Remove all leaf nodes from the binary search tree

Removing all leaf nodes from a binary search tree (BST) is a common operation in tree manipulation. This process involves deleting or pruning nodes from the BST that do not have any child nodes (i.e., they are leaf nodes). By removing leaf nodes, you can streamline and simplify the tree while retaining its BST properties.

What is a Binary Search Tree (BST)?

A BST is a binary tree data structure where each node has at most two children, commonly referred to as the left and right child.
The key property of a BST is that for each node:

All nodes in its left subtree have values less than the node's value.
All nodes in its right subtree have values greater than the node's value.

This ordering property allows for efficient searching, insertion, and deletion operations.

Identifying Leaf Nodes:

Leaf nodes in a BST are nodes with no children. In other words, they are nodes that do not have left or right subtrees.

Removing Leaf Nodes:

To remove all leaf nodes from a BST, you can perform a depth-first traversal (in-order, pre-order, or post-order) of the tree.
During the traversal, check if the current node is a leaf node (i.e., it has no children).
If the node is a leaf, remove it from the tree by updating its parent to null.
Continue this process until you have traversed the entire tree.

Code:

class newNode:
    # Constructor to create a new node
    def __init__(self, data):
        self.data = data
        self.left = None
        self.right = None

# Insert a Node in binary search tree.
def insert(root, data):
    if root is None:
        return newNode(data)
    if data < root.data:
        root.left = insert(root.left, data)
    elif data > root.data:
        root.right = insert(root.right, data)
    return root

# Function for inorder traversal in a BST.
def inorder(root):
    if root is not None:
        inorder(root.left)
        print(root.data, end=" ")
        inorder(root.right)

# Delete leaf nodes from binary search tree.
def leafDelete(root):
    if root is None:
        return None
    if root.left is None and root.right is None:
        return None

    # Else recursively delete in left
    # and right subtrees.
    root.left = leafDelete(root.left)
    root.right = leafDelete(root.right)

    return root

# Driver code
if __name__ == '__main__':
    root = None
    root = insert(root, 20)
    insert(root, 10)
    insert(root, 5)
    insert(root, 15)
    insert(root, 30)
    insert(root, 25)
    insert(root, 35)
    print("Inorder before Deleting the leaf Node.")
    inorder(root)
    root = leafDelete(root)
    print()
    print("Inorder after Deleting the leaf Node.")
    inorder(root)

Output:

Inorder before Deleting the leaf Node.
5 10 15 20 25 30 35 
INorder after Deleting the leaf Node.
10 20 30

Benefits:

Removing leaf nodes can help reduce the height of the tree and optimize various tree-based operations, including searching and traversal.

It can help simplify the tree structure and potentially improve the performance of other BST operations.

Potential Use Cases:

Removing leaf nodes from a BST might be beneficial in certain scenarios. For example:

When you want to reduce the memory footprint of a BST, especially if it contains a large number of leaf nodes.
When you're optimizing a BST for specific operations, and you believe that removing leaf nodes will improve performance.

Validation and Testing:

Before and after removing leaf nodes, it's essential to validate the BST properties of the tree to ensure that the operation didn't disrupt the ordering.
You can write test cases to verify that your removal algorithm is working correctly.

Implementations in Other Languages:

The provided Python example can serve as a starting point for implementing this operation in other programming languages like C++, Java, or JavaScript.
Language-specific features and memory management may vary, but the core logic remains consistent.

Complexities in Removing Non-Leaf Nodes:

Removing non-leaf nodes from a BST while maintaining its properties is more complex. It often requires finding suitable replacement nodes and reorganizing the tree. Deleting non-leaf nodes can be based on specific criteria, such as node values or the number of children.
These operations are typically implemented through more advanced algorithms like the deletion of a node with two children, which involves finding the node's in-order successor or predecessor.

In conclusion, removing all leaf nodes from a binary search tree is a useful operation that can help optimize the tree's structure and memory usage in certain situations. It is a relatively straightforward task compared to more complex tree manipulations and can be implemented with a recursive approach. Proper memory management and validation of the resulting tree are essential aspects of implementing this operation effectively.

Next TopicSort a stack using a temporary stack

← prev next →