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FIT1008-FIT2085 Fundamentals of algorithms - S1 2025

FIT1008-FIT2085 Fundamentals of algorithms - S1 2025

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We are trying to optimise the pivot selection of the Quicksort algorithm. For our pivot choice, we are using an algorithm to find the median of an unsorted list. The algorithm we opt to use for this takes O(n) time, where n is the size of the list we are partitioning. This would make the overall worst-case time complexity of Quicksort as O(nlogn). Why don't we use this approach in general?

There's no algorithm to calculate the median in O(n) time

While the linear overhead of finding the median is not visible in the asymptotic description, we assume it to be too large to be practical

100%

We would have to sort the list before we can calculate the median

This is a better approach and we should use it

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Is Quicksort a stable sorting algorithm?

Assume we have the following list: [10, 9, 3, 4, 2, 5] and we select 5 to be the pivot. What would the list be after one iteration of quicksort?

You should use the partition algorithm discussed in the pre-reading.

[2, 3, 4, 5, 9, 10]

[3, 4, 2, 5, 10, 9]

[2, 4, 3, 5, 9, 10]

[2, 4, 3, 5, 10, 9]

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I am trying to decide whether I should use Quicksort or Mergesort to sort a list. What factors would affect my choice?

Whether stability is important

Whether being incremental is important

Whether the list is already sorted

How large is the list and whether in-place sorting is preferred

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We are trying to optimise the pivot selection of the Quicksort algorithm. For our pivot choice, we are using an algorithm to find the median of an unsorted list. The algorithm for opt to use for this takes O(n) time, where n is the size of the list we are partitioning. What would the overall worst-case time complexity of this implementation of Quicksort be?

O(nlogn²)

O(n²)

50%

O(nlogn)

50%

O(n²logn)

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Quicksort is not a stable sorting algorithm. Can we make Quicksort stable?

True

False

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Assume we have the following list: [10, 9, 3, 4, 2, 5] and we select 4 to be the pivot. What would the list be after one iteration of quicksort?

You should use the partition algorithm discussed in the pre-reading.

[3, 2, 4, 10, 9, 5]

❌

[3, 2, 4, 10, 5, 9]

[2, 3, 4, 10, 9, 5]

20%

[2, 3, 4, 10, 5, 9]

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1. Briefly describe List ADT giving details about [4]

Main property of a List ADT; [2]
Key operations of the List ADT. [2]

2. What is the best-case and worst-case complexity of operation add() for a Sorted List ADT, if implemented with an array? Assume that item search is done with binary search. Explain the reason for the best and worst case. No explanation no marks. [3]

3. State (in total) three advantages and/or disadvantages of Linked Nodes data structures? [3]

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1. What does it mathematically mean that f(n) = O(g(n)), in your own words? [3]

2. Assuming that f(n) = O(n^2) and g(n) = O(n^2 logn), what should be f(n) + g(n)? Why? Simplify the resulting expression. [3]

3. What is the worst-case time complexity of the function "func2"? Explain. When providing your analysis, don't forget to specify what is the input size. [4]

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1. Briefly describe a bit-vector, giving details about

How an element of a set is represented by means of a bit-vector
How bit-vector based sets operate

Give an example of a set and its representation as a bit-vector. [3]

2. What is the best-case and worst-case time complexity of the remove() and intersection() operations for a Set ADT, if implemented with an array? Explain (no explanation, no marks). [4]

3. What are the main advantages and disadvantages of an array-based implementation of the Set ADT compared to a bitvector-based implementation? State the advantages and disadvantages as separate sections for each. [3]

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