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i Describe Bubble Sort's Advantage in the best case scenario over other methods. ii Bubble Sort need only pass through a nearly-d sorted list d times to ensure the list is sorted. Justify why this is the case. (Hint: consider the early termination condition of Bubble Sort)

i Describe Bubble Sort's Advantage in the best case scenario over other methods. ii Bubble Sort need only pass through a nearly-d sorted list d times to ensure the list is sorted. Justify why this is the case. (Hint: consider the early termination condition of Bubble Sort)

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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An array is **nearly-d sorted** if any element is not further than \(d\) spots from its sorted position. Consider the sorted list of elements: \[ X = [1, 5, 9, 10, 15, 20, 34, 57, 66, 91] \] The same elements form a nearly-sorted list: \[ A = [1, 5, 10, 15, 9, 20, 34, 57, 91, 66] \] with \(d = 2\) because each value is, at most, 2 spots from its sorted position. Consider that the value 9 is out of order as it is in index 4\(^2\) in \(A\) while it is in index 2 in \(B\). Similarly, \[ B = [1, 5, 10, 9, 15, 20, 34, 57, 91, 66] \] is nearly sorted with \(d = 1\) as value 9 is in index 3 instead of index 2, 66 is in index 9 instead of index 8 and so on. **Bubble Sort**, a sorting algorithm we have not covered, has an advantage over other methods when operating on nearly-\(d\) sorted lists. i. Describe Bubble Sort’s Advantage in the best case scenario over other methods. ii. Bubble Sort need only pass through a nearly-\(d\) sorted list \(d\) times to ensure the list is sorted. Justify why this is the case. (Hint: consider the early termination condition of Bubble Sort). --- \[ ^2 \text{We adopt the Python convention of indexing } 0, 1, 2, 3, \ldots \] \[ ^3 \text{Wikipedia is a great place to start your Bubble Sort studying } \text{https://en.wikipedia.org/wiki/Bubble_sort,} \] \text{the animation in particular was instructive. However, more kinesthetic learners may appreciate the following video too: } \\ \text{https://www.youtube.com/watch?v=lyZQPjUT5B4.}
Transcribed Image Text:An array is **nearly-d sorted** if any element is not further than \(d\) spots from its sorted position. Consider the sorted list of elements: \[ X = [1, 5, 9, 10, 15, 20, 34, 57, 66, 91] \] The same elements form a nearly-sorted list: \[ A = [1, 5, 10, 15, 9, 20, 34, 57, 91, 66] \] with \(d = 2\) because each value is, at most, 2 spots from its sorted position. Consider that the value 9 is out of order as it is in index 4\(^2\) in \(A\) while it is in index 2 in \(B\). Similarly, \[ B = [1, 5, 10, 9, 15, 20, 34, 57, 91, 66] \] is nearly sorted with \(d = 1\) as value 9 is in index 3 instead of index 2, 66 is in index 9 instead of index 8 and so on. **Bubble Sort**, a sorting algorithm we have not covered, has an advantage over other methods when operating on nearly-\(d\) sorted lists. i. Describe Bubble Sort’s Advantage in the best case scenario over other methods. ii. Bubble Sort need only pass through a nearly-\(d\) sorted list \(d\) times to ensure the list is sorted. Justify why this is the case. (Hint: consider the early termination condition of Bubble Sort). --- \[ ^2 \text{We adopt the Python convention of indexing } 0, 1, 2, 3, \ldots \] \[ ^3 \text{Wikipedia is a great place to start your Bubble Sort studying } \text{https://en.wikipedia.org/wiki/Bubble_sort,} \] \text{the animation in particular was instructive. However, more kinesthetic learners may appreciate the following video too: } \\ \text{https://www.youtube.com/watch?v=lyZQPjUT5B4.}
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