Act as a senior software engineer with 10+ years of experience in data structures and algorithms. Provide a step-by-step guide on how to implement a [MIN/MAX] heap in [PYTHON/JAVA/C++], including detailed explanations of key operations like insertion, deletion, and heapify. Cover both the [ARRAY-BASED] and [TREE-BASED] representations, highlighting their time complexities and use cases. Include code snippets with comments, edge cases to consider, and practical examples like [PRIORITY QUEUE] applications. Explain how to handle dynamic resizing and optimize for performance in [LARGE-SCALE SYSTEMS].