Solution Set 4
Explore the complexity of hash functions and how inefficient designs impact common operations in hash tables. Understand the importance of constant-time computations and how to manage collisions by analyzing space requirements, helping you design more efficient data structures.
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Solution 1
a- Kim is unfortunately using a bad hash function. Her function computes the sum of integers from 1 to n and hashes n to the slot numbered sum. To calculate the hash of a given k, the loop would run for k steps. The function thus has a complexity of O(k). Note, how a hash table using this hash function would fail to provide O(1) insert and retrieval operations.
b- The hash function is computing the sum of numbers from 1 to k. We already know that the summation of consecutive numbers from 1 to k can be represented by the following formula
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