PAT 1066 Root of AVL Tree(25分)

1066Root 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 integerN(≤20) which is the total number of keys to be inserted. ThenNdistinct 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:

70

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

思路

• 构建一个平衡二叉树，并输出根节点的值。
• 本题代码较长，尤其注意insert()函数的编写。

代码

#include <cstdio> 
#include <algorithm>

using namespace std;

const int maxn = 25;

struct node
{
    int data, height;
    node* lchild, *rchild;
};
int n;
int data[maxn];

node* newNode(int v)
{
    node* Node = new node;
    Node -> data = v;
    Node -> height = 1;
    Node -> lchild = Node -> rchild = NULL;
    return Node;
}

int getHeight(node* root)
{
    if (root == NULL)
        return 0;
    return root -> height;
}

int getBalanceFactor(node* root)
{
    return getHeight(root -> lchild) - getHeight(root -> rchild);
}

void updateHeight(node* root)
{
    root -> height = max(getHeight(root -> lchild), getHeight(root -> rchild)) + 1;    
}


//左旋 
void leftRotation(node* &root)
{
    node* temp = root -> rchild;
    root -> rchild = temp -> lchild;
    temp -> lchild = root;
    updateHeight(root);
    updateHeight(temp);
    root = temp;
}
//右旋
void rightRotation(node* &root) 
{
    node* temp = root -> lchild;
    root -> lchild = temp -> rchild;
    temp -> rchild = root;
    updateHeight(root);
    updateHeight(temp);
    root = temp;
}
//插入操作
void insert(node* &root, int v) 
{
    if (root == NULL)
    {
        root = newNode(v);
        return;
    }
    if (v < root -> data)
    {
        insert(root -> lchild, v);
        updateHeight(root);
        if (getBalanceFactor(root) == 2)
        {
            if (getBalanceFactor(root -> lchild) == 1)
            {
                rightRotation(root);
            }
            else if (getBalanceFactor(root -> lchild) == -1)
            {
                leftRotation(root -> lchild);
                rightRotation(root);
            }
        }
    }
    else
    {
        insert(root -> rchild, v);
        updateHeight(root);
        if(getBalanceFactor(root) == -2)
        {
            if (getBalanceFactor(root -> rchild) == -1)
            {
                leftRotation(root);
            }
            else if (getBalanceFactor(root -> rchild) == 1)
            {
                rightRotation(root -> rchild);
                leftRotation(root);
            }
        }
    }
}

node* create(int data[], int n)
{
    node* root = NULL;
    for (int i = 0; i < n; i ++)
    {
        insert(root, data[i]);
    }
    return root;
}

int main()
{
    scanf("%d", &n);
    for (int i = 0; i < n; i ++)
    {
        scanf("%d", &data[i]);
    }
    node* root = create(data, n);
    printf("%d\n", root -> data);
    return 0;
}