JavaScript Coding Test Course, Binary Tree

Introduction

Today, software developers need a deep understanding of algorithms and data structures. In particular, recursive structures like binary trees are useful for solving various problems. In this course, we will cover the basic concepts of binary trees and coding test problems that utilize them, explaining the approach and code step by step.

What is a Binary Tree?

A binary tree is a tree structure in which each node has at most two child nodes (left and right). Binary trees can take various forms, and the following are some major types of binary trees:

  • Complete Binary Tree: A tree where every node has child nodes, and all levels are completely filled except for the last level.
  • Balanced Binary Tree: A tree where, for every node, the height difference between the left and right subtrees is no more than 1.
  • Binary Search Tree: A tree that follows the rule where the left child node is smaller than the parent node, and the right child node is larger than the parent node.

Problem Description

In this problem, we will write a function to find the ‘maximum depth of a binary tree’. The maximum depth refers to the number of nodes from the root node to the deepest leaf node.

Problem: Find the Maximum Depth of a Binary Tree

function maxDepth(root) {
    // Given the root node of a binary tree, return the maximum depth.
}

Approach to the Problem

To solve this problem, we can use the following approach:

  1. Use recursion to calculate the depth of each node.
  2. Return the depth when reaching a leaf node.
  3. Compare the depths of each subtree and return the greater value to the parent node.

Step-by-Step Solution

Step 1: Set Up the Basic Structure

First, we need to define the node structure. Let’s define a binary tree in JavaScript using a node class.


class TreeNode {
    constructor(value) {
        this.value = value;
        this.left = null;
        this.right = null;
    }
}

Step 2: Define the Depth Calculation Function

Now, let’s define the recursive function for calculating depth. This function takes the current node as an argument and calculates the depth.


function maxDepth(root) {
    // Base case: if there is no node, the depth is 0
    if (root === null) {
        return 0;
    }
    // Calculate depth of left and right subtrees
    const leftDepth = maxDepth(root.left);
    const rightDepth = maxDepth(root.right);
    // Return the maximum depth
    return Math.max(leftDepth, rightDepth) + 1;
}

Step 3: Test the Function

Let’s test the function we wrote to confirm it works. We will construct a binary tree as follows:


const root = new TreeNode(1);
root.left = new TreeNode(2);
root.right = new TreeNode(3);
root.left.left = new TreeNode(4);
root.left.right = new TreeNode(5);
root.left.left.left = new TreeNode(6);

console.log(maxDepth(root)); // 4 - (1 -> 2 -> 4 -> 6)

Conclusion

We have explored a problem of calculating the maximum depth using binary trees and recursion. This structure is frequently used in many algorithm problems, so understanding binary trees can help solve various application problems. I hope you continue to build deeper algorithm skills through persistent practice and problem-solving!

Additional Learning Resources

If you want to practice more algorithm problems related to binary trees, I recommend the following resources:

  • LeetCode: Maximum Depth of Binary Tree problem
  • HackerRank: Tree: Height of a Binary Tree problem
  • GeeksforGeeks: Binary Tree Basics

References

You can deepen your knowledge of algorithms and data structures through the following references:

  • Introduction to Algorithms – Thomas H. Cormen et al.
  • Data Structures and Algorithms in JavaScript – Michael McMillan