PAT甲级1066 Root of AVL Tree (25 分)

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

 AVL树对我来说一直整不明白，太难了。

输出中位数也可以得到大部分结果，舒服了

#include<cstdio>
#include<algorithm>
using namespace std;
const int maxn = 30;
int n;
int num[maxn];

int main(){
    scanf("%d", &n);
    for(int i = 1; i <= n; i++){
        scanf("%d", &num[i]);
    }
    sort(num + 1, num + n + 1);
    if(n % 2 == 0)
        printf("%d", num[n / 2] );
    else
        printf("%d", num[ (n + 1) / 2] );
}

多重括号，容易发生错误 

#include<cstdio>
#include<algorithm>
using namespace std;
struct node {
	int v, height;
	node* lchild, * rchild;
}*root;

node* newNode(int v) {
	node* Node = new node;
	Node->v = v;
	Node->height = 1;
	Node->lchild = Node->rchild = NULL;
	return Node;
}

int getHeight(node* root) {
	if (root == NULL) return 0;
	return root->height;
}
void updateHeight(node* root) {
	root->height = max(getHeight(root->lchild), getHeight(root->rchild)) + 1;
}
int getBalanceFactor(node* root) {
	return getHeight(root->lchild) - getHeight(root->rchild);
}

void R(node*& root) {
	node* temp = root->lchild;
	root->lchild = temp->rchild;
	temp->rchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}

void L(node*& root) {
	node* temp = root->rchild;
	root->rchild = temp->lchild;
	temp->lchild = root;
	updateHeight(root);
	updateHeight(temp);
	root = temp;
}

void insert(node*& root, int v) {
	if (root == NULL) {
		root = newNode(v);
		return;
	}
	if (v < root->v) {
		insert(root->lchild, v);
		updateHeight(root);
		if (getBalanceFactor(root) == 2) {
			if (getBalanceFactor(root->lchild) == 1) { // LL型
				R(root);
			}
			else if (getBalanceFactor(root->lchild) == -1) {// LR
				L(root->lchild);
				R(root);
			}
		}
	}
		else {
			insert(root->rchild, v);
			updateHeight(root);
			if (getBalanceFactor(root) == -2) {
				if (getBalanceFactor(root->rchild) == -1) {
					L(root);
				}
				else if (getBalanceFactor(root->rchild) == 1) {
					R(root->rchild);
					L(root);
				}
			}
		}
	
}


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