1123 Is It a Complete AVL Tree (30point(s)) - C语言 PAT 甲级

1123 Is It a Complete AVL Tree (30point(s))

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 output the level-order traversal sequence of the resulting AVL tree, and to tell if it is a complete binary tree.

Input Specification:

Each input file contains one test case. For each case, the first line contains a positive integer N (≤ 20). 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, insert the keys one by one into an initially empty AVL tree. Then first print in a line the level-order traversal sequence of the resulting AVL tree. All the numbers in a line must be separated by a space, and there must be no extra space at the end of the line. Then in the next line, print YES if the tree is complete, or NO if not.

Sample Input:

5
88 70 61 63 65

Sample Output:

70 63 88 61 65
YES

Sample Input:

8
88 70 61 96 120 90 65 68

Sample Output:

88 65 96 61 70 90 120 68
NO

题目大意：

输入 N 个节点插入 AVL 树中，

输出 AVL 树的层序遍历，并判断是否为完全二叉树

设计思路：

• 建树直接上 AVL 代码
• 层序遍历用队列遍历
• 判断完全二叉树
  • 若一个节点没有孩子节点，则这个节点后的所有节点也没有孩子节点，即为完全二叉树
  • 否则不是完全二叉树

编译器：C (gcc)

#include <stdio.h>
#include <stdlib.h>

struct node {
        int d;
        struct node *left, *right;
};

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

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

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

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

struct node *right_left_rotate(struct node *root)
{
        root->right = right_rotate(root->right);
        return left_rotate(root);
}
struct node *left_right_rotate(struct node *root)
{
        root->left = left_rotate(root->left);
        return right_rotate(root);
}

struct node *insert(struct node *root, int d)
{
        if (root == NULL) {
                root = (struct node *)malloc(sizeof(struct node));
                root->d = d;
                root->left = NULL;
                root->right = NULL;
        } else if (d < root->d) {
                root->left = insert(root->left, d);
                if (get_height(root->left) - get_height(root->right) == 2)
                                root = d < root->left->d ? right_rotate(root) : left_right_rotate(root);
        } else {
                root->right = insert(root->right, d);
                if (get_height(root->left) - get_height(root->right) == -2)
                        root = d > root->right->d ? left_rotate(root) : right_left_rotate(root);
        }
        return root;
}

int main(void)
{
        int n;
        int i, t;
        struct node *root = NULL;
        scanf("%d", &n);
        for (i = 0; i < n; i++) {
                scanf("%d", &t);
                root = insert(root, t);
        }

        struct node *p[20], *temp;
        int front, rear, cnt;
        int child_null = 0, complete = 1;
        p[0] = root;
        front = 0;
        rear = 1;
        cnt = 1;
        while (cnt) {
                temp = p[front++];
                cnt--;
                printf("%s%d", temp == root ? "" : " ", temp->d);
                if (temp->left != NULL) {
                        if (child_null)
                                complete = 0;
                        p[rear++] = temp->left;
                        cnt++;
                } else {
                        child_null = 1;
                }

                if (temp->right != NULL) {
                        if (child_null)
                                complete = 0;
                        p[rear++] = temp->right;
                        cnt++;
                } else {
                        child_null = 1;
                }
        }
        printf("\n%s", complete ? "YES" : "NO");

        return 0;
}