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FIT1008-FIT2085 Fundamentals of algorithms - S1 2025
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1. Describe in bullet points the steps involved in the HeapSort algorithm [4 marks]2. What is the worst-case time complexity of HeapSort algorithm? Assume the input size N to be the number of elements in the input array. No explanation no marks. [4 marks]3. What are the two invariants of max heaps? Explain what each of these invariants mean. [2 marks]
1. What is a binary tree? Explain in one or two sentences [2 marks]2. Explain the concept of nodes; including parent and child nodes [4 marks]3. Given a binary tree containing N nodes, what is the maximum height such a tree can have? [2 marks]4. Explain the invariants of a binary search tree (write one line for each). You don't need to include the properties of Binary Trees in general. [2 marks]
I want to construct a Min Heap from a sorted list. What's the worst-case time complexity when using the best approach that we have introduced you to? You can assume n is the number of elements in the list.
What is the worst-case time complexity of rise operation on a Max Heap, if n is the number of items in the heap?
I want to implement a Priority Queue using the following Max Heap:
[None, 88, 75, 42, 41, 24, 12, 42, 4, 21, 15, 2, 5]What should be the state of the heap after I add 90 to the queue?
What is the worst-case time complexity of sink operation on a Max Heap, if n is the number of items in the heap?
Priority Queue could be implemented efficiently using a balanced Binary Search Tree?