Root of AVL Tree

An AVL tree is a self-balancing binary search tree. In a AVL tree, the heights of the subtrees of any node differ by at the most one; If at any time they differ by more than one, the rebalancing is the done to restore this property. Figures 1-4 illustrate the rotation rules.

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

Input Specification:

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

Output Specification:

For each test case, print ythe root of the resulting AVL tree on 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

Ideas for solving problems: creating AVL trees

Comprehension: 1, the Lrrevolve function can call the contents of the Llrevolve function directly, and then pay attention to the relation between the functions.

2, Insert_avltree function START I use if always error changed to else can be originally because the tree is if the previous sentence after processing may meet if conditions

1#include <iostream>2#include <cmath>3 using namespacestd;4typedefstructAvltreenode *Avltree;5typedefstructAvltreenode6 {7     intdata;8avltreenode*Left ;9avltreenode*Right ;Ten     intheight; One }; A intgethight (Avltree T) { -     if(!T) -     { the         return-1; -     } -     Else -         returnT->height; + } - intMax (intAintb) { +     if(a>b) A     { at         returnA; -     } -     Else returnb; - } - avltree llrevolve (Avltree T) { -Avltree A =T; inAvltree B = t->Left ; -A->left=b->Right ; toB->right =A; +A->height = Max (Gethight (A->left), Gethight (a->right)) +1; -B->height = Max (Gethight (B->left), Gethight (b->right)) +1; the     returnB; * } $ avltree rrrevolve (Avltree T) {Panax NotoginsengAvltree A =T; -Avltree B = t->Right ; theA->right = b->Left ; +B->left =A; AA->height = Max (Gethight (A->left), Gethight (a->right)) +1; theB->height = Max (Gethight (B->left), Gethight (b->right)) +1; +     returnB; - } $ //avltree lrrevolve (Avltree T) { $ //Avltree A = T; - //avltree B = t->left; - //avltree C = b->right; the //b->right = c->left; - //a->left = c->right;Wuyi //c->left = B; the //c->right = A; - //a->height = Max (Gethight (A->left), Gethight (a->right)) + 1; Wu //b->height = Max (Gethight (B->left), Gethight (b->right)) + 1; - //c->height = Max (Gethight (C->left), Gethight (c->right)) + 1; About //return C; $ //} - avltree lrrevolve (Avltree T) { -Avltree A =T; -A->left = Rrrevolve (a->Left ); A     returnllrevolve (A); + } the avltree rlrevolve (Avltree T) { -Avltree A =T; $Avltree B = t->Right ; theA->right = Llrevolve (a->Right ); the     returnrrrevolve (A); the } theAvltree Insert_avltree (intElemdata, Avltree T) { -     if(!T) in     { theT = (avltreenode*)malloc(sizeof(Avltreenode)); theT->data =Elemdata; AboutT->left =NULL; theT->right =NULL; theT->height =0; the     } +     Else if(Elemdata < t->data) -     { theT->left = Insert_avltree (Elemdata, t->Left );Bayi         if(Gethight (T->left)-gethight (t->right) = =2){ the             if(Elemdata < t->left->data) theT =llrevolve (T);  -             //if (Elemdata > T->left->data) -             Else theT =lrrevolve (T); the         } the     } the     Else if(Elemdata > t->data) { -T->right = Insert_avltree (Elemdata, t->Right ); the         if(Gethight (T->right)-gethight (t->left) = =2){ the             if(Elemdata > t->right->data) theT =rrrevolve (T);94             //if (Elemdata < T->right->data) the             Else theT =rlrevolve (T); the         }98     } AboutT->height = Max (Gethight (T->left), Gethight (t->right)) +1; -     returnT;101 }102 103 intMain () {104     intNumber ; theCIN >>Number ;106Avltree T =NULL;107      for(inti =0; I < number; i++)108     {109         intElemdata; theCIN >>Elemdata;111t=Insert_avltree (elemdata,t); the     }113cout << t->data<<Endl; the     return 0; the}

Root of AVL Tree