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Chapter 7: Problem 19

Give two instances for which the Mergesort algorithm is the most appropriate choice.

Short Answer

Expert verified
Mergesort is most appropriate when dealing with large datasets due to its \(O(n \log n)\) time complexity. Additionally, it is beneficial when the data is stored in slow-to-access media since Mergesort requires fewer number of write operations.

Step by step solution

01

Understanding Mergesort

Mergesort is a divide-and-conquer algorithm that divides an input array into two halves, sorts them, and then merges them. It has a time complexity of \(O(n \log n)\) in the best, average, and worst-case scenarios, which is effective for large datasets. Moreover, it is a stable sort, meaning that equal elements remain in their original order after sorting. It is also efficient for data stored in slow-to-access media like disk storage or network attached storage.
02

Instance 1: Large Datasets

One instance where Mergesort is the best choice is when dealing with large datasets. Since Mergesort has a time complexity of \(O(n \log n)\), it is efficient for large volumes of data. Even in the worst-case scenario, the time complexity stays the same, providing predictability for performance tuning.
03

Instance 2: Use of Slow-to-Access Media

Mergesort is also efficient when data is being read from slow-to-access sequential media. This is because Mergesort performs fewer number of writes compared to other algorithms due to its merge process. This can be advantageous when the read and write operations are significantly more expensive, like in disk or network-attached storage. Also, it becomes a good choice when stability is an important consideration.

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