Kth Ancestor of Node 🎯

Welcome to an exciting lesson on Data Structures and Algorithms! Today, we'll dive into a common problem faced during tree traversals - finding the Kth ancestor of a node in a binary tree.

What is a Binary Tree? 📝

A binary tree is a data structure that consists of nodes, where each node has at most two children, referred to as the left child and the right child. The node without any children is called a leaf node.

Understanding the Problem - Kth Ancestor of Node 💡

Given a binary tree and an integer k, find the kth ancestor of a given node in the tree. An ancestor of a node is any node on the path from the node to the root of the tree.

Breaking Down the Problem 📝

Traverse the tree from the given node towards the root.
Keep track of the number of nodes we visit (from the given node to the root).
If the count equals k, we have found the kth ancestor.
If the count exceeds k, we have gone past the required ancestor and can stop the traversal.

Implementing the Solution 💡

Let's write a recursive function to find the Kth ancestor in a binary tree. Here's a simple example in Python:

python

class Node:
    def __init__(self, key):
        self.left = None
        self.right = None
        self.key = key

def kthAncestor(root, k, node, ancestor=None):
    if not root:
        return ancestor

    # If root is the node itself
    if root.key == node:
        return root

    # Move to the left or right child depending on the count
    if k <= ancestor is None:
        return kthAncestor(root.left, k, node, root.key) if root.left else kthAncestor(root.right, k, node, root.key)

    # Move to the left or right child based on ancestor's count
    k -= ancestor + 1
    return kthAncestor(root.left, k, node, root.left.key) if k >= 0 else kthAncestor(root.right, k, node, root.right.key)

# Test the function with the following binary tree:
#     1
#    /   \
#   2     3
#  /  \
# 4    5

root = Node(1)
root.left = Node(2)
root.right = Node(3)
root.left.left = Node(4)
root.right.right = Node(5)

node = 4  # The given node
k = 2     # The required depth

print(kthAncestor(root, k, node).key)  # Output: 2

Practical Application 💡

The Kth ancestor problem is crucial in various real-world scenarios, such as:

In social networks, finding common ancestors in family trees.
In data validation, ensuring that nodes in a tree structure have valid relationships with their ancestors.
In debugging, tracing the root cause of an issue in a complex system.

Kth Ancestor of Node 🎯

Kth Ancestor of Node 🎯

What is a Binary Tree? 📝

Understanding the Problem - Kth Ancestor of Node 💡

Breaking Down the Problem 📝

Implementing the Solution 💡

Practical Application 💡

Quiz 🎯