# A0: Warmup

Welcome to the first assignment in CS 3110!

This assignment is a warmup: it’s some gentle practice that’s meant to prepare you for the rest of the assignments, which will be more intense. It will also give you the opportunity to verify that your OCaml environment is set up correctly, and to experience the 3110 assignment workflow. The assignment will be worth only 1% of your final grade to ensure that any initial stumbles won’t have a seriously negative effect.

Please track the time that you spend working on this assignment. We ask you to report it in your submission, and we will make a statistical summary available afterwards. On a similar (but somewhat easier) assignment last year, the mean was 6.4 hours, and the standard deviation was 3.4 hours.

Collaboration policy: This assignment is to be completed as an individual. Before continuing with this assignment, it is mandatory that you read the course Academic Integrity policies.

What you’ll do: Implement three short, unrelated functions; document them; and test them with assertions.

Objectives:

• Use OCaml operators, if expressions, functions, recursion, lists, and assertions.
• Write specification comments in OCaml.
• Begin to appreciate good vs. poor style in OCaml.

Lectures covered: This assignment relies on material from lectures 1–4. Only the last problem relies on material from lecture 4, so you can safely wait until that lecture has occurred before attempting it.

## Before Beginning

It is mandatory that you immediately read all five documents linked at the top of the programming assignments page. They describe how your work will be graded, and they answer many questions that you will have. You also need to read this entire assignment handout. Do that before you ask any questions, and before you write any code, just so that you have an idea where you are headed.

Thanks for your help with this! It will keep the entire course running more smoothly.

## Getting Started

Download the release code from CMS. Run make check from the folder containing the release code. You should get output that includes the following (other lines might be interspersed):

===========================================================
Your OCaml environment looks good to me.  Congratulations!
===========================================================
Your function names and types look good to me.
Congratulations!
===========================================================


If instead you get warnings about your OCaml environment, seek help immediately from a consultant. Assuming your environment is good, you should not get warnings about about your function names and types. After completing each function, you should re-run make check to ensure that you haven’t changed any required names or types.

There are a few other targets provided in the release code:

• Running make will open the toplevel and automatically #use your code. That should be useful for any interactive testing you want to do.
• Running make test will build and non-interactively run your solution. There won’t be any output to the screen, unless an assertion fails or you’ve added a print statement.
• Running make docs will extract your documentation comments to HTML and put it in the doc/ directory. Open doc/Warmup.html to browse it.
• Running make clean will delete files generated from your source code.
• Running make finalcheck will do the same as make check as well as two other things, which are described under the submission instructions at the end of this handout.

Now you’re ready to implement each of the following three functions in the file warmup.ml. In doing so, consider: how elegant can you make your implementation?

## Function 1: Valid Date

Define a function valid_date : int -> string -> int -> bool that takes an an integer y, a string m, and an integer d as input. The function returns true if y and m and d form a valid date, and returns false otherwise. For this problem, we define a valid date as having

• a year that is strictly positive (i.e., greater than or equal to 1);

• a month that is one of the following 3-letter capitalized abbreviations: Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec;

• a day that is between 1 and the number of days in that month, inclusive, taking leap years into account. Use the usual leap year rule for the Gregorian calendar: “Every year that is exactly divisible by four is a leap year, except for years that are exactly divisible by 100, but these centurial years are leap years if they are exactly divisible by 400.”

For example, valid_date 2020 "Feb" 29 = true, and valid_date 2010 "Jun" 50 = false.

(Calendar geeks: pretend that the entire Common Era has used the Gregorian calendar.)

Testing: We encourage you to get into the habit of testing your implementation early and often. Of course, it’s convenient to do that in the toplevel. But for repeatability, it’s important to express tests as part of your code base. For this warmup, please put assertions in your warmup.ml to test your function. (Later assignments will use amore powerful unit testing tool called OUnit.)

The test cases provided above are a good starting point. Here they are, expressed as assertions:

(* Test leap day in a non-century leap year. *)
let () = assert (valid_date 2020 "Feb" 29)

(* Test invalid day. *)
let () = assert (not (valid_date 2010 "Jun" 50))


Now add at least three more assertions to test other inputs. Before each, add a brief comment (like the ones above) to explain why you chose that test case. Make sure that none of your test cases are (with high probability) redundant: don’t, for example, add a test of day 51, because we already have a test for day 50.

After those three, you are free to add even more assertions, but you do not have to keep commenting them.

Code quality: Now, take some extra time to make your code as readable and elegant as you can. See the code quality rubric at the end of this handout for suggestions.

## Function 2: Syracuse

Define a function syr : int -> int that takes a strictly positive integer n as input, applies the following Collatz operation repeatedly to that input until the result is 1, and returns the number of times the Collatz operation had to be applied. If the input is already 1, the function returns 0.

• If n is even, divide it by 2.

• If n is odd, triple it and add 1.

For example, syr 1 = 0, because the Collatz operation doesn’t need to be applied at all: the input is already 1. Further, syr 2 = 1, because applying the operation once produces 1. Similarly, syr 10 = 6.

Your function does not have to be tail recursive, nor does it have to handle integer overflow.

(Why call this function syr? Because it is related to the Collatz conjecture aka the Syracuse problem.
See Wikipedia and XKCD. As far as we know, the function terminates on all positive OCaml integers.)

Testing: Follow the same instructions for testing as Function 1: at least three commented, non-redundant cases, plus more test cases as you wish.

Code quality: Again, take some extra time to make your code as readable and elegant as you can. See the code quality rubric at the end of this handout for suggestions.

This is the stopping point for satisfactory scope.

## Function 3: Nacci

This problem relies on lists, which we will cover in the next lecture.

In the Fibonacci sequence, each number is the sum of the previous two numbers in the sequence. The $$n$$-step Fibonacci sequence generalizes that to the sum of the previous $$n$$ numbers in the sequence, where $$n$$ must be at least 1. Let $$F_k^{(n)}$$ denote element $$k$$ of the $$n$$-step Fibonacci sequence, defined as follows:

• For all $$n$$, let $$F_1^{(n)} = 1$$ and $$F_2^{(n)} = 1$$.

• For all $$n$$, and for all $$k$$ such that $$k > 2$$, let $F_k^{(n)} = \sum_{i=1}^n F_{k-i}^{(n)}.$

• Since the summation above might need to include some “nonexistent” elements of a sequence, let them be 0. Formally, for all $$n$$, and for all $$k$$ such that $$k \leq 0$$, let $$F_k^{(n)} = 0$$.

Define a function nacci : int -> int -> int list that takes an integer n and an integer k as input, both of which must be strictly greater than zero, and returns the first k elements of the n-step Fibonacci sequence. For example, nacci 2 6 = [1; 1; 2; 3; 5; 8]. Your function does not have to handle integer overflow.

Efficiency: Your implementation of nacci must be tail recursive, and it must run in time that is polynomial in k and n. It is actually quite easy to design a naive exponential-time algorithm by simply implementing the equations above in code, and you might even try that first. If you’ve forgotten the difference between polynomial and exponential time, here’s what’s important: your algorithm is going to have to avoid recomputing values in the sequence. That is, if the algorithm has already computed $$F_k^{(n)}$$, then it should not recompute that value as part of computing $$F_{k+1}^{(n)}$$. It is your responsibility to invent the algorithm. We strongly suggest that you design it on paper first, rather than immediately trying to implement it.

Concrete execution time bounds are somewhat meaningless, since some people have slower or faster machines. But as an example, when n is 2 and k is 1 million, a polynomial-time algorithm will probably execute within about 2 seconds. That execution time will of course increase as the inputs increase.

Testing: Follow the same instructions for testing as Function 1: at least three commented, non-redundant cases, plus more test cases as you wish. For this function, you will probably want to have several more to convince yourself that your implementation is correct.

Code quality: You know what to do by now.

This is the stopping point for good scope. There is no excellent scope on this assignment.

## Rubric

• 30 points: submitted and compiles
• 25 points: satisfactory scope
• 25 points: good scope
• 10 points: testing
• 10 points: code quality

Testing Rubric. Later in the semester we will focus much more heavily on developing test suites. For this first assignment, though, here is what the graders will assess:

• Each of the three required functions, whether it was implemented fully or not, has at least three test cases that are explained in a comment and are non-redundant.
• Any test cases that are failing are commented out, so that the program does not actually produce an exception when executed.

Code Quality Rubric. There are many aspects of quality that make code easier to read. We will focus on just a few for this first assignment. The graders will assess the following aspects of your source code:

• The programmer’s name and NetID are supplied at top of file.
• Each of the three required functions has a specification comment documenting the function in the way described by the 3110 textbook in sections 2.3.7 and 2.3.8, including preconditions. You may not punt by writing, “see the handout.” But, it is fine to copy information from this handout. You may assume the reader knows the definitions of the terms “leap year rule”, “Collatz operation” and “n-step Fibonacci sequence”. Anything else has to be explained. Other functions you add ought to have specification comments, too, but we won’t assess it on this assignment.
• White space (the space character and empty lines) is used effectively.
• Indentation of let and if follows the OCaml Community guidelines.
• Identifiers consistently use snake_case, not camelCase.
• No line is wider than 80 columns.
• No tabs (ASCII character 9) are used, only spaces.

## Submission

Set the hours_worked variable at the end of warmup.ml to the number of hours you spent working on this assignment, rounded to the nearest integer. Please don’t include the time that you spent installing OCaml or the VM.

Ensure that your solution passes make finalcheck. That will do the same as make check, as well as two other things. First, it will check to make sure you’ve set hours_worked. Second, it will compute a short “fingerprint” of your submission called an MD5 sum.

Submit your warmup.ml on CMS. The MD5 sum that CMS reports for your submission should be the same as the MD5 sum that make finalcheck reported. If not, you probably uploaded the wrong file. Double-check before the deadline that you have submitted the intended version of your file.

Congratulations! You’ve finished your first 3110 assignment!