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FIT1008-FIT2085 Fundamentals of algorithms - S1 2025

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I have decided to use a balanced Binary Search Tree (BST) to implement Separate Chaining in a Hash Table. What is the complexity of searching for an item in such a hash table?

O(hash) - complexity of the hash function

n - the largest number of items in a bucket

m - the number of slots in the hash table

O(comp) - the cost of key comparison

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I want to generate a balanced BST from a list with numbers from 1 to 10 inclusive and apply no self-balancing. To do that, what order should I insert items in?

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Provide the result of pre-order traversal of the following Binary Search Tree (BST) as a sequence of nodes.

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When deleting a node from a Binary Search Tree (BST), the worst case of this operation occurs when we try to remove the root node of the tree.

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Provide the result of in-order traversal of the following Binary Search Tree (BST) as a sequence of nodes.

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Assume we have the following list: [10, 9, 3, 4, 2, 5and we select 3 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.

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You have decided to use Quicksort to sort a list. What benefits will you have over MergeSort?

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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(nlogn) time, where n is the size of the list we are partitioning. What would the overall worse-case time complexity of this implementation of Quicksort be?
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Is Mergesort a stable sorting algorithm?

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You have decided to use Mergesort to sort a list. What benefits will you have over Quicksort?

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