Find - binary sort tree

First, the definition

Binary sort tree (Binary Sort Tree) or an empty tree, or to meet the following properties of a non-null binary tree T:

1. If the left subtree of T is not empty, then the left subtree of all the nodes is smaller than the value of the root of T;
2. If the right subtree of T is not empty, all the right subtree root node is greater than the value of T;
3. T left subtree and right subtree are binary sort tree.

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Second, find keywords

(1) algorithm ideas

(2) achieve

typeof struct BTNode
{
	int key;
	struct BTNode *lchild;
	struct BTNode *rchild;
}BTNode;

BTNode * BSTsearch(BTNode *bt,int key)
{
	if(bt==NULL)
		return NULL;
	else
	{
		if(bt->key==key)
			return bt;	//	等于根结点中的关键字，查找成功，返回关键字所在的结点指针
		else if(key<bt->key)
			return BSTsearch(bt->lchild,key);
		else
			return BSTsearch(bt->rchild,key);
	}
}

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Third, insert keywords

(1) algorithm ideas

(2) achieve

typeof struct BTNode
{
	int key;
	struct BTNode *lchild;
	struct BTNode *rchild;
}BTNode;

int BSTinsert(BTNode *&bt,int key)	//	因为指针bt要改变，所以要用引用型指针
{
	if(bt==NULL)
	{
		bt=(BTNode*)malloc(sizeof(BTNode));	//	创建新结点
		bt->lchild=bt->lchild=NULL;
		bt->key=key;
		return 1;	//	插入成功，返回1
	}
	else
	{
		if(bt->key==key)
			return -1;	//	等于根结点中的关键字，插入失败，返回-1
		else if(key<bt->key)
			return BSTsearch(bt->lchild,key);
		else
			return BSTsearch(bt->rchild,key);
	}
}

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Create four binary sort tree

(1) algorithm ideas

(2) achieve

void CreateBST(BTNode *&bt,int key[],int n)
{
	int i;
	bt=NULL;	//	将树清空
	for(i=0;i<n;i++)
		BSTinsert(bt,key[i]);
}

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V. delete keywords

(1) algorithm ideas

When you delete a keyword in the binary sort tree, not to the node where the key is the root of the subtree are deleted, but only delete a node, and retention characteristics binary sort tree. Procedure to remove the node p is divided into the following three cases

1. p is a leaf node the node (if the node p 21)

• Deleted directly
  

2. p junction only, without the right subtree of the left subtree, and no or only a left subtree right subtree. (If p is the node 56)

• At this time, only you need to delete p, then p subtree pointer connected directly connected to the original p f to its parent node.

3. p nodes have both left subtree right subtree. (If p junction 64, then node 56 r)

• The root node in the left subtree pointer p has a right to go right, until a node went right subtree rightmost
• It is then replaced by p r keywords in the keyword.
• Final judgment, if r is a leaf node, then according to (1) Method remove r; r if non-leaf node, then according to (2) Method remove r.