04-树5-树4 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

 就只是训练AVL树的一些基本操作

#include<stdio.h>
#include<malloc.h>
typedef struct TreeNode* AVLTree;
struct TreeNode{
	AVLTree left;
	AVLTree right;
	int elem;
	int height; 
};
AVLTree SingleLeftRotate(AVLTree T);
AVLTree SingleRightRotate(AVLTree T);
AVLTree DoubleRightLeft(AVLTree T);
AVLTree DoubleLeftRight(AVLTree T);
int MAX(int a, int b){
	return (a>b)?a:b;
}
int Height(AVLTree T){
	if (T == NULL)
		return -1;
	else
		return T->height;
}
AVLTree Insert(AVLTree T, int data){
	if ( T == NULL){
		T = (AVLTree)malloc(sizeof(struct TreeNode));
		T->elem = data;
		T->left = T->right = NULL;
		T->height = 0;
	}
	if (data < T->elem){
		T->left = Insert(T->left, data);
		if (Height(T->left) - Height(T->right) == 2)
			if (data < T->left->elem)
				T = SingleLeftRotate(T);
			else
				T = DoubleLeftRight(T);
	}
	else
	if (data > T->elem){
		T->right = Insert(T->right, data);
		if (Height(T->right) - Height(T->left) == 2){
			if (data > T->right->elem)
				T = SingleRightRotate(T);
			else
				T = DoubleRightLeft(T);
		}
	}
	T->height = MAX(Height(T->left),Height(T->right)) + 1;
	return T;
}

AVLTree SingleLeftRotate(AVLTree T){
	AVLTree temp;
	temp = T->left;
	T->left = temp->right;
	temp->right = T;
	T->height = MAX(Height(T->left),Height(T->right)) + 1;
    temp->height = MAX(Height(temp->left), Height(temp->right)) + 1;
	return temp;
}
AVLTree DoubleLeftRight(AVLTree T){
	T->left = SingleRightRotate(T->left);
	T = SingleLeftRotate(T);
	return T;
} 

AVLTree SingleRightRotate(AVLTree T){
	AVLTree temp;
	temp = T->right;
	T->right = temp->left;
	temp->left = T;
	T->height = MAX(Height(T->left),Height(T->right)) + 1;
	temp->height = MAX(Height(temp->left),Height(temp->right)) + 1;
	return temp;
}
AVLTree DoubleRightLeft(AVLTree T){
	T->right = SingleLeftRotate(T->right);
	T = SingleRightRotate(T);
	return T;
}
int main(){
	int N;
	int i;
	int data;
	AVLTree T = NULL;
	scanf("%d",&N);
	for ( i = 0; i < N; i++){
		scanf("%d",&data);
		T = Insert(T, data);
	}
	printf("%d", T->elem);
}