Question $1$

Algorithm analysis is an important part of computational complexity theory,which provides theoretical estimation for the required resources of an algorithmto solve a specific computational problem. Discuss any FIVE $(5)$ criteria inselecting algorithm for various application development.

$(10$ marks$)$

Question $2$

You are given a list of items in the following sequence:$42,56,78,18,88,20,45,32,36,38,53,55$Design a Red$-$Black Tree $($RBT$)$ based on the list given by using single circle torepresent black node and double circle to represent red node.

$(10$ marks$)$

Question $3$

Design a $2-3$ Tree for the following item insertion:$32,46,68,8,78,10,35,22,26,38,43,45$

$(10$ marks$)$

Question $4$

You are given the following data entered as a sequential set:$30,25,40,15,33,28,17,12,55,20$a$)$ Design a binary search tree $($BST$)$ based on the list data entry.

$(5$ marks$)$

b$)$ Based on your answer in $($a$),$ design an AVL trees using proper rotation.

$(5$ marks$)$Question $5$

Consider the following set of $10$ items:$73,42,58,91,27,64,35,80,56,19$Perform the sorting of these items using the Heap Sort technique. Show the step$-$by$-$step process of building the max heap, extracting the maximum element, andthe final sorted array.

$(10$ marks$)$

Question $6$

Consider the following set of $10$ items:$56,23,41,8,37,19,72,45,65,12$Perform the sorting of these items using the Quicksort technique. Show the step$-$by$-$step process of partitioning and sorting.

$(10$ marks$)$