Question $1$A $(21$ Marks$)($a$)$ Suppose you have been tasked with designing an algorithm that finds and stores all the prime numbers between two arbitrary numbers, N and M$,$ where N $<$ M$.$ Required: $($i$)$ State the appropriate data structure you can use to store the prime numbers $[1]($ii$)$ Justify your choice of data structure in $($i$)$ above $[2]($b$)$ Consider the following words: Brenda, James, Aaron, Andrew, Mukai, Tatenda, Nyabiko, Ntsoaki, Axiel, Bobby Required: $($i$)$ Populate a BST using the words above. $[5]($ii$)$State with justification whether the tree you drew above is or is not a: a$.$ Complete binary tree $[1]$ b$.$ strictly binary tree $[1]$ c$.$ perfect binary tree $[1]($iii$)$ Show the order of traversal of the tree using each of the following methods: a$.$ Preorder $[2]$ b$.$ In$-$order $[2]$ c$.$ Post$-$order $[2]$ d$.$ Depth$-$first search $[2]($iv$)$ Calculate the maximum number of permissible nodes for this tree. $[2]$