$($a$)$ Approximate the runtime complexity for the following block of code. $[$NB: Do not find Time

$($b$)$ Assume that each of the expressions below gives the processing time $T(n)$ spent by an algorithm for

solving a problem of size $n.$ Select the dominant term$($s$)$ having the steepest increase in $n$ and

specify the lowest Big Oh complexity of each algorithm.$($c$)$ What type of algorithm block will give rise to a time complexity of $O(MNP)?$ Explain with an

example of your own.

$($d$)$ If an algorithm is $O(n^2)$ and it runs for $20$ seconds for a problem size $(n)$ of $1000.$ If the problem size

increases to $10000,$ approximate how much time $($or cost of execution$)$ in seconds the algorithm

requires to complete processing the $10000$ sized problem?Question $2$ Searching and Sorting

$($a$)$ List all the divide and conquer algorithms covered in class.

$($b$)$ Determine which search algorithm would you apply to search for an item in a list of unsorted items.

State the reasons why your choice is the best for this search.

$($c$)$ On the sorted input list, what is the running time of insertion sort, shellsort, mergesort, and

quicksort?

$($d$)$ Sort the sequence $8,1,4,2,5,9,3,7,6$ using insertion sort. Show working.