Introduction to Programming
                      Assignment 1, 15 Aug, 2008
                         Due Mon 25 Aug, 2008

1. Define the function
 
          leastTwo :: Int > Int-> Int -> Int

   that returns the sum of the smallest two of its three inputs.

   For instance:

          leastTwo 3 1 2 = 3
          leastTwo 3 4 3 = 6
          leastTwo 8 8 3 = 11

2. Define the function

          largestDivisor :: Int -> Int

   that takes a positive integer n as input and returns the
   largest proper divisor of n --- that is, the largest divisor
   of n strictly smaller than n.

   For instance:

          largestDivisor 12 = 6
          largestDivisor 27 = 9
          largestDivisor 13 = 1

3. Define a function

          charsToNum :: [Char] -> Int

   that converts a list of characters representing numbers to its
   corresponding value as an integer.  

   To do this, use an auxiliary function

          charToDigit :: Char -> Int

   that converts a digit like '8' to its value, 8.  The value of
   non-digits should be taken to be 0.  In other words,
   charToDigit maps '0','1',...,'9' to 0,1,...,9 respectively and
   maps all other characters are mapped to 0.  

   Here are some typical results that charsToNum should report:

          charsToNum ['1','3','8']     should return 138
          charsToNum ['1','a','b','9']  should return 1009

4. Define a function 

          descending :: [Int] -> Bool

   that returns True if each element in its input list is at
   least as big as the one before it.

   For instance:

          descending [] = True
          descending [4,4,3] =  True
          descending [19,17,18,7] = False

5. Define a function

          alternating :: [Int] -> Bool

   that returns True if the values in the input list alternately
   go up and down (in a strict manner).

   For instance:

          alternating [] = True
          alternating [1,3,2,3,1,5] = True
          alternating [3,2,3,1,5] = True
          alternating [3,2,2,1,5] = False
          alternating [3,2,1,3,5] = False

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