04-树5 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 $N$ ($\le 20$) 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

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

#define MaxTree 10
#define Null -1
#define ERROR -1

typedef int ElementType;
typedef struct AVLNode *AVLTree;
struct AVLNode {
	ElementType Element;
	AVLTree Left, Right;
	int Height;
};

int Max(int a, int b);
int GetHeight(AVLTree A);
AVLTree SingleLL(AVLTree A);
AVLTree SingleRR(AVLTree A);
AVLTree DoubleLR(AVLTree A);
AVLTree DoubleRL(AVLTree A);
AVLTree Insert(AVLTree T, ElementType ElemX);

int main()
{
	int i, N, ElemX;
	AVLTree T1;
	scanf("%d\n%d", &N,&ElemX);

	T1 = (AVLTree)malloc(sizeof(struct AVLNode));
	T1->Element = ElemX;
	T1->Height = 0;
	T1->Left = T1->Right = NULL;

	for (i = 1; i < N; i++)
	{
		scanf("%d", &ElemX);
		T1 = Insert(T1, ElemX);
	}

	printf("%d\n", T1->Element);
	system("pause");
	return 0;
}

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

int GetHeight(AVLTree A)
{
	int Height;
	if (!A)
		Height = 0;
	else
		Height = Max(GetHeight(A->Left), GetHeight(A->Right))+1;
	return Height;
}

AVLTree SingleLL(AVLTree A)
{
	AVLTree B = A->Left;
	A->Left = B->Right;
	B->Right = A;

	A->Height = Max(GetHeight(A->Right), GetHeight(A->Left)) + 1;
	B->Height = Max(GetHeight(B->Right), GetHeight(B->Left)) + 1;

	return B;
}

AVLTree SingleRR(AVLTree A)
{
	AVLTree B = A->Right;
	A->Right = B->Left;
	B->Left = A;

	A->Height = Max(GetHeight(A->Right), GetHeight(A->Left)) + 1;
	B->Height = Max(GetHeight(B->Right), GetHeight(B->Left)) + 1;

	return B;
}

AVLTree DoubleLR(AVLTree A)
{
	/* 将A、B与C做两次单旋，返回新的根结点C */

	/* 将B与C做右单旋，C被返回 */
	A->Left = SingleRR(A->Left);
	/* 将A与C做左单旋，C被返回 */
	return SingleLL(A);
}

AVLTree DoubleRL(AVLTree A)
{
	A->Right = SingleLL(A->Right);

	return SingleRR(A);
}

AVLTree Insert(AVLTree T, ElementType ElemX)
{
	if (!T)
	{
		T = (AVLTree)malloc(sizeof(struct AVLNode));
		T->Element = ElemX;
		T->Height = 0;
		T->Left = T->Right = NULL;
	}
	else if (ElemX < T->Element)
	{
		T->Left = Insert(T->Left, ElemX);
		if (GetHeight(T->Left) - GetHeight(T->Right)==2)
		if (ElemX < T->Left->Element)
			T = SingleLL(T);
		else
			T = DoubleLR(T);
	}
	else if (ElemX>T->Element)
	{
		T->Right = Insert(T->Right, ElemX);
		if (GetHeight(T->Right) - GetHeight(T->Left) == 2)
		if (ElemX > T->Right->Element)
			T = SingleRR(T);
		else
			T = DoubleRL(T);
	}

	T->Height = Max(GetHeight(T->Left), GetHeight(T->Right)) + 1;

	return T;
}