Assignment 1:  Comparing Languages (Tree Enumeration)

This, the first graded assignment of the semester asks you to solve a simple problem in each of five different programming languages (six if you’re in 454): 

454 students must also write in Scheme. 

The problem is Exercise 6.23 in the textbook: 

Construct a program that outputs (in some order) all structurally distinct binary trees of n nodes.  Two trees are considered structurally distinct if they have different numbers of nodes or if their left or right subtrees are structurally distinct.  There are, for example, 5 structurally distinct trees of 3 nodes: 

picture of 5 trees

These are most easily output in “dotted parenthesized form”: 

        (((.).).)
        ((.(.)).)
        ((.).(.))
        (.((.).))
        (.(.(.)))

You can think of the parenthesized expressions as being generated by the following simple grammar:

T →    a tree can be empty
T → (T.T)    or a node with left & right children

Finding trees is a naturally recursive problem (iterative solutions are also possible).  The easiest and most elegant solutions employ a recursive set of iterators, which are abstractions used to drive a for loop.  We will study iterators in Section 6.5.3; you may want to read ahead.  In the terminology of that section, you’ll find that Python and C# have “true” iterators.  Prolog’s search mechanism can be used to create the equivalent of iterators, and yields a very elegant solution.  Ada and Scheme have no special iterator support; for these you’ll have to work with lists (or find some other solution—e.g., tasks in Ada).  For what it’s worth, Java and C++ (which you can try for extra credit) have iterator objects, which are sort of half of what you want. 

If you already knew all the languages, you’d probably find your task easiest in Prolog and hardest in Ada, with the other languages ranging in between.  (Of course you probably don’t know all the languages already, so the unfamiliar ones will be the hardest.)  A hint: the companion site for the fourth edition of the textbook contains working versions of all the nontrivial examples in the book.  For Ada and C# you might find it helpful to start with one of these:  it will already import appropriate libraries and contain examples of the control constructs, I/O calls, etc. 

When run, your programs should read a single integer n from standard input; most should then print the appropriate trees to standard output (as dotted lists, one per line, in arbitrary order).  For Prolog, which runs in an interpreter, please arrange for trees(n, L) to produce successive trees (values for L) in response to a semicolon prompt.  For Scheme, please arrange for (trees n) to evaluate to a list of trees, each of which is a (nested) list. 

Division of labor and writeup

You may work alone on this project or in teams of two.  If you split up the languages, whoever takes Ada should probably do two; the other person should do three.  However you divide the programming, each team member must write his or her own README file (no sharing of text on this allowed), and turn in the project separately (with all five or six programs, which will be the same as the partner’s code).  This means, of course, that you’ll need to really understand your partner’s code. 

Be sure to read the instructions on the grading page regarding the turn-in procedure and requirements.  To turn in your code, use the following procedure, which will be the same for all assignments this semester:  On a csug machine, put your write-up in a README.txt, README.md, or README.pdf file in the same directory as your code, and (while still in that directory) run the script ~cs254/bin/TURN_IN.  The script will package the contents of the directory (and any subdirectories) into a bundle and send it to the TAs for grading (so clean up any mess you might have in the directory first).  Be sure your write-up (README file) describes any features of your code that the TAs might not immediately notice.  In addition, for this assignment, your README file must compare and contrast the programming experience in the different languages you used (all five/six of them).  What was easy?  What was hard?  Are there noticeable differences in speed?  What do you like/dislike?  Did you find iterators to be helpful? 

Resources

We will be using the following language implementations.  The Ruby, Python, and Prolog interpreters, the Haskell interpreter and compiler, the Ada and Rust compilers, and the OCaml interpreter and compiler are found in /usr/bin.  The Scheme interpreter is found in /usr/staff/bin. The remaining implementations (for C#, Go, and Swift) are in /u/cs254/bin, which you should append to your PATH environment variable (ask a friend or one of the TAs if you don’t know how). 

Ada
Compile your code with gnatmake (a wrapper for the GNU Ada translator).  It produces native executables. 
C#
Compile your code with mcs (the Mono project C# compiler) and run with the mono JIT/run-time system. 
Go
Run your code from the command line with go
Haskell
Run your code under the ghci interpreter, or compile with ghc (the Glasgow Haskell Compiler) to produce native binaries. 
Prolog
Run your code under the swipl interpreter. 
Python
Run your code under the python3 interpreter. 
OCaml
Run your code under the ocaml interpreter, or compile with ocamlc to produce native binaries. 
Ruby
Run your code under the ruby interpreter. 
Rust
Compile your code with rustc.
Scheme (for 454 or extra credit)
Run your code at the command line with plt-r5rs or, under X, with the drracket GUI.  Be sure to configure the latter to use the R5RS language standard (it boots up expecting a vastly expanded language that will try to force you to use modules and other features you don’t want to have to learn at this point.) 
Swift
Run your code under the swift interpreter, or compile with swiftc

You are welcome to work with other language implementations and/or platforms, but you must ensure that your final versions compile and run correctly using the implementations listed above.  We will be testing using only these. 

I won’t be devoting lecture time to how to use these languages.  You’ll need to find on-line tutorials or other resources, and teach yourself.  Here are some decent starting points: 

Ada
C#
Go
Haskell
Prolog
Python
OCaml
Ruby
Rust
Scheme
Swift

Extra Credit suggestions

  1. Try some other languages—from the lists above or beyond.  Java or C++ (with iterator objects) would be interesting.  Swift is not currently available on our variant of Linux, but you could try it on a Mac. 
  2. Give a closed form formula for T(n), the number of trees produced by your code for a given parameter n, and prove that it’s correct. 
  3. Determine the asymptotic (big-O) time and space requirements of your various programs.  Are some of them better than others? 
  4. Display your trees graphically.  (Note that this is an extra option, and should be enabled by some special mechanism.  By default, your code must generate dotted lists.)  One suggestion would be to output in GraphViz's dot format.

Grading Rubric

Trivia Assignment

Before the end of the day on Sunday, January 26, complete the T1 trivia assignment found on Blackboard

MAIN DUE DATE: 

Sunday February 9, at 11:59pm; no extensions. 
Last Change:  30 December 2024 / Michael Scott's email address