Due: February 23 by 11:59pm

Submit: To submit this assignment, create a zip file of all the files in your R project folder for this assignment. Name the zip file`hw6-netID.zip`

, replacing`netID`

with your netID (e.g.,`hw6-jph.zip`

). Use this link to submit your file.

Weight: This assignment is worth 5% of your final grade.

Purpose: The purposes of this assignment are:

- To practice using vectors in R.
- To practice computational problem solving with vectors.

Assessment: Each question indicates the % of the assignment grade, summing to 100%. The credit for each question will be assigned as follows:

- 0% for not attempting a response.
- 50% for attempting the question but with
majorerrors.- 75% for attempting the question but with
minorerrors.- 100% for correctly answering the question.
The reflection portion is always worth 10% and graded for completion.

Rules:

- Problems marked
SOLOmay not be worked on with other classmates, though you may consult instructors for help.- For problems marked
COLLABORATIVE, you may work in groups of up to 3 students who are in this course this semester. You may not split up the work – everyone must work on every problem. And you may not simply copy any code but rather truly work together and submit your own solutions.

## Using the autograder

- You can check your solutions to problems 2 - 6 by logging into the autograder and uploading your
`hw6.R`

file.The file must be named`hw6.R`

or it won’t work.- Your user name is your netID, and your password is inside the
`readme.txt`

file in the Box folder I shared with you.

Download and use this template for your assignment. Inside the “hw6” folder, open and edit the R script called “hw6.R” and fill out your name, GW Net ID, and the names of anyone you worked with on this assignment.

Writing test functionsFor each of the following functions, write a test function first, and then write the function.

Your test functions will count for half of the available credit for each problem. Think carefully about the test cases to include in your test functions.

Using good styleFor this assignment, you must use good style to receive full credit. Follow the best practices described in this style guide.

`vectorFactorial(n)`

[SOLO, 10%]Write the function `vectorFactorial(n)`

which computes the
factorial of `n`

using vectors to avoid using a loop. Hint:
there are some useful functions listed on the vectors lesson page for
performing operators on a numeric vector.

`nthHighestValue(n, x)`

[SOLO, 15%]Write a function to find the nth highest value in a given vector. For
example, if `x`

equals `c(5, 1, 3)`

, then
`nthHighestValue(1, x)`

should return `5`

, because
`5`

is the 1st highest value in `x`

, and
`nthHighestValue(2, x)`

should return `3`

because
it’s the 2nd highest value in `x`

. Assume only numeric
inputs, and assume that `n <= length(x)`

. You may not use
loops.

`dotProduct(a, b)`

[COLLABORATIVE, 20%]**Background**: the “dot product” of two vectors is the
sum of the products of the corresponding terms. So the dot product of
the vectors `c(1,2,3)`

and `c(4,5,6)`

is
`(1*4) + (2*5) + (3*6)`

, or `4 + 10 + 18 = 32`

.
With this in mind, write the function `dotProduct(a, b)`

.
This function takes two vectors and returns the dot product of those
vectors. If the vectors are not equal length, ignore the extra elements
in the longer vector. You may not use loops.

`middleValue(a)`

[COLLABORATIVE, 20%]Write the function `middleValue(a)`

that takes a vector of
numbers `a`

and returns the value of the middle element (or
the average of the two middle elements).

`rotateVector(a, n)`

[COLLABORATIVE, 20%]Write the function `rotateVector(a, n)`

which takes a
vector `a`

and an integer `n`

and returns a new
vector where each element in `a`

is shifted to the right by
`n`

indices. For example, if `a`

is
`c(1, 2, 3, 4)`

and `n`

is `1`

, the
result should be `c(4, 1, 2, 3)`

, but if `n`

is
`-1`

, the result should be `c(2, 3, 4, 1)`

. If
`n`

is larger than the length of `a`

, the function
should continue to rotate the vector beyond its starting point. So, if
`a = c(1, 2, 3, 4)`

and `n = 5`

, then the result
should be `a = c(4, 1, 2, 3)`

.

Read and reflect on next week’s readings on strings. Afterwards, in a comment
(`#`

) in your R file, write a short reflection on what you’ve
learned and any questions or points of confusion you have about what
we’ve covered thus far. This can just few a few sentences related to
this assignment, next week’s readings, things going on in the world that
remind you something from class, etc. If there’s anything that jumped
out at you, write it down.

Thursdays | 12:45 - 3:15 PM EST | Tompkins 208 | Dr. John Paul Helveston | jph@gwu.edu

LICENSE: CC-BY-SA