Project 1: Arithmetic Tutor

CMSC 330, Sections 0201/0202

written by Michael L. Scott, edited by Vibha Sazawal

You are building an arithmetic tutor to help elementary-school children learn longhand multiplication and division. As part of the tutor, you need two functions, lmult and ldiv, that output answers to arithmetic questions in longhand.

1. Write a Scheme function lmult, to display the longhand multiplication of two nonnegative integers. For example, if you type

        > (lmult 1234 567)
    

   you should see the output

     1234
      567
   ------
     8638
    74040
   617000
   ------
   699678
    

   Similarly, if you type

        > (lmult 567 1234)
    

   you should see

      567
     1234
   ------
     2268
    17010
   113400
   567000
   ------
   699678
    

   The output of your lmult function should look EXACTLY like the format shown above. It should work for arbitrarily large numbers.
2. Write a Scheme function ldiv to display the longhand division of two nonnegative integers. Instead of computing a terminating or repeating decimal, print out a remainder. For example, if you type

        > (ldiv 573 45)
    

   you should see the output

         12R33
       ----
   45 | 573
        45
        ---
        123
         90
        ---
         33
    

   As another example, if you type

       > (ldiv 24 2)
   

   you should see the output

       12 
      ---
   2 | 24
       2 
       --
        4
        4
        -
        0
   

   Do not write R0 if the remainder is zero. Also, attempted division by zero should result in an error message.

      > (ldiv 402 2)
   

   outputs

       201
      ----
   2 | 402
       4
       --
        0
        0
        --
         2
         2
         -
         0
   

   > (ldiv 2 402)
   

   outputs

         0R2
        --
   402 | 2
         0
         -
         2  
   

   > (ldiv 4861 12)
   

   outputs

         405R1
       -----
   12 | 4861
        48
        ---
          6
          0
          --
          61
          60
          --
           1
   

IMPORTANT NOTES: PLEASE READ

• Use only the functional features of Scheme. There should be no functions that end in an exclamation point in your code. You are allowed to use load, display, and newline.
• I will run your code using Guile. You are welcome to develop your code with DrScheme, but you should run your code with Guile (on linuxlab) to make sure it works there before you submit.
• Put all of your code in one file named "proj1.scheme". Using Guile, I will use load to load your file. Then I will call functions lmult and ldiv from the command prompt. You must use the function names lmult and ldiv.
• For references, you can use the Guile Manual and the Scheme Manual. You may find Chapter 6 of the Scheme Manual on built-in functions to be very helpful.
• DO NOT USE any other Internet sources.
• DO NOT SHARE code with anyone other than your project partner. You may work with one 330 student who is also in your section.
• The only source you are allowed to copy code from is The Little Schemer. If you do take a function from the book, you must write a comment above the function that says "Taken from The Little Schemer." If there is no comment, you get a zero.
• Be sure to check out the Grading Rubric.
• Each student should submit something. I expect project partners to submit identical documents.

Deadlines

• March 27th, 11:59 PM: Using the submit server, upload one file named "proj1.scheme" to Project 1a. The file must have a fully working version of lmult.
• April 8th, 11:59 PM: Using the submit server, upload a zip file to Project 1b. The zip file must contain two files: a file named "proj1.scheme" that contains a fully working version of both lmult and ldiv, and a design document in PDF format. Please read the guidelines for the design document carefully.