Find a binary search tree, insert and delete

Find a binary search tree, insert and delete

Binary search tree (BST, Binary Search Tree)

Binary search tree: a binary tree, may be empty; if not empty, then the following properties:

1. All key non-empty left subtree <root of its key

2. All keys nonempty right subtree <its root keys

3. Left and right sub-trees are binary search trees

A, bst Find

Including data search and find the minimum maximum values.

Position Find (ElementType X, BinTree BST): Find the element X from the BST in the return address which the node resides.

Ideas: Find the root from the beginning, if the tree is empty, return NULL

If the search tree is not empty, then the root keyword and X are compared, and different treatments:

(1) If X <root key, simply continue to search in the left subtree

(2) if X> root key, the search continues in the right subtree

(3) if x = root key, the search is completed, the node returns a pointer pointing to this

code

def find(self, root, val):
    if not root:
        return False
    if root.val == val:
        return True
    elif root.val < val:
        return find(root.left, val)
    elif root.val > val:
        return find(root.right, val)

Position FindMin (BST): find and return address of the node from where the smallest element of BST.

code

def findMin(self, root):
    if root.left:
        return findMin(root.left)
    else:
        return root

Position FindMax (BST): Finds and returns the address of the node where the largest element from BST in.

code

def findMax(self, root):
    if root.right:
        return findMax(root.right)
    else:
        return root

Two, bst insertion

Starting from the root, if the inserted value is smaller than the value of the root node, then insert it into the left sub-tree root node; if greater than the value of the root node, it is inserted into the right sub-tree root node. This operation can be implemented using recursion.

code

def insert(self, root, val):
    if not root:
        root = TreeNode(val)
    elif val < root.val:
        root.left = self.insert(root.left, val)
    elif val > root.val:
        root.right = self.insert(root.right, val)
    return root

Third, delete the bst

three conditions:

1. Delete leaf nodes: delete, and modify a pointer to its parent node

   

2. Nodes removed only one child node: The parent node pointer pointing to the node you want to remove child nodes

   

3. Alternatively the largest element to be deleted node with a right subtree of the smallest element of another node or left subtree: To delete a node has left and right two subtrees

   Replace the current minimum node elements with the right subtree

   

   The maximum current tree element in place with the left child node

   

   code

def delNode(self, root, val):
    if not root:
        return
    if val < root.val:
        root.left = self.delNode(root.left, val)
    elif val > root.val:
        root.right = self.delNode(root.right, val)
    else:
        if root.left and root.right:
            # 既有左子树又有右子树
            temp = self.findMin(root.right)
            # 右子树的最小值
            root.val = temp.val
            # 将当前结点替换成右子树中最小值
            root.right = self.delNode(root.right, temp.val)
            # 将右结点删除
        elif not root.right and not root.left:
            # 左右子树都为空
            root = None
        elif not root.right:
            # 只有左子树
            root = root.left
        elif not root.left:
            # 只有右子树
            root = root.right
        return root