Chapter 4 Discussion V

Scrabble

In the game of Scrabble you try to fit a word into spaces with some letters already in place. In this question you will write a function to determine if a word fits into a certain space.

    wordFits :: String -> String -> Bool
    wordFits "jerk" "_or_" == False
    wordFits "work" "__r_" == True

Along the way you may want to use a helper function to determine if
characters from the same place match. 

    letterFits :: Char -> Char -> Bool
    letterFits 'j' '_' == True
    letterFits 'e' 'o' == False

The strings given to `wordFits` will be the same length.

Game of 24

In the game of 24 you are supposed to find a way to combine four whole numbers using addition, subtraction, multiplication, and division, in order to get 24 as the final answer.

1. pairPossible produces all of the numbers that you can get from a single pair of numbers. Only consider the results of division when the answer is an integer.

   pairPossible 3 12 == [-9,9,15,36,4]
   pairPossible 3 4 == [-1,1,7,12]
   pairPossible 49 2 == [-47,47,51,98]
   

   Danger: 49/2 is not 24, so pairPossible 49 2 should not include 24 in the list! (Trouble? See the notes below.)

2. allPairs produces a list of all of the possible two number pairs given a list of four numbers.

   allPairs :: [Int] -> [(Int,Int)]
   allPairs [1,2,3,4] == [(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)]
   

3. allPossible1 produces a list of all numbers that could be produced by using any pair of numbers from the list. Duplicates are ok.

Advanced

• Make allPairs work for any length input list.

• Make choose k nums that gives all k item subsets of nums. For example, when k is 3 and nums is [1,2,3,4,5], the result should be

    choose 3 [1..5] == [[1,2,3],[1,2,4],[1,2,5],[2,3,4],[2,3,5],[3,4,5]]
  

• Finish the 24-solver. There are two different groupings that could lead to 24: (((ab)c)d) and ((ab)(cd)). You can use your allPairs function but as you build all of the possibilities for four numbers, I think you will have to handle both of these cases separately.

  Examples: $(49 - 1) / (5 - 3)$ and $((15 / 3)+1)*4$ are both 24.

Notes

Many people have problems determining when a fraction is an integer. The bad way to do this is

isInt :: Float -> Bool
isInt x = 
   x == round x

Oops, that does not work because round produces an Integral output. Free that up with fromIntegral:

isInt x = 
   x == fromIntegral (round x)

A better way to solve the same problem is to determine if division will produce a fraction before you do the division. Use the integer division (quotient) and remainder functions.