HIT 220 - Algorithms and Complexity - Lab Assessment Answers

Assessment Details:

Question 1.
(a) Draw the BST constructed by inserting the values [50, 11, 25, 68, 4, 97, 64, 3, 13, 82, 92, 27, 52, 14] in the order shown, into an initially empty tree.

(b) Using the tree traversal algorithms and the BST from question 1(a), show the output sequence for a:
i. Preorder traversal
ii. Postorder traversal

(c) Deleting Nodes
i. Delete the node with value 25 and draw the resultant tree.
ii. Briefly explain the method you have used to perform the delete operation.
iii. Briefly describe an alternate method that could have been used to delete the node.

Question 2.
Using Python Code, or Pseudocode, provide a recursive algorithm which will take a string as input and return the string in reverse. 

Eg: Input: “CDU is great”
Output: “taerg si UDC”

Question 3.
The following functions have been calculated as the runtime complexity of various algorithms. Identify the Big-O complexity, and provide witness values to support
your answer. Clearly highlight your answer and show any working out you do. 

Question 4.
Suppose you are given two integer values x and y. Construct a recursive algorithm that uses any combination of the following (addition/subtraction/comparison) to
calculate the remainder of x divided by y. Specify a set of example values for x & y which will result in at least 3 or more recursive calls, and draw the recursion trace
diagram for your example.

Question 5.
a) Create a new AVL Tree using the following sequence of values. Draw the tree at each step, specifying what rotation is necessary to balance the tree. Sequence: [1, 77, 55, 34, 78, 82, 95, 85, 12, 11, 35, 38, 43]
b) Remove nodes 12 & 77 and redraw the tree.

Question 6.
Given the following sequence of data [90,65,32,67,37,30,40,26,72,20,52,68,95]:
a) Draw a Binary Heap diagram implementing the min-heap property. Draw the diagram for each step.
b) Draw a Binary Heap diagram implementing the max-heap property. Draw the diagram for each step.
c) Using the final heap diagram from both (a) and (b), redraw them after removing the root node. Clearly label each diagram. 

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