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FIT1008-FIT2085 Fundamentals of algorithms - S1 2025

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Can separate chaining conflict resolution can be implemented using Array instead of linked nodes? 

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Why don't we use an extremely large prime (eg: around 2 million) for the table size?

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Which of the following operations is not part of the Dictionary ADT?

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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 insert() for a List ADT, if implemented with an array? Explain the reason for the best and worst case. No explanation no marks. [2]

3. For a sorted list of elements, what is the difference between applying linear search and binary search? Give the best-case and worst-case complexity of both. Explain. [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 add() and intersection() operations for a Set ADT, if implemented with an array? (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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1. What is an Abstract Data Type and how does it differ from a Data Type? Give an example in your explanation. [3]

2. Briefly describe the Queue ADT giving details about [4]

- The main property of the Queue ADT [2]

- Key operations of the Queue ADT [2]

3. What is the best-case and worst case time complexity of operation serve() for a Queue ADT, if implemented with an array? (no explanation, no marks). [3]

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In a queue ADT, which operation removes an element from the Queue?
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1. What is normally meant to be the input size if the algorithm’s input is i) an integer (numeric algorithm), ii) collection of elements or iii) a string? What do we count when calculating the time complexity of an algorithm? [3]

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

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

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Apply two outer loop iterations of Insertion Sort to the list [9, 3, 2, 7]. What is the result?
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Given the below code what is the value of the union of the two sets x and y at the end of the following block of code:

x = ASet(10)

y = ASet(10)

x.add(1)

x.add(1)

y.add(9)

y.add(2)
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