Root of AVL Tree

• 题目描述：
  

• 题目思路：

这道题主要为了考察对AVL树的插入与旋转等操作。

• C语言实现

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

struct AVLNode
{
	int Data;  //节点数据
	struct AVLNode* Left;  //指向左子树
	struct AVLNode* Right;  //指向右子树
	int Height;  //树高
};

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

//返回树的高度
int GetH(struct AVLNode* T)
{
	if (T)
	{
		return T->Height;
	}
	else
	{
		return -1;
	}
}

//右单旋 RR
struct AVLNode* RR(struct AVLNode* A)
{
	struct AVLNode* B;  //旋转后的根节点
	B = A->Right;
	A->Right = B->Left;
	B->Left = A;
    //更新树的高度
	A->Height = Max(GetH(A->Left),GetH(A->Right)) + 1;
	B->Height = Max(GetH(B->Left),A->Height) + 1;
	return B;
}

struct AVLNode* LL(struct AVLNode* A)
{
	struct AVLNode* B;
	B = A->Left;
	A->Left = B->Right;
	B->Right = A;
	A->Height = Max(GetH(A->Left),GetH(A->Right)) + 1;
	B->Height = Max(GetH(B->Left), A->Height) + 1;
	return B;
}

//LR双旋直接实现
struct AVLNode* LR(struct AVLNode* A)
{
	struct AVLNode* B, *C;
	B = A->Left;
	C = B->Right;
	B->Right = C->Left;
	A->Left = C->Right;
	C->Left = B;
	C->Right = A;

	B->Height = Max(GetH(B->Left), GetH(B->Right)) + 1;
	A->Height = Max(GetH(A->Left),GetH(A->Right)) + 1;
	C->Height = Max(B->Height,A->Height) + 1;
	return C;
}

//RL双旋直接实现
struct AVLNode* RL(struct AVLNode* A)
{
	struct AVLNode* B, *C;
	B = A->Right;
	C = B->Left;
	B->Left = C->Right;
	A->Right = C->Left;
	C->Left = A;
	C->Right = B;

	B->Height = Max(GetH(B->Left), GetH(B->Right)) + 1;
	A->Height = Max(GetH(A->Left), GetH(A->Right)) + 1;
	C->Height = Max(A->Height, B->Height) + 1;
	return C;
}

//作用:将x插入AVL树T中，并且返回调整后的AVL树
struct AVLNode* Insert(struct AVLNode* T, int x)
{
	if (!T)
	{
		//若插入空树 则新建包含一个节点的树
		T = (struct AVLNode*)malloc(sizeof(struct AVLNode));
		T->Data = x;
		T->Left = NULL;
		T->Right = NULL;
		T->Height = 0;
	}
	else if (x < T->Data)
	{
		//插入T的左子树
		T->Left = Insert(T->Left, x);
		
		//如果需要左旋
		if (GetH(T->Left) - GetH(T->Right)  == 2)
		{
			if (x < T->Left->Data)
			{
				//左单旋
				T = LL(T);
			}
			else
			{
				//左右双旋
				T = LR(T);
			}
		}
	}
	else if (x > T->Data)
	{
		//插入T的右子树
				//插入T的左子树
		T->Right = Insert(T->Right, x);

		//如果需要左旋
		if (GetH(T->Left) - GetH(T->Right) == -2)
		{
			if (x > T->Right->Data)
			{
				//右单旋
				T = RR(T);
			}
			else
			{
				//右左双旋
				T = RL(T);
			}
		}

	}//else if 插入右子树结束

	//更新树高
	T->Height = Max(GetH(T->Left),GetH(T->Right)) + 1;
	return T;
}

int main()
{
	int N;
	int K;
	struct AVLNode* T = NULL;
	scanf("%d",&N);
	for (int i = 0; i< N;i++)
	{
		scanf("%d",&K);
		T = Insert(T, K);
	}
	printf("%d",T->Data);
	//system("pause");
	return 0;
}