1066 Root of AVL Tree

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:

70

 

Sample Input 2:

7
88 70 61 96 120 90 65

 

Sample Output 2:

88

题意：

　　给出一组数字，要求按照给出的顺序插入到一棵平衡二叉树中，最后求这棵AVL Tree的根结点中的数值。

思路：

　　首先应该清楚，在构建的过程中四种旋转的的情况。应该先利用递归将结点插入，然后再判断是否需要旋转。

Code：

#include <bits/stdc++.h>

using namespace std;

typedef struct Node* node;

struct Node {
    int val;
    node left;
    node right;
    Node(int v) {
        val = v;
        left = NULL;
        right = NULL;
    }
};

node rightRotate(node root) {
    node temp = root->left;
    root->left = temp->right;
    temp->right = root;
    return temp;
}

node leftRotate(node root) {
    node temp = root->right;
    root->right = temp->left;
    temp->left = root;
    return temp;
}

node rightLeft(node root) {
    root->right = rightRotate(root->right);
    return leftRotate(root);
}

node leftRight(node root) {
    root->left = leftRotate(root->left);
    return rightRotate(root);
}

int findHeight(node root) {
    if (root == NULL) return 0;
    int l = findHeight(root->left);
    int r = findHeight(root->right);
    return max(l, r) + 1;
}

void insertNode(node& root, int val) {
    if (root == NULL) {
        root = new Node(val);
    } else if (root->val > val) {
        insertNode(root->left, val);
        int l = findHeight(root->left);
        int r = findHeight(root->right);
        if (abs(r - l) > 1) {
            if (root->left->val > val) {
                root = rightRotate(root);
            } else {
                root = leftRight(root);
            }
        }
    } else {
        insertNode(root->right, val);
        int l = findHeight(root->left);
        int r = findHeight(root->right);
        if (abs(r - l) > 1) {
            if (root->right->val < val) {
                root = leftRotate(root);
            } else {
                root = rightLeft(root);
            }
        }
    }
}

void preTraveser(node root) {
    if (root == NULL) return;
    cout << root->val << " ";
    preTraveser(root->left);
    preTraveser(root->right);
}

int main() {
    int n, t;
    cin >> n;
    node root = NULL;
    for (int i = 0; i < n; ++i) {
        cin >> t;
        insertNode(root, t);
    }
    cout << root->val << endl;
    return 0;
}