04-树3. Root of AVL Tree

/* ***********************************************
Author        :xryz
Email         :523689985@qq.com
Created Time  :4-8 22:26:56
File Name     :RootofAVLTree.cpp
************************************************ */

#include <stdio.h>
#include <string.h>
#include <iostream>
#include <algorithm>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <string>
#include <math.h>
#include <stdlib.h>
#include <time.h>
using namespace std;

typedef struct avltreenode *avltree;
typedef struct avltreenode{
    int data;
    avltree left;
    avltree right;
    int height;
};

int getheight(avltree a)
{
    if(a==NULL) return -1;
    return a->height;
}

//a必须有一个左子结点b
//a与b做左单旋，更新a与b高度，返回新的根结点b
avltree singleleftrotation(avltree a)
{
    avltree b=a->left;
    a->left=b->right;
    b->right=a;
    a->height=max(getheight(a->left),getheight(a->right))+1;
    b->height=max(getheight(b->left),a->height)+1;

    return b;
}

//右单旋转
avltree singlerightrotation(avltree a)
{
    avltree b=a->right;
    a->right=b->left;
    b->left=a;

    a->height=max(getheight(a->left),getheight(a->right))+1;
    b->height=max(getheight(b->right),a->height)+1;

    return b;
}

//a必须有一个左子结点b，且b必须有一个右子结点c
//a，b，c，做两次单旋，返回新的根结点c
avltree doubleleftrightrotation(avltree a)
{
    a->left=singlerightrotation(a->left);

    return singleleftrotation(a);
}

avltree doublerightleftrotation(avltree a)
{
    a->right=singleleftrotation(a->right);

    return singlerightrotation(a);
}

avltree avl_insertion(int x,avltree t)
{
    /*将X插入avl树T中，并返回调整后的avl树*/
    if(!t)/*插入空树，则新建包含一个结点的树*/
    {
        t=(avltree)malloc(sizeof(struct avltreenode));
        t->data=x;
        t->height=0;
        t->left=t->right=NULL;
    }/*插入空树结束*/
    else if(x<t->data)
    {
        t->left=avl_insertion(x,t->left);
        if(getheight(t->left)-getheight(t->right)==2)
        {
            /*需要左旋*/
            if(x<t->left->data)
                t=singleleftrotation(t);//左单旋 singleleftrotation
            else
                t=doubleleftrightrotation(t);//左右双旋
        }
    }
    else if(x>t->data)
    {
        t->right=avl_insertion(x,t->right);
        if(getheight(t->left)-getheight(t->right)==-2)
        {
            /*需要右旋*/
            if(x>t->right->data)
                t=singlerightrotation(t);//右单旋
            else
                t=doublerightleftrotation(t);//右左双旋
        }
    }

    //x=data，无须插入
    t->height=max(getheight(t->left),getheight(t->right))+1;
    return t;
}


int main()
{
    int n,i,num;
    avltree root;
    while(~scanf("%d",&n))
    {
        for(i=0;i<n;i++)
        {
            scanf("%d",&num);
            root=avl_insertion(num,root);
        }
        printf("%d
",root->data);
        free(root);
    }
    return 0;
}

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