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 (≤) 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:

5

88 70 61 96 120

Sample Output 1:

Sample Input 2:

7

88 70 61 96 120 90 65

Sample Output 2:

#include<cstdio>

#include<algorithm>

using namespace std;

struct Node

{

    int v;

    int height;

    Node *lchild, *rchild;

}*root;

void Insert(Node* &root,int v);

Node* NewNode(int v);

void updateHeight(Node *root);

int getHeight(Node* root);

int getBalanceFactor(Node* root);

Node* R(Node* &root);

Node* L(Node* &root);

int main()

{

    int n;

    int v;

    scanf("%d",&n);

    for (int i = ; i < n; i++)

    {

        scanf("%d",&v);

        Insert(root,v);

    }

    printf("%d",root->v);

    return ;

}

void Insert(Node* &root, int v)

{

    if (NULL == root)

    {

        root = NewNode(v);

        return ;

    }

    if (root->v > v)

    {

        Insert(root->lchild,v);

        updateHeight(root);

        if ( == getBalanceFactor(root))

        {

            if ( == getBalanceFactor(root->lchild))

            {

                R(root);

            }

            else if(- == getBalanceFactor(root->lchild))

            {

                L(root->lchild);

                R(root);

            }

        }

    }

    else

    {

        Insert(root->rchild,v);

        updateHeight(root);

        if (- == getBalanceFactor(root))

        {

            if (- == getBalanceFactor(root->rchild))

            {

                L(root);

            }

            else if( == getBalanceFactor(root->rchild))

            {

                R(root->rchild);

                L(root);

            }

        }

    }

}

Node* NewNode(int v)

{

    Node* node = new Node;

    node->lchild = node->rchild = NULL;

    node->v = v;

    node->height = ;

    return node;

}

void updateHeight(Node *root)

{

    root->height = max(getHeight(root->lchild),getHeight(root->rchild)) + ;

}

int getHeight(Node* root)

{

    if (NULL == root)

    {

        return ;

    }

    else

    {

        return root->height;

    }

}

int getBalanceFactor(Node* root)

{

    return getHeight(root->lchild) - getHeight(root->rchild);

}

Node* R(Node* &root)

{

    Node *tmp = root->lchild;

    root->lchild = tmp->rchild;

    tmp->rchild = root;

    updateHeight(root);

    updateHeight(tmp);

    root = tmp;

}

Node* L(Node* &root)

{

    Node *tmp = root->rchild;

    root->rchild = tmp->lchild;

    tmp->lchild = root;

    updateHeight(root);

    updateHeight(tmp);

    root = tmp;

}

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