Start by clarifying requirements and constraints, then design a hash table using open addressing with linear probing to handle collisions. Implement the frozenset operations (membership, length, iteration, equality, hash) on top of this table, ensuring immutability and a stable hash. Discuss trade-offs and edge cases like resizing and collision resolution.
Pro tip: Emphasize that the hash of the frozenset must be order-independent and stable; a common approach is to XOR the hashes of all elements, but be prepared to discuss potential collisions and improvements like using a commutative operation with better mixing.
Confirm that no built-in hash-based structures (dict, set) can be used, and that only arrays (lists) are allowed. Discuss expected operations and performance requirements.
Choose open addressing with linear probing for collision resolution. Define the underlying array, size, and load factor threshold for resizing.
Write methods for insertion, membership testing, and resizing. Ensure iteration works by scanning the array and skipping empty slots.
For equality, check that both sets have the same size and that every element of one is in the other. For hashing, combine element hashes in an order-independent way (e.g., XOR) and cache the result for stability.
Test with edge cases (empty set, collisions, resizing). Discuss trade-offs: open addressing vs. chaining, load factor choice, and hash collision handling.
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