Description

Code golf!

This assignment is simple: there are three tasks listed below. For each task, you should submit a Haskell function with the required name and type signature which accomplishes the given task and is as short as possible.
Rules
• Along with your solution for each task you must include a comment explaining your solution and how it works. Solutions without an explanatory comment will get a score of zero. Your comment should demonstrate a complete understanding of your solution. In other words, anything is fair game but you must demonstrate that your understand how it works. If in doubt, include more detail.
• Comments do not count towards the length of your solutions.
• Type signatures do not count towards the length of your solutions.
• Whitespace does not count towards the length of your solutions. So there is no need to shove all your code onto one line and take all the spaces out. Use space as appropriate, indent nicely, etc., but otherwise try making your code as short as you can.
• Your final submission should be named Golf.hs. Your file should define a module named Golf, that is, at the top of your file you should have module Golf where
• The three shortest solutions (counting the total number of characters, excluding whitespace and the other exceptions listed above) for each task will receive two points of extra credit each. You can get up to a total of four extra credit points.
Hints
• Use functions from the standard libraries as much as possible— that’s part of the point of this assignment. Using (say) map is much shorter than implementing it yourself!
• In particular, try to use functions from the standard libraries that encapsulate recursion patterns, rather than writing explicitly recursive functions yourself.
• If the specification of a task is unclear, feel free to ask for a clarification on Piazza.
• We will test your functions on other inputs besides the ones given as examples, so to be safe, so should you!
Tasks
Exercise 1 Hopscotch
Your first task is to write a function
skips :: [a] -> [[a]]
The output of skips is a list of lists. The first list in the output should be the same as the input list. The second list in the output should contain every second element from the input list. . . and the nth list in the output should contain every nth element from the input list.
For example:
skips “ABCD” == [“ABCD”, “BD”, “C”, “D”]
skips “hello!” == [“hello!”, “el!”, “l!”, “l”, “o”, “!”]
skips [1] == [[1]]
skips [True,False] == [[True,False], [False]] skips [] == []
Note that the output should be the same length as the input.
Exercise 2 Local maxima
A local maximum of a list is an element of the list which is strictly greater than both the elements immediately before and after it. For example, in the list [2,3,4,1,5], the only local maximum is 4, since it is greater than the elements immediately before and after it (3 and
1). 5 is not a local maximum since there is no element that comes after it.
Write a function localMaxima :: [Integer] -> [Integer]
which finds all the local maxima in the input list and returns them in order. For example:
localMaxima [2,9,5,6,1] == [9,6] localMaxima [2,3,4,1,5] == [4] localMaxima [1,2,3,4,5] == []
Exercise 3 Histogram
For this task, write a function histogram :: [Integer] -> String
histogram [1,1,1,5] ==
*
*
* *
========== 0123456789 histogram [1,4,5,4,6,6,3,4,2,4,9] ==
*
*
* *
****** *
==========
0123456789
Important note: If you type something like histogram [3,5] at the ghci prompt, you should see something like this:
” * * ========== 0123456789 ”
This is a textual representation of the String output, including escape sequences to indicate newline characters. To actually visualize the histogram as in the examples above, use putStr, for example, putStr (histogram [3,5]).