PAT 甲级 1066 Root of AVL Tree

Posted 2021-02-08 zlrrrr

https://pintia.cn/problem-sets/994805342720868352/problems/994805404939173888

 

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 Ndistinct 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

 

代码：

#include <bits/stdc++.h>
using namespace std;
struct node {
    int val;
    struct node *left, *right;
};
node *rotateLeft(node *root) {
    node *t = root -> right;
    root -> right = t -> left;
    t -> left = root;
    return t;
}

node *rotateRight(node *root) {
    node *t = root -> left;
    root -> left = t -> right;
    t -> right = root;
    return t;
}

node *rotateLeftRight(node *root) {
    root -> left = rotateLeft(root -> left);
    return rotateRight(root);
}

node *rotateRightLeft(node *root) {
    root -> right = rotateRight(root -> right);
    return rotateLeft(root);
}

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

node *insert(node *root, int val) {
    if(root == NULL) {
        root = new node();
        root -> val = val;
        root -> left = root -> right = NULL;
    } else if(val < root -> val) {
        root -> left = insert(root -> left, val);
        if(getHeight(root -> left) - getHeight(root -> right) == 2)
            root = val < root -> left -> val ? rotateRight(root) : rotateLeftRight(root);
    } else {
        root -> right = insert(root -> right, val);
        if(getHeight(root -> left) - getHeight(root -> right) == -2)
            root = val > root -> right -> val ? rotateLeft(root) : rotateRightLeft(root);
    }
    return root;
}

int main() {
    int n, val;
    scanf("%d", &n);
    node *root = NULL;
    for(int i = 0; i < n; i ++) {
        scanf("%d", &val);
        root = insert(root, val);
    }
    printf("%d", root -> val);
    return 0;
}

　　AVL 树的模板题 第一次写 AVL 树 还不是很会 还有那么多题没写 不会的越来越多？烦

FH