1066. Root of AVL Tree (25)【AVL树】——PAT (Advanced Level) Practise

最新推荐文章于 2018-03-09 16:29:30 发布

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最新推荐文章于 2018-03-09 16:29:30 发布

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本文介绍了一种自平衡二叉搜索树——AVL树的实现方法。通过旋转操作确保树的高度平衡，并给出了具体的代码实现及示例输入输出。

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题目信息

1066. Root of AVL Tree (25)

时间限制100 ms
内存限制65536 kB
代码长度限制16000 B

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.
这里写图片描述

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 ythe 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

解题思路

建个avl树，没啥技巧

AC代码

#include <cstdio>
#include <algorithm>
using namespace std;
struct node{
    node *left, *right;
    int v, w;
    node(int value, node* l, node* r) : v(value), left(l), right(r), w(0) {}
};
node *nil = new node(0, NULL, NULL);
node *head = nil;
void leftrotate(node *&head){
    node *t = head->right;
    head->right = t->left;
    t->left = head;
    head = t;
    head->left->w = max(head->left->right->w, head->left->left->w) + 1;
    head->w = max(head->right->w, head->left->w) + 1;
}
void rightrotate(node *&head){
    node *t = head->left;
    head->left = t->right;
    t->right = head;
    head = t;
    head->right->w = max(head->right->right->w, head->right->left->w) + 1;
    head->w = max(head->right->w, head->left->w) + 1;
}
void insert(node *&head, int v){
    if (head == nil){
        head = new node(v, nil, nil);
    }else if (v > head->v){
        insert(head->right, v);
        if (2 == head->right->w - head->left->w){
            if (v > head->right->v){
                leftrotate(head);
            }else{
                rightrotate(head->right);
                leftrotate(head);
            }
        }
    }else{
        insert(head->left, v);
        if (2 == head->left->w - head->right->w){
            if (v <= head->left->v){
                rightrotate(head);
            }else{
                leftrotate(head->left);
                rightrotate(head);
            }
        }
    }
    head->w = max(head->left->w, head->right->w) + 1;
}
int main()
{
    int n, a;
    scanf("%d", &n);
    while (n--){
        scanf("%d", &a);
        insert(head, a);
    }
    printf("%d\n", head->v);
    return 0;
}