Number your problem answers clearly, such as Problem $(1.$a$),(1.$b$),(1.$c$),(1.$d$),(1.$e$),$ Problem $2,$

Problem $(2.$a$),(2.$b$),...,(4.$d$),$ and arrange the answers to the problems in order. Use only a

Word file $(.$docx$)$ to answer the questions; PDF files will be graded without feedback. Failure to

use a Word file will result in non$-$feedback or a deduction of $10$ points.

If you attach a PDF page in your Word file for solutions, please leave a few lines blank after

your solution page to allow for comments. You will not get any feedback if there is difficulty.

The total number of points for this assignment, As$01,$ is $60.$

You can use only logical operators, relational operators, boolean expressions, if$,$ if$-$else, if$-$elseif, nest$-$if$,$ and while statements. You can use statements to input x and y and output their

quotient and remainder.

$1.[20$ pts$.]$ Extend the iterative version of the division function division$($x$,$ y$)$ to compute

x$/$y using the addition operator, where x and y are integers, and the output is x $=$ q $*$ y $+$ r$,$

q and r are integers. Write a program to compute x$/$y iteratively. $($For credits, please copy

and paste your program into a Word file$)$ for submission. You also need to submit your

program, which allows us to execute it with another set of inputs.$)$

$2.[20$ pts$.]$ To improve the iterative version, write a recursive function division$($x$,$ y$)$ to

compute x$/$y using the addition operator, where x and y are integers, and the output is x $=$

q $*$ y $+$ r$,$ q$,$ and r are integers. Write a program to compute x$/$y iteratively. $($For credits,

please copy and paste your program into a Word file$)$ for submission. You also need to

submit your program, which allows us to execute it with another set of inputs.$)$

$3.[10$ pts$.]$ For problem $1,$ what is your input size? How many iterations do you need to

compute x$/$y$?$ Justify your solutions.

$4.[10$ pts$.]$ For problem $2.$ What is your input size? How many recursive calls do you need

to compute x$/$y$?$ Justify your solutions.

Your test data will be the following set $\{($X$,$ Y$)\}.$ Your output should be as follows: x $=$ q$*$y $+$ r$.$