Which of the following statements about hashing is correct:

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Question: Which of the following statements about hashing is correct?

Options:
1) The hash function must generate similar hash values for keys that are near each other
2) The strings being hashed must be composed solely of alphabetic characters
3) The hash function must always make use of a table size that is a prime number
4) The hash function must be designed so that only one key can be mapped to each possible hash value
5) The hash function used must be deterministic, and must always give the same hash value for any given key

Option 1 analysis:
- This statement claims that similar keys yield similar hash values. While some hashing schemes aim for uniform distribution, a good hash function does not guarantee that nearby keys produce similar hashes. In fact, many well-known hash functions (like modulo-based functions, or cryptographic hashes) do not rely on locality. Therefore, this is not a correct general rule about hashing.

Option 2 analysis:
- The claim that input strings must be alphabetic-only is false. Hash functions operate on arbitrary data bytes, including numbers, punctuation, and binary data. Requiring only alphabetic characters would unnecessarily restrict practical use cases and is not a defining property of hashing.

Option 3 analysis:
- The statement that a hash function must always use a prime table size is a common design tip in some contexts, but it is not a universal requirement. Hash tables can use various sizing strategies (including powers of two, prime numbers, or dynamic resizing) depending on the chosen hashing scheme and collision resolution method. Therefore, this is not a universal requirement of hashing.

Option 4 analysis:
- The idea that a hash function must map each possible key to a unique hash value (i.e., injective) is incorrect for hashing in hash tables. Hash functions are typically designed to map a potentially large set of keys to a limited range of hash values, intentionally allowing collisions. Preventing any collisions would be impractical for general use and is not a defining property of hashing.

Option 5 analysis:
- This statement asserts determinism: the hash function must be deterministic and yield the same hash value for a given key every time. Determinism is a fundamental property of hash functions used in hash tables, databases, and many algorithms: the same input must consistently produce the same hash, so that lookup, comparison, and integrity checks are reliable. This aligns with the essential expectation of hashing in practice.

Summary of reasoning across options:
- Options 1, 2, 3, and 4 each describe properties that are either not universally required or are explicitly incorrect for hash functions used in standard contexts like hash tables.
- Option 5 captures a core, universally required property: determinism, ensuring consistent hash values for identical inputs.

Put together, the analysis shows that the statement aligned with the fundamental characteristics of hashing is that the hash function used must be deterministic, and must always give the same hash value for any given key.

COMP10002_2025_SM2 Supplementary or Special Exam: Foundations of Algorithms (COMP10002_2025_SM2)- Requires Respondus LockDown Browser

Which of the following statements about hashing is correct:

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