题目描述

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

Sample Input 2:

7
88 70 61 96 120 90 65

Sample Output 2:

88

考点

平衡二叉树的插入

思路

如何平衡二叉树
平衡二叉树的失衡调整主要是通过旋转最小失衡子树来实现的。总共有LL、LR、RL、RR四种情况，分别对应右旋、左旋、先右旋再左旋、先左旋再右旋。RL和LR都可以调用LL、RR的代码实现。

代码

#include <iostream>
#include <algorithm>
using namespace std;
typedef struct node {
    int data;
    struct node *left, *right;
}node;
node *LRotate(node *p) {
    node *q = p->right;
    p->right = q->left;
    q->left = p;
    return q;
}
node *RRotate(node *p) {
    node *q = p->left;
    p->left = q->right;
    q->right = p;
    return q;
}
node *LRRotate(node *p) {
    p->left = LRotate(p->left);
    return RRotate(p);
}
node *RLRotate(node *p) {
    p->right = RRotate(p->right);
    return LRotate(p);
}
int getHeight(node *p) {
    if (p == NULL) return 0;
    return max(getHeight(p->left), getHeight(p->right)) + 1;
}
node *insert(node *p, int data) {
    if (p == NULL) {
        p = new node();
        p->data = data;
    }
    else if (p->data > data) {
        p->left = insert(p->left, data);
        if (abs(getHeight(p->left) - getHeight(p->right)) >= 2) {
            if (p->left->data > data) p = RRotate(p);
            else p = LRRotate(p);
        }
    }
    else {
        p->right = insert(p->right, data);
        if (abs(getHeight(p->left) - getHeight(p->right)) >= 2) {
            if (p->right->data < data) p = LRotate(p);
            else p = RLRotate(p);
        }
    }
    return p;
}
int main() {
    int n, i;
    cin >> n;
    node *p = NULL;
    for (i = 0; i < n; i++) {
        int d;
        cin >> d;
        p=insert(p, d);
    }
    cout << p->data;
    return 0;
}