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Michael Locasto                       Introduction to Computer Programming in C
Homework 3                                                            Fall 2005
$Id: hw3.txt,v 1.3 2005/11/22 17:31:37 locasto Exp $
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Due: November 22nd, 2005 Before Class (Courseworks timestamp).

0) Checksum a file. (40 pts)

   Create a checksum program that can read in a file and produce a value
   to be used as a checksum of the file. A checksum value ensures that
   a file has not been changed in transit. This program is similar to the
   md5sum and sha1sum programs commonly distributed with the Linux platform.

   Your tool should be called csum and should take an argument specifying
   which file to process and the particular checksum algorithm to use.
   
   Command line usage:

   csum --file [file] --algorithm [name]
   csum --file [file]
   csum --help | -h
   csum --version | -v

   Where the algorithm name is one of:

    * xor (default)
    * parity
    * mod32sum

   This assignment challenges you to deal with command line arguments and
   file I/O. You should also provide a generic calc_sum() function that
   can perform different checksum algorithms based on the command line
   parameters.

   XOR: take each byte and XOR with the previous result

   PARITY: take each bit and add it to the next

   MOD32SUM: take each byte, mod by 32, and add it

   Questions:
   1. Which is the best checksum algorithm? Why?

   Extra Credit: (20 pts)
   Add the md5 algorithm to your program. This means that you have to
   go look up the source code for md5 and see what it means to use it
   as a checksum.


1) Learn to play roulette. (60 pts)

   Roulette is a popular game of chance. Professor Candide believes that 
   roulette is a losing game, but Professor Hulme assures him that there 
   exist strategies that can win.

   Provide a rough proof that Professor Candide is correct. If you cannot,
   then show that Professor Hulme is correct (that is, there exists at least
   one winning strategy). Hint: not playing is *not* a winning strategy.
   Hint 2: use proof by contradiction. Hint 3: use proof by sheer math.
   (10 pts)

   Although I am not requiring a formal proof, even an informal proof
   requires some knowledge of how roulette is played. Write a program
   to play roulette. The computer acts as the house and the user acts
   as the gambler.
   (40 pts)

   Your program should play roulette as follows:

   There are 38 spots on the board. Play proceeds by having each player
   place their bets on the board. The house halts betting at a certain
   time and spins the roulette wheel, producing a random number. Winning
   bets are paid out and losing bets are collected by the house. Then
   the house signals that players are free to begin placing bets again.
   Players must either place their bets completely *inside* or completely
   *outside* (these terms will become clear when you read further). The
   minimum bet for your program is 5 dollars. Players can have $1 chips,
   $5 chips, $20 chips, or $100 chips. The maximum bet is $5000 dollars.
   Payouts of over 1 000 000 must be authorized by the house.

   The roulette board is divided into a number of categories. There are
   38 numbers: 1 to 36 and 0 and 00. Numbers are either odd or even
   (except 0 or 00), red or black (except 0 or 00), in 1 of 3 columns,
   in 1 of 3 rows. Your program does not have to deal with bets that are
   placed between numbers or columns (on 'corners'). Bets must be 
   completely 'inside' (i.e., on a specific number) or completely
   'outside' (i.e., one of the other aggregate categories).

   Payouts are calculated at these odds: any hit on a single number is
   paid out at 35:1. Any red/black or odd/even hit is paid 1:1. Any
   column or row hit is paid 2:1. If the gambler does not hit, the house
   collects the entire bet, except for a special case.

   Questions: (10 pts)

    0) Formulate a good strategy (a good strategy tries to keep the
       odds as even as possible or in the favor of the player).
    1) Is it possible to have a payout of over 1 000 000?
    2) What is the expected value of your winnings if you bet 5 dollars
       once?
    3) What is the expected value of your winnings if you bet 5 dollars
       10 times in a row?
    4) What happens if you bet odd/even or red/black and 0 or 00 comes up?