《大话数据结构》中平衡二叉树创建源码

最新推荐文章于 2024-05-29 23:09:00 发布

原创最新推荐文章于 2024-05-29 23:09:00 发布 · 208 阅读

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CC 4.0 BY-SA版权

本文介绍了一种自平衡二叉查找树——AVL树的插入操作及左右旋转实现平衡的过程。通过具体代码展示了如何在插入节点后维持AVL树的高度平衡特性，并提供了一个简单的示例程序用于验证。

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#include <bits/stdc++.h>
using namespace std;

//左高、等高、右高
#define LH 1
#define EH 0
#define RH -1
enum Status { False, Success };
//定义树的数据类型
typedef int Type;
typedef struct Tree {
	Type data;
	int bf;  
	struct Tree *lchild, *rchild;
}Tree;

//左旋
Status R_Rotate(Tree **T)
{
	Tree *p = (*T)->lchild;
	(*T)->lchild = p->rchild;
	p->rchild = *T;
	*T = p;
	return Success;
}

//右旋
Status L_Rotate(Tree **T)
{
	Tree *p = (*T)->rchild;
	(*T)->rchild = p->lchild;
	p->lchild = *T;
	*T = p;
	return Success;
}

//左平衡:说明左边高了
Status LeftBalance(Tree **T)
{
	Tree *p = (*T)->lchild;
	switch (p->bf)
	{
		case LH:
		{
			(*T)->bf = p->bf = EH;
			R_Rotate(T);
			break;
		}	
		case RH:
		{
			Tree *rp = p->rchild;
			switch (rp->bf)
			{
				case LH:
				{
					(*T)->bf = RH;
					p->bf = EH;
					goto END;
				}
				case EH:
				{
					(*T)->bf = EH;
					p->bf = EH;
					goto END;
				}
				case RH:
				{
					(*T)->bf = EH;
					p->bf = LH;
					goto END;
				}
				END:
				{
					rp->bf = EH;
					L_Rotate(&p);
					R_Rotate(T);
				}
			}
		}
	}
	return Success;
}

//右平衡:说明右边高了
Status RightBalance(Tree **T)
{
	Tree *p = (*T)->rchild;
	switch (p->bf)
	{
	case RH:
	{
		(*T)->bf = p->bf = EH;
		L_Rotate(T);
		break;
	}
	case LH:
	{
		Tree *lp = p->lchild;
		switch (lp->bf)
		{
		case LH:
		{
			(*T)->bf = EH;
			p->bf = RH;
			goto END;
		}
		case EH:
		{
			(*T)->bf = EH;
			p->bf = EH;
			goto END;
		}
		case RH:
		{
			(*T)->bf = LH;
			p->bf = EH;
			goto END;
		}
	END:
		{
			lp->bf = EH;
			R_Rotate(&p);
			L_Rotate(T);
		}
		}
	}
	}
	return Success;
}

Status InsertAVL(Tree **T, Type key, bool &taller)
{
	//没找到
	if (!(*T))
	{
		*T = (Tree *)malloc(sizeof(Tree));
		(*T)->lchild = (*T)->rchild = NULL;
		(*T)->data = key;
		(*T)->bf = EH;
		taller = true;
	}
	else
	{
		if (key == (*T)->data)
		{
			taller = false;
			return False;
		}
		if ((*T)->data > key)
		{
			if (!InsertAVL(&((*T)->lchild), key, taller))
				return False;
			if (taller)
			{
				switch ((*T)->bf)
				{
				case LH:
				{
					LeftBalance(T);
					taller = false;
					break;
				}
				case EH:
				{
					(*T)->bf = LH;
					taller = false;
					break;
				}
				case RH:
				{
					(*T)->bf = EH;
					taller = false;
					break;
				}
				}
			}
		}
		else
		{
			if (!InsertAVL(&((*T)->rchild), key, taller))
				return False;
			if (taller)
			
{
				switch ((*T)->bf)
				{
				case LH:
				{
					(*T)->bf = EH;
					taller = false;
					break;
				}
				case EH:
				{
					(*T)->bf = RH;
					taller = false;
					break;
				}
				case RH:
				{
					LeftBalance(T);
					taller = false;
					break;
				}
				}
			}
		}
	}
	return Success;
}

//先序遍历
void Ergodic(Tree *T)
{
	if (T)
	{
		Ergodic(T->lchild);
		cout << T->data<<" ";
		Ergodic(T->rchild);
	}
}

int main()
{
	int a[] = { 3,2,1,4,5,6,7,10,9,8 };
	Tree *T = NULL;
	bool taller = false;
	for (auto i : a)
	{
		InsertAVL(&T, i, taller);
	}
	Ergodic(T);
	return 0;
}