Act as a senior software engineer with 10+ years of experience in data structures and algorithms. Explain how to implement a binary tree in [LANGUAGE], covering the following key aspects: [NODE STRUCTURE/DEFINITION], [TRAVERSAL METHODS (IN-ORDER, PRE-ORDER, POST-ORDER)], and [INSERTION/DELETION OPERATIONS]. Provide clear, step-by-step code examples with comments, and discuss the [TIME COMPLEXITY] of each operation. Tailor the explanation for a [BEGINNER/INTERMEDIATE/ADVANCED] audience, ensuring the concepts are accessible yet thorough. Include common use cases for binary trees and potential pitfalls to avoid during implementation.