Chapter 3 Test C

You may use the book, but not other reference materials, especially not Stack Overflow or any of your old homework.

1. The odd negative integers greater than -12 are [-11,-9,-7,-5,-3,-1]. Their product is 10395. The sign of this answer is +1 and the last two digits are 95, so q1 (-12) = (1,95).

   A similar process with -14 produces a product of -135135, so the sign is -1 and the last two digits are 35.

   Find the product of all odd negative integers greater than n. Create a tuple containing the sign (+1 or -1) and the last two digits (the tens and units digit). Example:

    q1 (-12) = (1,95)
    q1 (-14) = (-1,35)
    q1 _     = (0,0) -- wrong
   

   Test your code by printing q1 (-2018)

   Warning: The parentheses around the negative is important!

2. Create a list of lists called vigenere to represent the inside of this Vigènere cipher table.

3. (base3) Write a function to convert a number to a list representing the number in base 3. Put the ones digit first.

    base3 (1+2*3+1*9+0*27+1*81) == [1,2,1,0,1]
   

4. (inCirc) Given an integer w, create a list of all integers x that have the property that the point (x,-x) (meaning $y$ is the opposite of $x$) inside the circle of radius 2*w centered at (w,w). This means you are looking for integer coordinate points on the line $y=-x$ that are within distance $2*w$ of the point $(w,w)$.

   Haskell will prefer that you call all of the points involved Double. The other choice is to write your own distance function and use fromIntegral.

    inCirc :: Double -> [Double]
   

   You can use your own distance function or this one:

    dist :: (Double,Double) -> (Double,Double) -> Double
    dist (x0,y0) (x,y) = sqrt $ (x-x0)^2 + (y-y0)^2
   

   Here is an image showing the situation where $w=4$ and there are 9 integer coordinate points that are distance $d \le 8$ from $(4,4)$ and on the line $y=-x$.

   

5. (vig) You can encode messages using the table from question 2. Write a single letter encoder by using the letter from the message to choose the row and the letter from the key to choose the column:

    vig :: Char -> Char -> Char
    vig msg key = undefined
    checkit = (vig 'C' 'X' == 'Z') -- should be True
   

6. (vigen) Enhance your single letter encoder from the previous question to encode messages. Take in two strings: the message and a key, and match up corresponding letters. (Repeat the key as necessary.)

   An example from Wikipedia using the secret key “LEMON”.

    vigen :: String -> String -> String
    vigen "ATTACKATDAWN" "LEMON" == "LXFOPVEFRNHR"