[SOLVED] Csci 4230 – assignment 4

For this assignment you must write the following functions in Scheme:
1. Write a function called letterGrade that takes a number between 0 and 100 and returns a string
containing the corresponding letter grade where 90 and above is an A, 80-89 is a B, and so on. Use a cond
expression to implement this. If the number is out of range, return the string “Error: out of range”.2. Write a function called countdown that takes a positive integer and uses a do expression to display a
sequence of numbers counting down to 1, each on its own line, then displaying the string “Blastoff!”.
3. Write a recursive function called eval-poly that takes a list of numbers representing the coefficients
of a polynomial and a value for x and evaluates the polynomial for the given value of x. The list of
coefficients should start with the term of lowest degree and end with the term of highest degree. If
any term of intermediate degree is missing from the polynomial it should have a coefficient of zero.
For example, the polynomial x
3 + 4x
2 + 2 would be represented by the list ’(2 0 4 1). Hint: the
polynomial above can be rewritten as 2 + x · (0 + x · (4 + x · 1))4. Write a tail-recursive version of the previous problem called eval-poly-tail. It should call a helper
function called eval-poly-tail-helper that uses tail recursion to keep a running sum of the terms
evaluated so far. You might want to use the expt function to take a number to a power.
5. Write a recursive function called split that takes a list and returns a list containing two lists, each of
which has roughly half the items in the original list. The easiest way to do this is to alternate items
between the two lists, so that (split ’(1 2 3 4 5)) would return ’((1 3 5) (2 4)). I recommend
using two base cases: one for an empty list and the other for a list containing one item.
6. Write a recursive function called merge that takes two sorted lists of numbers and merges them together
into one sorted list containing all of the number in both lists including duplicates.7. Write a recursive function called mergesort that sorts a list by doing the following:
(a) Use split to split the list into two roughly equal-sized partitions.
(b) Recursively sort both partitions.
(c) Use merge to merge the sorted partitions together.
Once again you will need two base cases, one for the empty list and the other for a single-element list.What to Hand In
Implement all of the functions described above in a source file called yourlastnameAssign4.scm with your
actual last name. Make sure to put your name, CSCI 4230, and Assignment 4 in the comments (comments
in Scheme start with ;;). Upload the source file to D2L to the dropbox called Assignment 4.