Chapter 4 Discussion V

1. 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

2. 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. In this question we do a few steps toward that.

   1. pairPossible produces all of the numbers that you can get from a single pair of numbers. Omit non-integral results of division.

      pairPossible 3 12 == [-9,9,15,36,4]
      pairPossible 3 4 == [-1,1,7,12]
      

   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.