Comparing Languages

Solve a simple programming problem in each of five different programming languages,

CSC254: Project 1
Comparing Languages
In this project, you will solve a simple programming problem in each of five different
programming languages (six for CSC454 students).
Pascal’s Triangle


A binomial coefficient, written nk for integers 0 ≤ k ≤ n, is the coefficient of the xk
term in the polynomial expansion of (1 + x)n . Binomial coefficients
occur throughout
mathematics and computing. For example, you should know that nk is the number of
subsets of size k from a set of n elements (“n choose k”).
Work out the expansion of (1 + x)n for the first few values of n. Write the coefficients for
each row on a different line. You should notice a pattern.
DO THAT NOW, THEN KEEP READING.
Pascal’s Triangle is a triangular table where row n contains the binomial coefficients for
that n and all 0 ≤ k ≤ n. It also illustrates the relationship between the coefficients. This
is easiest to see if you write the rows centered rather than left-aligned.
DO THAT NOW, THEN KEEP READING.


The first row contains just a single entry, 00 , which is the coefficient of the x0 term
in the
expansion of (1 + x)0 . Since (1 + x)0 = 1 and the x0 term is the constant term, 00 = 1.
MAKE SURE YOU UNDERSTAND THAT, THEN KEEP READING.


After the first row, each binomial coefficient nk is the sum of the numbers “above” it.
That is, each binomial coefficient is the sum of the binomial coefficient above and to the
left of it and above and to the right of it. The row above row n is row n − 1. The position
above and to the left is k − 1 in that row and the position to the right is k.
With that
observation, can you come up with a recursive definition of the binomial coefficient nk ?
TRY IT NOW BEFORE TURNING TO THE NEXT PAGE
1
DID YOU TRY IT YOURSELF BEFORE TURNING TO THIS PAGE? BECAUSE YOU
WON’T LEARN ANYTHING IF YOU DON’T TRY TO DO IT YOURSELF.
2
Each binomial coefficient is the sum of the binomial coefficient above and to the left of

it and above and two the right of it. The binomial coefficient above and the left is n−1
k−1


and the one above and to the left is n−1
.
So:
k
  
 

n
n−1
n−1
=
+
k
k−1
k
for any integer n > 0 and 0 ≤ k ≤ n.
That is so cool.
There is also an iterative method for computing binomial coefficients, and there is a
method that uses the factorial function (which itself has natural recursive and iterative
versions and which you may have learned back in your discrete math class).
3
Project Requirements
You MUST write programs that print the first n rows of Pascal’s Triangle using the following programming languages:
• Imperative: C or C++, Java, Rust
• Functional: Lisp, OCaml
• CSC454 students must also use Haskell
For programs in functional languages, your implementation MUST be based on the recursive definition of the binomial coefficients. For the other languages you can use
whatever method you like (but recursion works fine in them also).
Your programs MUST get the value of n from the command-line. Note that it will be a
string, which you MUST convert into an integer.
Your programs MUST print the triangle with each row left-aligned on a separate line and
each coefficient separated by a single space.
You MUST submit a single ZIP archive containing a README file and the source code
for all of your programs.
We will build and run your programs on the CSC instructional machines using the
instructions in your README.
Programs that do not build will receive a grade of 0 (zero).
Programs that crash will receive a grade of 0 (zero).
Late submissions without an approved accommodation will receive a grade of 0 (zero).
Detailed requirements and additional information follows.
4
README
You MUST submit a README file in text or PDF format.
This document MUST include:
• Name and NetID for all members of the team (maximum two)
• Instructions for building AND running your programs from the command-line using
the tools available on the CSC instructional machines
It is your job to make it clear and easy for us to cut-and-paste from your README to
build and run your programs.
Java
The Java compiler is javac and to run Java programs you use the java program, as
in:
java TheClassToRun foo bar baz
Here “TheClassToRun” is the name of the class whose main method will be run, and
any additional arguments become the String[] argument to that method.
I hope that you knew that already.
C/C++
You may use either C or C++. You should all know C from your previous courses. I
suggest learning some C++ if you don’t know it already, but it is not required.
For C, the compiler on the CSC instructional machines is gcc. For C++, it is g++. You
probably knew that already.
You MUST use the following compiler options: “-Wall -Werror”.
5
If you do not do your development on the CSC instructional machines, I STRONGLY
suggest that you test both building and running on the CSC instructional machines. No
excuses.
For C and C++, the command-line arguments become the argc and argv arguments
to main. Note that argv[0] is the name of the executable program. I hope that you
knew that already.
Rust
The Rust compiler is rustc.
For Rust programs, the command-line arguments are in env::args() which is defined
in the std::env module. As in C, the first element of that array is the name of the
program being executed.
Lisp
For this course, we will use the latest version of Armed Bear Common Lisp (abcl.org).
ABCL runs on the Java Virtual Machine (JVM). To run it, use:
java -jar path/to/abcl.jar
where you provide the path to the ABCL jar downloaded from its website.
For the help message, give “–help” after the jarfile. Check out the “–load”, “–eval”,
and “–batch” options.
Any remaining arguments become the command-line arguments to the Lisp program.
Note that if the first such argument starts with a hyphen (“-”), you must precede it with
“–”.
Those command-line arguments, if any, are available as the value of the variable
EXTENSIONS:*COMMAND-LINE-ARGUMENT-LIST*, which will be a list.
6
The CSC instructional network proves CMU Common Lisp (CMU CL) via the lisp command. That should be fine (any Common Lisp implementation should be fine), but we
will use ABCL and so should you.
OCaml
To run your code under the ocaml interpreter and pass the numbers 3, 1, and 2 as
command-line arguments, use:
ocaml project1.ml 3 1 2
You may also compile with ocamlc to produce native binaries.
In OCaml, the command-line arguments are the value of Sys.argv. This will be an
array whose first element is the name of the program being run. You may find the
OCaml library function Array.to list helpful in working with it.
Haskell
The Haskell compiler is ghc. There is also an interpreter: ghci.
In Haskell, the System.Environment module provides access to the command-line
arguments:
• Computation getProgName has type “IO String” and returns the name of the
program being run
• Computation getArgs has type “IO [String]” and returns a list of the arguments given to the program on the command-line
7
Policies
Late Policy
Late projects will receive a grade of 0. You MUST submit what you have by the deadline. If there are extenuating circumstances, submit what you have before the deadline
and then explain yourself via email.
If you have a medical excuse (see the course syllabus), submit what you have and
explain yourself as soon as you are able.
Collaboration Policy
I assume that you are in this course to learn. You will learn the most if you do the projects
yourself.
That said, collaboration on projects is permitted, subject to the following requirements:
• Teams of no more than 2 (two) students, all currently taking CSC254/454.
• You MUST be able to explain anything you or your team submit, IN PERSON AT
ANY TIME, at the instructor’s or TA’s discretion.
• One member of the team should submit code on the team’s behalf in addition to
their writeup. The other team member MUST submit a README (only) indicating
who their teammate is.
• Both members of a collaborative team will get the same grade on the project.
Working in a team only works if you actually do all parts of the project together. If
you only do one half of the project, then you only learn one half of the material. If
one member of a team doesn’t do their part or does it incorrectly (or dishonestly), all
members pay the price.
8
Academic Honesty
I assume that you are in this course to learn. You will learn nothing if you do not do the
projects yourself.
Do not copy code from other students or from the Internet.
Avoid Github and StackOverflow completely for the duration of this course.
The use of generative AI tools is NOT permitted in this course.
Do NOT submit code that you can’t explain.
Posting homework and project solutions to public repositories on sites like GitHub is a violation of the University’s Academic Honesty Policy, Section V.B.2 “Giving Unauthorized
Aid.” Honestly, no prospective employer wants to see your coursework. Make a great
project outside of class and share that instead to show off your chops.
9