Which is True?

Question

Which is True?

BlackTom AI · Accepted Answer

Question: Which is True?

Option a: Perfect hash functions always have a time complexity of O(length of key).
- This statement is misleading. A perfect hash function maps a known set of keys to a set of unique indices with no collisions, but the time complexity is not defined solely by the key length. Depending on the hash function design and the implementation, lookup time can be O(1) on average, but the claim that it 'always' has time complexity O(length of key) is incorrect because the hash evaluation is typically a function of the key bits, not strictly the key length as a complexity measure, and O(1) lookups are common after the function is built.

Option b: Perfect hash functions can be possible if we know the keys in advance.
- This statement is true. Perfect hash functions are constructed specifically for a known set of keys (static dictionary). If we know all keys beforehand, we can design a hash function that maps each key to a unique index, eliminating collisions for that key set. This is the essence of a perfect hash function in the static case. The design process relies on the collection of keys being fixed and known ahead of time.

Option c: Perfect Hash functions are commonly used.
- This is not generally accurate. While perfect hash functions exist and are useful in certain contexts (e.g., static dictionaries, compiler symbol tables), they are not as widely used as standard hash functions because they require knowledge of the entire key set in advance and may lack flexibility for dynamic data. They are less common in everyday hashing tasks compared to generic hash maps.

Option d: Perfect Hash functions are not possible and are only an idea.
- This is false. Perfect hash functions are indeed real and implementable for a fixed set of keys. They are not merely a theoretical concept; there are algorithms to construct them, such as minimal perfect hashing. The statement claiming they are not possible contradicts established knowledge in data structures.

In summary, option b correctly states the condition under which a perfect hash function can exist: when the keys are known in advance. The other options contain overgeneralizations or inaccuracies about complexity, commonality, or the existence of perfect hash functions.

Which is True?

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