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:

588 70 61 96 120

Sample Output 1:

70

Sample Input 2:

788 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;}