二叉搜索树(Binary Search Tree)，又称为“二叉排序树”、“二叉查找树”。定义为：该树的每个结点都有一个作为搜索依据的关键码。对任意结点而言，其左子树（如果存在）上的每个结点的关键码均小于该结点的关键码，其右子树（如果存在）上的所有结点的关键码都大于该结点的关键码。

其中，根据二叉搜索树的定义，二叉树结点之间的关系可以通过结点间的位置关系来得到，常用的算法是分割式查找，查找结点的平均长度；

插入操作时，新插入的结点总是叶子结点，首先查找插入结点的父亲结点，再判断左右子树；

删除操作时，由于结点位置的不同，使得删除结点操作比较复杂，有多种情况需要考虑，主要包含三种：删除叶子结点、删除只有一个孩子的结点、删除左右孩子都有的结点，其中删除左右孩子都有的结点时，使用合并操作，查找被删除结点p的左子树中最右值最大的结点r，将结点r的右子树指向结点p的右子树的根，然后用结点p的左子树的根代替被删除的结点p，最后删除结点p。

例如：

代码如下

import queue
'''
二叉树结点
'''  

class TreeNode:
    def __init__(self,val=None,left=None,right=None):
        self.val = val
        self.left = left
        self.right = right
    def settag(self,tag=None):
        self.tag = tag
'''
插入结点
'''
def InsertNode(root,treenode):
    tmp = root
    if(root is None):
        root = treenode
    while(tmp is not None):
        if(treenode.val == tmp.val):
            break
        elif(treenode.val < tmp.val):
            if(tmp.left is None):
                tmp.left = treenode
            else: tmp = tmp.left
        else:
            if(tmp.right is None):
                tmp.right = treenode
            else: tmp = tmp.right
    return root

'''
查找结点
'''
def search(root,key):
    tmp = root
    while(tmp is not None and key != tmp.val):
        if(key < tmp.val):
            tmp = search(tmp.left, key)
        else:
            tmp = search(tmp.right, key)
    return tmp

'''
获取结点的父亲结点
'''
def getparent(root,treenode):
    tmp = root
    if(root == treenode): return None
    while(tmp is not None):
        if(tmp.right == treenode or tmp.left == treenode):
            return tmp
        elif(treenode.val < tmp.val):
            tmp = tmp.left
        else:
            tmp = tmp.right
    return None
'''
合并删除结点
'''
def mergedeletenode(root,treenode):
    tmp = treenode
    parentnode = getparent(root, tmp)
    if(parentnode is not None):
        if(treenode.right is None and treenode.left is None):
            if(parentnode.right == treenode): parentnode.right = None
            else: parentnode.left = None
        elif(treenode.right is not None and treenode.left is None):
            if(parentnode.right == treenode): parentnode.right = tmp.right
            else: parentnode.left = tmp.right
        elif(treenode.right is None and treenode.left is not None):
            if(parentnode.right == treenode): parentnode.right = tmp.left
            else: parentnode.left = tmp.left
        else:
            tmp = treenode.left
            while(tmp.right!=None):
                tmp = tmp.right
            tmp.right = treenode.right
            if(parentnode.right == treenode): parentnode.right = treenode.left
            else: parentnode.left = treenode.left 
    else:#删除根节点
        if(treenode.right is None and treenode.left is None):
            root = None
        elif(treenode.right is not None and treenode.left is None):
            root = tmp.right
        elif(treenode.right is None and treenode.left is not None):
            root = tmp.left       
        else:
            tmp = tmp.left
            while(tmp.right is not None):
                tmp = tmp.right
            tmp.right = treenode.right
            root = treenode.left
    return root    

测试代码

if __name__=='__main__':
    nodes = [5,1,7,4,6,9,8]
    root = None
    for i in range(len(nodes)):
        node = TreeNode(nodes[i])
        root = InsertNode(root, node)
    PreOrderWithoutRecursion(root)
    print()
    InOrderWithoutRecursion(root)
    print()
    tmp = search(root, 5)
    print(tmp.val)
    root = mergedeletenode(root, tmp)
    PreOrderWithoutRecursion(root)
    print()
    InOrderWithoutRecursion(root)

输出结果

5 1 4 7 6 9 8 
1 4 5 6 7 8 9 
5
1 4 7 6 9 8 
1 4 6 7 8 9