pat 1066. Root of AVL Tree (25)

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 illustrate
the rotation rules.


    



    


Now given a sequence of insertions, you are supposed to tell the root of the resulting AVL tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (<=20) which is the total number of keys to be inserted. Then N distinct integer keys are given in the next line. All the numbers in a line are separated
by a space.

Output Specification:

For each test case, print ythe root of the resulting AVL tree in one line.

Sample Input 1:

5
88 70 61 96 120

Sample Output 1:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

avl树。

链接：http://www.cppblog.com/cxiaojia/archive/2013/07/22/187776.html

#include<iostream>
using namespace std;
#include<stdio.h>
#include<vector>
#include<map>
#include<math.h>
#include<queue>
#include<string.h>
#define MS(a,b) memset(a,b,sizeof(a))
#include<algorithm>
int n;
struct node
{
int value,height;
node *left,*right;
node(int u):value(u),left(NULL),right(NULL),height(0){}
};
int high(node *t)
{
if(t==NULL)return -1;
else return t->height;
}
bool isbalanced(node *left,node *right)
{
return abs(high(left)-high(right))<2;
}
node *Single_LL(node *t2)
{
node *t1;
t1=t2->left;
t2->left=t1->right;
t1->right=t2;
t2->height=max(high(t2->left),high(t2->right))+1;
t1->height=max(high(t1->left),high(t1->right))+1;
return t1;
}
node *Single_RR(node *t2)
{
node *t1;
t1=t2->right;
t2->right=t1->left;
t1->left=t2;
t2->height=max(high(t2->left),high(t2->right))+1;
t1->height=max(high(t1->left),high(t1->right))+1;
return t1;
}
node *Double_LR(node *t3)
{
t3->left=Single_RR(t3->left);
return Single_LL(t3);
}
node *Double_RL(node *t3)
{
t3->right=Single_LL(t3->right);
return Single_RR(t3);
}
node *insert1(int u,node *rt)
{
if(rt==NULL)
{
rt=new node(u);
return rt;
}
if(u>rt->value)
{
rt->right=insert1(u,rt->right);
if(!isbalanced(rt->left,rt->right))
if(u>rt->right->value)
rt=Single_RR(rt);
else rt=Double_RL(rt);
}
else
{
rt->left=insert1(u,rt->left);
if(!isbalanced(rt->left,rt->right))
if(u<rt->left->value)
rt=Single_LL(rt);
else rt=Double_LR(rt);
}
rt->height=max(high(rt->left),high(rt->right))+1;
return rt;
}
int main()
{
int i,num;
scanf("%d",&n);
node *rt=NULL;
for(i=0;i<n;i++)
{
scanf("%d",&num);
rt=insert1(num,rt);
}
printf("%d\n",rt->value);
return 0;
}