Problem Description

This interview consists of two distinct parts:

Part 1: Hash Map Internal Implementation

Explain the internal implementation details of a hash map. Your explanation should cover:

• The underlying array or bucket layout.
• Choices and properties of hash functions.
• Common collision resolution strategies, specifically discussing separate chaining versus open addressing.
• The role of load factor thresholds and the process of resizing/rehashing.
• Semantics for deleting elements.
• Expected versus worst-case time complexities for common operations (insertion, lookup, deletion).
• Typical memory trade-offs associated with different design choices.

Part 2: Array Intersection Problem

Given k integer arrays, solve the following two problems:

1. Return a sorted list of integers that appear in every array.
2. Extend your solution to return a sorted list of integers that appear in at least t of the k arrays, where 1 ≤ t ≤ k.

For both parts, you must:

• Provide detailed algorithms.
• Analyze the time and space complexity of your solutions.
• Discuss edge cases, such as duplicate integers within an array or empty input arrays.