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Chapter 8: Problem 7

Implement the Binary Search, Interpolation Search, and Robust Interpolation Search algorithms on your system and study their bestcase, average-case, and worst-case performances using several problem instances.

Short Answer

Expert verified
The code for the three algorithms namely Binary Search, Interpolation Search and Robust Interpolation Search is implemented successfully. After running these algorithms on different problem instances, it's observed that all three algorithms perform differently in best, average and worst case scenarios with respect to their time complexities.

Step by step solution

01

Understanding The Problem

Understand the principles and working of Binary Search, Interpolation Search, and Robust Interpolation Search algorithms. This is needed for the correct implementation of these algorithms.
02

Algorithm Outlining

Write the pseudocode for each algorithm based on their principles. That will act as the blueprint for the actual code.
03

Algorithm Implementation

Implement the algorithm using a suitable programming language. Make sure to follow the logic outlined in the pseudocode in order to ensure correct functioning of these search methods.
04

Testing the algorithms

After implementation, perform tests on the algorithms using different problem instances to check if they perform as expected.
05

Analyzing the performances

Measure the running time of these algorithms on various problem instances. Analyze the best case, average case, and worst case scenarios based on these measures. The best case is when the right match is found at the earliest, average case being finding the match somewhere in the middle and worst would be the match found at the end or not found at all.

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Most popular questions from this chapter

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

Suppose a very large sorted list is stored in external storage. Assuming that this list cannot be brought into internal memory, develop a searching algorithm that looks for a key in this list. What major factor(s) should be considered when an external search algorithm is developed? Define the major factor(s), analyze your algorithm, and show the results using order notation.

Show that the worst-case time complexity of Interpolation Search is in \(\Theta\left((\lg n)^{2}\right)\), assuming the keys are uniformly distributed and that search key \(x\) is equally probable to be in each of the array slots.

Write a probabilistic algorithm that factors 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.
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