"For a given hash function, two records will never be mapped to the same index.". True or False.

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Question prompt: 'For a given hash function, two records will never be mapped to the same index.' True or False.
Option 1: True. This claim asserts that a hash function never maps two distinct records to the same index. In practice, most hash functions are designed to be deterministic and uniform, but they operate over a finite set of indices; different inputs can produce the same index, which is known as a collision. Therefore, stating that two records will never share the same index is incorrect because collisions are possible and even expected in many hashing scenarios.
Option 2: False. This statement is accurate because hash functions can and do produce collisions where two different records hash to the same index. To handle this, data structures or strategies such as chaining or open addressing are often used to manage multiple records sharing a bucket. The existence of collisions is a fundamental property of hash tables with finite buckets, and it contradicts the claim that no two records map to the same index.
Summary of misconceptions:
- If you think hash functions always produce unique indices, you’re overlooking collisions that arise from a finite range of indices relative to potentially infinite inputs.
- Believing that collisions cannot occur ignores standard collision-resolution techniques and the pigeonhole principle that underpins why collisions must occur when mapping many items into a limited number of buckets.
- Remember that a hash function’s quality affects collision frequency but does not eliminate collisions entirely; a good hash function minimizes collisions but does not guarantee zero collisions.

4510_COMP_SCI_X_0010 W09 Quiz

"For a given hash function, two records will never be mapped to the same index.". True or False.

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