Lowest Common Ancestor in BST in C, C++, Java & Python – Code with Explanation & Examples in Short and Simple

   

C Program

#include<stdio.h>
#include<stdlib.h>

struct Node {
    int val;
    struct Node *left, *right;
};

struct Node* lca(struct Node* root, int p, int q) {
    if (root->val > p && root->val > q)
        return lca(root->left, p, q);
    if (root->val < p && root->val < q)
        return lca(root->right, p, q);
    return root;
}

C Output

Input Tree: [6, 2, 8, 0, 4, 7, 9]
Find LCA of 2 and 8 → Output: 6

C++ Program

#include<iostream>
using namespace std;

struct Node {
    int val;
    Node *left, *right;
    Node(int x): val(x), left(NULL), right(NULL) {}
};

Node* lca(Node* root, int p, int q) {
    if (root->val > p && root->val > q)
        return lca(root->left, p, q);
    if (root->val < p && root->val < q)
        return lca(root->right, p, q);
    return root;
}

C++ Output

Input: LCA(2, 8)
Output: 6

JAVA Program

class Node {
    int val;
    Node left, right;
    Node(int x) { val = x; }
}

Node lca(Node root, int p, int q) {
    if (root.val > p && root.val > q)
        return lca(root.left, p, q);
    if (root.val < p && root.val < q)
        return lca(root.right, p, q);
    return root;
}

JAVA Output

Input: LCA of 2 and 8
Output: 6

Python Program

def lca(root, p, q):
    if root.val > p and root.val > q:
        return lca(root.left, p, q)
    if root.val < p and root.val < q:
        return lca(root.right, p, q)
    return root

Python Output

Input: Find LCA of 2 and 8
Output: 6

In-Depth Explanation

Example

Suppose you’re given a binary search tree like this:

      6

     / \

    2   8

   / \ / \

  0  4 7  9

If you're required to determine the LCA of 2 and 8, the answer is obviously 6 — since the two nodes are in opposite subtrees of 6. But if you're required to find the LCA of 2 and 4, the answer is 2, since 2 is the smallest node which has both itself and 4 as its descendants.

Real-Life Analogy

Consider a corporate org chart where every node is an employee and the tree is flowing from CEO down to interns. When two employees report through various chains, their lowest common manager is analogous to the LCA. It's the first individual up the hierarchy who manages both employees. This assists in settling disputes, sharing common projects, or discovering common departments — similar to LCA in computing shared ancestry in trees.

Why It Matters

Locating the LCA is a fundamental and useful operation in trees. It is extensively applied in different systems such as file systems, genealogy programs, taxonomy categorization, version control systems, and network routing. The LCA assists in finding the nearest common point between two items within a hierarchy, an operation that is very powerful and often required.

What You Learn from This

This idea shows you how to use BST properties — having values in the left subtree as less and the right subtree as higher. It develops logical thinking and recursive solving abilities. You find out how to search in an efficient manner without ever checking all the nodes. The ease of the logic also shows you how recursion can easily solve decision-tree problems. 

Interview Use Case and Real-World Projects

In technical interviews, this is used to test your skill of traversing trees based on constraints such as ordering. It's usually generalized to finding LCA in non-BST trees, which is harder. But this version for BST is an introduction to tree ancestry problems. In actual projects, the same reasoning is applied in document object models (DOM) in browsers, directory resolution in Linux, and hierarchical path calculation in databases or file servers.

SEO-Optimized Explanation

Knowing how to compute the Lowest Common Ancestor in a Binary Search Tree is vital to becoming proficient in tree traversal methods within coding interviews and actual systems. This method effectively calculates the nearest common parent node of two provided values by capitalizing on the BST's ordered nature. Using straightforward recursive reasoning, this LCA algorithm prevents unwarranted traversal and provides a quicker method for answering hierarchy-based queries. Whether you're getting ready for elite tech interviews or coding hierarchical data models in applications, a grasp of LCA in BST is an initial step towards learning high-level tree operations.