5 Best Ways to Find the Lowest Common Ancestor of a Binary Tree Using Python

by

💡 Problem Formulation: Finding the lowest common ancestor (LCA) in a binary tree involves locating the lowest node in the tree that has two given nodes as descendants. For example, given a binary tree and two node values, the function should return the LCA node value. For input nodes 4 and 5 in a binary tree, where 2 is their LCA, the output should be 2.

Method 1: Recursive Approach

The recursive approach involves breaking down the problem into smaller sub-problems. It checks if either of the two nodes matches the current node, then explores the left and right subtrees. The function specification should find and return the LCA node using recursion.

Here’s an example:

class TreeNode:
    def __init__(self, x):
        self.val = x
        self.left = None
        self.right = None

def findLCA(root, n1, n2):
    if root is None:
        return None
    if root.val == n1 or root.val == n2:
        return root
    left_lca = findLCA(root.left, n1, n2)
    right_lca = findLCA(root.right, n1, n2)

    if left_lca and right_lca:
        return root
    return left_lca if left_lca is not None else right_lca

# Constructed binary tree is
#         1
#       /   \
#      2     3
#     / \   / \
#    4   5 6   7
root = TreeNode(1)
root.left = TreeNode(2)
root.right = TreeNode(3)
root.left.left = TreeNode(4)
root.left.right = TreeNode(5)
root.right.left = TreeNode(6)
root.right.right = TreeNode(7)

lca = findLCA(root, 4, 5)
print('LCA of 4 and 5 is', lca.val)

The output of this code snippet:

LCA of 4 and 5 is 2

This code defines a tree structure and a recursive function findLCA() to find the lowest common ancestor. The function recursively searches both sides of the tree and returns the node that is common to both paths leading to the given nodes.

Method 2: Path-Based Approach

Add a section here…

Method 3: Iterative Approach

Add a section here…

Method 4: Tarjan’s Offline LCA Algorithm

Add a section here…

Bonus One-Liner Method 5: Using Dictionary Comprehensions and Set Intersections

Add a section here…

Summary/Discussion

  • Method 1: Recursive Approach. Strengths: Easy to understand and implement. Weaknesses: Could cause stack overflow for very deep binary trees due to recursion.