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Chapter 8: Problem 32

Give at least two examples of situations in which hashing is not appropriate.

Short Answer

Expert verified
Hashing is not appropriate when the data needs to be retrieved in the order it was originally input (e.g., for time-series data), or when the original data needs to be recovered from the hashed output (e.g., for encryption).

Step by step solution

01

Situation 1 - Original Order Retrieval

If the order in which data was originally entered or recorded matters for the application at hand, using a hash function could disrupt that order. As hash functions map input data to numerical values in a deterministic but seemingly random way, there's no way to reverse-engineer the input's original order from the hashed output. For instance, consider an application which records the time-series data (e.g. stock prices). If this data is hashed, the time-series information will be lost.
02

Situation 2 - Reversible Data

If you need to retrieve the original data from the hashed output, hashing is not appropriate. Although hash functions are deterministic, they are designed to be difficult to reverse. In other words, if you know the output of a hash function, it should still be computationally infeasible to determine what the input was. This is a feature, not a bug, for many applications (for example, storing password data). But for applications such as encryption where you want to be able to recover the original data by reversing the action, hashing is inappropriate. Encryption requires using a deterministic function that's easily reversible with the right key.

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Most popular questions from this chapter

Let \(S\) and \(T\) be two arrays of \(n\) numbers that are already in nondecreasing order. Write an algorithm that finds the median of all \(2 n\) numbers whose time complexity is in \(\Theta(\lg n)\)

Write a probabilistic algorithm that factorizes any integer using the functions prime and factor. Function prime is a boolean function that returns "true" if a given integer is a prime number and returns "false" if it is not. Function factor is a function that returns a nontrivial factor of a given composite integer. Analyze your algorithm, and show the results using order notation.

Theorem 8.3 states that, for a successful search, the average search time over all inputs containing \(n\) keys, using binary search trees, is in \(\Theta(\lg n)\). Show that this result still holds if we consider an unsuccessful search as well.

Write an algorithm that finds the largest key in a binary search tree. Analyze your algorithm, and show the results using order notation.

Write an algorithm that creates a \(3-2\) tree from a list of keys. Analyze your algorithm, and show the results using order notation.
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