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FIT1008-FIT2085 Fundamentals of algorithms - S1 2025

FIT1008-FIT2085 Fundamentals of algorithms - S1 2025

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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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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:

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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What is the worst-case time complexity of inserting an element into a sorted linked list of size n? (Ignore the cost of item comparison.)