For a hash table designed to hold 50 entries, what is a valid hash function?

A valid hash function for a hash table designed to hold 50 entries is one that produces an index within the range of available slots, which in this case is 0 to 49 (since the total number of slots is 50). Using the modulus operator, a hash function that computes key % 50 ensures that any integer key will produce a valid index within this specified range.

This approach effectively maps keys to index positions in the hash table, allowing for efficient storage and retrieval. The modulus reduces the key to a manageable number that fits within the bounds of the table size, ensuring that all entries are cyclically distributed across the available indices. Therefore, all resulting values will be in the appropriate range for the hash table, making it a suitable choice for this scenario.

Other functions provided can potentially yield indices that fall outside the range of 0-49. For example, using a modulus of 25 or 10 could result in collisions or gaps in the hash table, as these sizes do not effectively utilize the full capacity of the 50-entry table. A modulus of 100 would also produce indices that exceed the maximum range, making it inappropriate for a hash table designed for 50 entries.