不如知识本身来的直接，但其中所蕴含的思考方式却
值得后人的借鉴，也更有利于知识被更好的理解。
========================================================================================*/