二叉树（数据结构）

时间：2025-03-14 08:04:08

介绍

  • 树（Tree）是n(n >= 0)个结点的有限集合，n = 0 时称为空树。在任意一棵非空树中：
    (1)有且仅有一个特定的称为根(Root)的结点；
    (2)当n > 1 时，其余结点可分为m(m > 0)个互不相交的有限集T1,T2,……Tm，其中每个集合本身又是一棵树，并且称为根的子树(SubTree);
  • 注意两点：(1) 根节点是唯一的；(2) 子树互不相交。

二叉树

  • 二叉树是一种特殊的树，它的特点是每个结点最多有两个子树（即二叉树的度不能大于2），并且二叉树的子树有左右之分，其次序不能颠倒。
  • 一棵深度为k 且有2^k -1 个结点的二叉树称为满二叉树。
  • 如果有深度为k 的，有n 个结点的二叉树，如果其每一个结点都与深度为k 的满二叉树中编号从1 至n 的结点一一对应，则称之为完全二叉树。
  • 二叉树性质：
    性质1：在二叉树的第i 层上最多有2^(i – 1)个结点。
    性质2：深度为k 的二叉树至多有2^i – 1 个结点。
/*************************************************************************
	> File Name: 
	> Author: mrhjlong
	> Mail: mrhjlong@ 
	> Created Time: 2016年05月07日 星期六 09时57分04秒
 ************************************************************************/

#include<>
#include<>
#include<>
#include<>

typedef int type_t;

typedef struct node
{
	type_t data;

	struct node *left;
	struct node *right;
}Node;

//创建结点
Node *node_create(type_t data)
{
	Node *p = (Node *)malloc(sizeof(Node));

	p->data = data;
	p->left = NULL;
	p->right = NULL;

	return p;
}

//中序遍历
void tree_in_order(Node *tree)
{
	if(tree == NULL)
		return;
	else
	{
		tree_in_order(tree->left);
		printf("in: %d\n", tree->data);
		tree_in_order(tree->right);
	}
}

//前序遍历
void tree_pre_order(Node *tree)
{
	if(tree == NULL)
		return;
	else
	{
		printf("pre: %d\n", tree->data);
		
		tree_pre_order(tree->left);
		tree_pre_order(tree->right);
	}
}

//后序遍历
void tree_post_order(Node *tree)
{
	if(tree == NULL)
		return;
	else
	{
		tree_post_order(tree->left);
		tree_post_order(tree->right);
		printf("next: %d\n", tree->data);
	}
}

void node_insert_by_recursion(Node **pTree, Node *pNode)
{
	if(*pTree == NULL)
	{
		*pTree = pNode;
	}
	else if((*pTree)->data >= pNode->data)
	{
		node_insert_by_recursion(&((*pTree)->left), pNode);
	}
	else
	{
		node_insert_by_recursion(&((*pTree)->right), pNode);
	}
}

void node_insert(Node **pTree, Node *pNode)
{
	if(*pTree == NULL)
	{
		*pTree = pNode;
	}
	else
	{
		Node *p = *pTree;
		Node *pre = p;
		while(p != NULL)
		{
			pre = p;
			if(pNode->data <= p->data)
				p = p->left;
			else
				p = p->right;
		}
		
		if(pNode->data <= pre->data)
		{
			pre->left = pNode;
		}
		else
		{
			pre->right = pNode;
		}
	}
}

//查找结点
Node *tree_search_by_recursion(Node *tree, type_t data)
{
	if(tree == NULL)
	{
		printf("%d is not found!\n", data);
		return NULL;
	}
	else if(tree->data == data)
	{
		return tree;
	}
	else if(data <= tree->data)
	{
		tree_search_by_recursion(tree->left, data);
	}
	else
	{
		tree_search_by_recursion(tree->right, data);
	}
}

Node *tree_search(Node *tree, type_t data)
{
	Node *p = tree;
	while(p != NULL)
	{
		if(p->data == data)
			return p;
		else if(data <= p->data)
			p = p->left;
		else
			p = p->right;
	}

	return p;
}

//求二叉树高度
int tree_height(Node *tree)
{
	int left = 0;
	int right = 0;

	if(tree == NULL)
		return 0;
	else
	{
		left = 1 + tree_height(tree->left);
		right = 1 + tree_height(tree->right);
		return (left > right ? left : right);
	}
}

//销毁二叉树
void tree_destroy(Node **pTree)
{
	if(*pTree == NULL)
		return;
	else
	{
		tree_destroy(&((*pTree)->left));
		tree_destroy(&((*pTree)->right));
		free(*pTree);
		*pTree = NULL;
	}
}

//删除结点
void node_delete(Node **pTree,type_t data)
{
	Node *pFind = *pTree;
	Node *pParent = NULL;

	//查找要删除的结点及其父结点
	while(pFind != NULL)
	{
		if(pFind->data == data)
			break;
		else if(data < pFind->data)
		{
			pParent = pFind;
			pFind = pFind->left;
		}
		else
		{
			pParent = pFind;
			pFind = pFind->right;
		}
	}

	if(pFind == NULL)
		return;
	else if(pFind->left == NULL || pFind->left->right == NULL)
	{
		if(pParent == NULL)
		{
			*pTree = pFind->right;
		}
		else
		{
			if(pParent->left == pFind)
				pParent->left = pFind->right;
			else
				pParent->right = pFind->right;
		}
		free(pFind);
		return;
	}
	else
	{
		pParent = pFind->left;
		Node *pos = pParent->right;
		while(pos->right != NULL)
		{
			pParent = pos;
			pos = pos->right;
		}
		pParent->right = pos->left;
		pFind->data = pos->data;
		free(pos);
		return;
	}
	

}


int main()
{
	Node *tree = NULL;
	int a[] = {45, 23, 65, 100, 29, 55, 89, 10, 3, 43, 36};
	int i = 0;
	Node *p = NULL;
	
	for(i = 0; i < sizeof(a) / sizeof(a[0]); i++)
	{
		p = node_create(a[i]);
		node_insert(&tree, p);
	}

//	tree_destroy(&tree);
	Node *pSea = tree_search(tree, 36);
	if(pSea != NULL)
	{
		printf("search: %d\n", pSea->data);
		printf("pSea: %p\n", pSea);
		printf("pNode: %p\n", p);
	}
	printf("height: %d\n", tree_height(tree));

	node_delete(&tree, 29);	

	tree_in_order(tree);
	printf("\n");
	tree_pre_order(tree);
	printf("\n");
	tree_post_order(tree);

	return 0;
}

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