HW 3: Haskell

CS314 HW 3: Haskell

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.
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] == []
3. Histogram
For this task, write a function histogram :: [Integer] - String which
takes as input a list of Integers between 0 and 9 (inclusive), and outputs
a vertical histogram showing how many of each number were in the input
list. You may assume that the input list does not contain any numbers
less than zero or greater than 9 (that is, it does not matter what your
function does if the input does contain such numbers). Your output must
exactly match the output shown in the examples below.
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: " * *\n==========\n0123456789\n"
This is a textual representation of the String output, including \n escape
sequences to indicate newline characters. To actually visualize the histogram as in the examples above, use putStr, for example, putStr (histogram [3,5]).
Submission
Please submit a single file named hw3.hs on Sakai.
2