二叉排序树BST

二叉排序树BST

一. SearchBST(T, key)

伪代码

void SearchBST(BiTree& T, int key) {

	if (T为空)
		cout<<"没有该元素";
	else if (T->data == key)
		cout<< "查找成功";
	else if (key < T->data)
		递归查找左子树;
	else
		递归查找右子树;
}

代码实现

void SearchBST(BiTree& T, int key) {

	if (T == NULL)
		cout<<"没有该元素";
	else if (T->data == key)
		cout<< "查找成功";
	else if (key < T->data)
		SearchBST(T->lchild, key);
	else
		SearchBST(T->rchild, key);
}

二. InsertBST(T, key)

伪代码：

void InsertBST(BiTree& T, int key)
{

	if (T为空)
	{
		创建一个新节点T;
		T->data == key;
		T->lchild = T->rchild = NULL;
	}
	else if (T->data == key)
			输出错误;
	else if (T->data > key)
		InsertBST(T->lchild, key);
	else
		InsertBST(T->rchild, key);

}		

代码实现：

void InsertBST(BiTree& T, int key)
{

	if (T == NULL)
	{
		T = new BiTNode;
		T->data = key;
		T->lchild = T->rchild = NULL;
	}
	else if (T->data == key)
		cout << "此数存在";
	else if (T->data > key)
		InsertBST(T->lchild, key);
	else
		InsertBST(T->rchild, key);

}

三. CreateBST(T)

伪代码：

void CreateBST(BiTree &T)
{
	
	输入二叉排序树节点个数n;
	int a[n];
	cout << "输入数据，中间空格";
	for (int i = 0;i < n;i++)
	{
		cin >> a[i];
		InsertBST(T, a[i]);
	}
	
}

代码实现：

void CreateBST(BiTree &T)
{
	int n;
	cout<< "输入添加的节点个数"<<endl;
	cin >> n;
	int a[100];
	cout << "输入数据，中间空格"<<endl;
	for (int i = 0;i < n;i++)
	{
		cin >> a[i];
		InsertBST(T, a[i]);
	}
}

四. DeleteBST(T, key)

伪代码：

void DeleteBST(BiTree &T, int key)
{
	if (!T)
		cout << "error";
	else
	{
		if (T->data == key)
		{
			删除节点;//分三种情况
			{
				BiTree q, s;
				if (没有左孩子)
				{
					q = T;
					T指向右孩子;
					删除q节点;
				}
				else if (没有右孩子)
				{
					q = T;
					T指向左孩子;
					删除q节点;
				}
				else//两个孩子都有
				{
					q = T;
					s = q->lchild;
					while (s->rchild)
					{
						q = s;
						s = s->rchild;
					}
					T->data = s->data;
					if (q != T)
					{
						q->rchild = s->lchild;
					}
					else
					{
						q->lchild = s->lchild;
					}
					delete s;
				}
			}
			  
			cout << "删除成功";
		}
		else if (key < T->data)
			return DeleteBST(T->lchild, key);
		else 
			return DeleteBST(T->rchild, key);
	}
	
}

代码实现：

void DeleteBST(BiTree &T, int key)
{

	if (!T)
		cout << "error"<<endl;
	else
	{
		if (T->data == key)
		{
			//删除节点分三种情况
			{
				BiTree q, s;
				if (!T->lchild)
				{
					q = T;
					T = T->rchild;
	                delete q;
				}
				else if (!T->rchild)
				{
					q = T;
					T = T->lchild;
					delete q;
				}
				else//两个孩子都有
				{
					q = T;
					s = q->lchild;
					while (s->rchild)
					{
						q = s;
						s = s->rchild;
					}
					T->data = s->data;
					if (q != T)
					{
						q->rchild = s->lchild;
					}
					else
					{
						q->lchild = s->lchild;
					}
					delete s;
				}
			}

			cout << "删除成功"<<endl;
		}
		else if (key < T->data)
			return DeleteBST(T->lchild, key);
		else
			return DeleteBST(T->rchild, key);
	}
}

五.主函数部分与中序遍历

void midOrderTraverse(BiTree T)
{
	if (T) 
    {
	midOrderTraverse(T->lchild);
    cout << T->data << " ";
    midOrderTraverse(T->rchild);
    }
 }
 
int main()
{
	BiTree T = NULL;
	CreateBST(T);
	midOrderTraverse(T);
	cout << endl;
	int n;
	cout << "删除的元素大小"<<endl;
	cin >> n;
	DeleteBST(T, n);
	midOrderTraverse(T);

}

六.运行结果展示