04-树5 Root of AVL Tree

题目

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:

5
88 70 61 96 120

Sample Output 1:

70

解答

 

#include <iostream>

int max(int a, int b) { return a > b ? a : b; }

class Node
{
public:
    int data;
    int height;
    Node *left;
    Node *right;

    Node(int d = 0, Node *p = nullptr, Node *q = nullptr) : data(d), height(0), left(p), right(q) {}
};

int getHeight(Node *r) { return !r ? -1 : r->height; }

class AVL
{
private:

    void traverse(Node *r)
    {
        if (!r)
            return;
        std::cout << r->data << '-' << r->height << ' ';
        traverse(r->left);
        traverse(r->right);
    }

    Node *insert(Node *r, int d)
    {
        if (!r)
            r = new Node(d);
        else if (d < r->data)
        {
            r->left = insert(r->left, d);
            if (getHeight(r->left) - getHeight(r->right) == 2)
            {
                if (d < r->left->data)
                    r = singleLeftRotation(r);
                else
                    r = doubleLeftRightRotation(r);
            }
        } else if (d > r->data)
        {
            r->right = insert(r->right, d);
            if (getHeight(r->right) - getHeight(r->left) == 2)
            {
                if (d > r->right->data)
                    r = singleRightRotation(r);
                else
                    r = doubleRightLeftRotation(r);
            }
        }
        r->height = max(getHeight(r->left), getHeight(r->right)) + 1;
        return r;
    }

public:
    Node *root;

    AVL()
    {
        root = nullptr;
    }

    void insert(int d) { root = insert(root, d); }

    void traverse() { traverse(root); }

    Node *findMin(Node *r)
    {
        if (!r->left)
            return r;
        else
            return findMin(r->left);
    }

    static Node *singleLeftRotation(Node *r)
    {
        Node *p = r->left;
        r->left = p->right;
        p->right = r;
        r->height = max(getHeight(r->left), getHeight(r->right)) + 1;
        p->height = max(getHeight(p->left), r->height) + 1;
        return p;
    }

    static Node *singleRightRotation(Node *r)
    {
        Node *p = r->right;
        r->right = p->left;
        p->left = r;
        r->height = max(getHeight(r->left), getHeight(r->right)) + 1;
        p->height = max(getHeight(p->right), r->height) + 1;
        return p;
    }

    static Node *doubleLeftRightRotation(Node *r)
    {
        r->left = singleRightRotation(r->left);
        return singleLeftRotation(r);
    }

    static Node *doubleRightLeftRotation(Node *r)
    {
        r->right = singleLeftRotation(r->right);
        return singleRightRotation(r);
    }
};

int main()
{
    int n;
    int d;
    AVL t;
    std::cin >> n;
    for (int i = 0; i < n; ++i)
    {
        std::cin >> d;
        t.insert(d);
    }
    std::cout << t.root->data << '\n';
    return 0;
}