C# Coding Test Course, Finding the Lowest Common Ancestor 2

Introduction

In this course, we will discuss how to solve the ‘Lowest Common Ancestor (LCA)’ problem using the C# programming language.
The Lowest Common Ancestor refers to the deepest node that is a common ancestor of two nodes in a binary tree.
We will explain the process of solving this problem in detail using specific algorithms and data structures.

Problem Description

The problem is to find the lowest common ancestor of two given nodes A and B in a given binary tree.
The binary tree is non-empty, and all nodes have unique values.
Additionally, nodes A and B are assumed to exist in the tree.

Input Format

                - First line: Number of nodes in the tree N (1 ≤ N ≤ 10^5)
                - Second line: N space-separated integers representing the node values of the tree
                - Third line: Two integers A, B (A, B exist in the tree)
            

Output Format

                - The value of the lowest common ancestor of A and B
            

Example Problem

                Input:
                7
                3 5 1 6 2 0 8
                5 1

                Output:
                3
            

Solution Method

There are various methods to find the lowest common ancestor, but it is generally effective to explore the tree
using Depth First Search (DFS) while considering the depth of the tree.
In the case of a Binary Search Tree (BST), it is possible to efficiently find the ancestor by determining which
subtree A and B belong to. However, in a general binary tree, utilizing information from the parent nodes is necessary.

Algorithm Design

The main steps of the algorithm are as follows.

1. Construct the tree given in the input.
2. Store the parent node for each node in a map or array.
3. Record the path from node A to the root.
4. Record the path from node B to the root.
5. Find the first common node in the two paths.

C# Code Implementation

Below is the C# code implementing the above algorithm.

                
using System;
using System.Collections.Generic;

class TreeNode {
    public int Value;
    public TreeNode Left, Right;
    
    public TreeNode(int value) {
        this.Value = value;
        this.Left = null;
        this.Right = null;
    }
}

class Program {
    static Dictionary nodeMap = new Dictionary();
    static TreeNode root;

    public static void Main(string[] args) {
        int N = Convert.ToInt32(Console.ReadLine());
        int[] values = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
        int A = Convert.ToInt32(Console.ReadLine());
        int B = Convert.ToInt32(Console.ReadLine());

        BuildTree(values, 0, N);
        TreeNode ancestor = FindLCA(root, A, B);
        Console.WriteLine(ancestor.Value);
    }

    static TreeNode BuildTree(int[] values, int index, int N) {
        if (index < N) {
            TreeNode node = new TreeNode(values[index]);
            nodeMap[values[index]] = node;
            node.Left = BuildTree(values, 2 * index + 1, N);
            node.Right = BuildTree(values, 2 * index + 2, N);
            return node;
        }
        return null;
    }

    static TreeNode FindLCA(TreeNode node, int A, int B) {
        if (node == null) return null;
        if (node.Value == A || node.Value == B) return node;

        TreeNode leftLCA = FindLCA(node.Left, A, B);
        TreeNode rightLCA = FindLCA(node.Right, A, B);

        if (leftLCA != null && rightLCA != null) return node;
        return (leftLCA != null) ? leftLCA : rightLCA;
    }
}
                
            

Code Explanation

1. TreeNode Class: Represents a node in a binary tree. Each node has a value and left and right children.

2. Main Method: The starting point of the program. It receives input from the user and builds the tree, then finds the LCA.

3. BuildTree Method: Constructs the binary tree using an array. It is called recursively to build the tree.

4. FindLCA Method: Recursively traverses the tree to find the lowest common ancestor of the two nodes A and B.

Time Complexity

The time complexity of this algorithm is O(N).
It increases proportionally to the number of nodes since it visits each node once while traversing the tree.
The space complexity is also O(N), which is due to the space used by the recursive call stack and for storing node information.

Conclusion

In this course, we learned how to solve the lowest common ancestor problem using C#.
By understanding the principles of the algorithm and implementing the code, you would have gained insights on how to effectively tackle similar tree problems in coding tests.
In the next session, we will delve deeper into other data structures or algorithm problems.
Thank you.