04-树5 Root of AVL Tree

04-树5 Root of AVL Tree   (25分)

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 the 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

思路：

基础题，建一个AVL树

#include <iostream>using namespace std;typedef struct TNode* AVLTree;struct TNode{    int height;    AVLTree left;    AVLTree right;    int data;};int Max(int x,int y){    int q;    x>y?q=x:q=y;    return q;}int Height(AVLTree t){    if(t == NULL)        return -1;    else        return t->height;}AVLTree SingleRotateWithLeft(AVLTree T) //LL{    AVLTree k;    k = T->left;    T->left = k->right;    k->right = T;    k->height = Max(Height(k->left), Height(k->right)) + 1;    T->height = Max(Height(T->left), Height(T->right)) + 1;    return k;}AVLTree SingleRotateWithRight(AVLTree T) //RR{    AVLTree k;    k = T->right;    T->right = k->left;    k->left = T;    k->height = Max(Height(k->left), Height(k->right)) + 1;    T->height = Max(Height(T->left), Height(T->right)) + 1;    return k;}AVLTree DoubleRotateWithLeft(AVLTree T) //LR{    T->left = SingleRotateWithRight(T->left);    T = SingleRotateWithLeft(T);    return T;}AVLTree DoubleRotateWithRight(AVLTree T) //RL{    T->right = SingleRotateWithLeft(T->right);    T = SingleRotateWithRight(T);    return T;}AVLTree Insert(AVLTree T, int x){    if(T == NULL)    {        T = new TNode;        T->left = T->right = NULL;        T->data = x;    }    else if(x < T->data)  //left child    {        T->left = Insert(T->left, x);        if(Height(T->left) - Height(T->right) == 2)        {            if(x < T->left->data)                T = SingleRotateWithLeft(T);//LL            else if(x > T->left->data)                T = DoubleRotateWithLeft(T);//LR        }    }    else if(x > T->data)  //right child    {        T->right = Insert(T->right, x);        if(Height(T->right) - Height(T->left) == 2)        {            if(x > T->right->data)                T = SingleRotateWithRight(T);//RR            else if(x < T->right->data)                T = DoubleRotateWithRight(T);//RL        }    }    //update T's height    T->height = Max(Height(T->left), Height(T->right)) + 1;    return T;}int main(){    int n,x;    AVLTree T = NULL;    cin>>n;    for(int i=0; i<n; i++)    {        cin>>x;        T = Insert(T,x);    }    cout << T->data << endl;    return 0;}