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Homework 10

Assigned 1 Dec, due 10 Dec

Essay, to be written individually

Re-read the adages page, the material on Pair Programming, and perhaps this article on computational thinking for non-computer-scientists. Choose one (or several closely-related) adages, or one longer article, that mean more to you than they did at the beginning of the term.

Write an essay of one to five well-structured paragraphs on what this adage really means in practice. Do you agree or disagree? Support your claims with specific examples from your experience this semester.

You may also want to comment on your experience of Pair Programming: how well did it work, what were the advantages and disadvantages, what would make it work better, etc.?

Programming problems

Do not turn these in: I won't have time to grade them anyway. However, they're good exercises to do, and will help you prepare for the final exam.

Problems on natural numbers, covered Nov 24

• Develop a function named add-up-to which takes in a natural number and returns the sum of all the natural numbers up to and including it.
  Example:

  (check-expect (add-up-to 3) 6)
  (check-expect (add-up-to 5) 15)
  (check-expect (add-up-to 10) 55)
  

  Note: there is a formula for this, but I want you to do it recursively, using only addition (no multiplication or division).

• Develop a function named dot-grid that takes two natural numbers width and height, and produces a rectangular grid of circles with width columns and height rows.
  Example:
  

• Develop a function randoms that takes two natural numbers how-many and limit and produces a list of how-many numbers, each chosen randomly from 0 up to limit.
  Example:

  (randoms 10 15)
  (list 11 7 5 3 14 2 14 5 13 10)

  Note: as usual with random functions, you won't be able to specify exactly what the right answer should be, so just describe the answer (e.g. "should be a list of 7 numbers ranging between 0 and 5 inclusive")

• Develop a function table-of-squares which takes in a natural number and returns a list of posns representing a table of numbers and their squares up to the given number.
  Example:

  (check-expect (table-of-squares 4)
  (list (make-posn 4 16) (make-posn 3 9) (make-posn 2 4) (make-posn 1 1) (make-posn 0 0))

  Note: I've put these in descending order because it's easier to write the function that way. It's a good additional exercise to produce the table in increasing order instead.

Problems involving higher-order functions, covered Dec 1

For these problems, you'll need to be in DrScheme's Intermediate language.

• Develop a function remove-if which takes in a list of X's (for any data type X), and a function from X to boolean, and returns a list of X's containing only the ones for which the function is false.

• Develop a function fire-over-100K that takes in a list of employees (see worked exercises 16.2.1 and 16.4.1) and returns a list of the employees who earn under $100,000.
  Hint: you should be able to do this in one or two lines by re-using previously-defined functions.

• Develop a function give-10%-raises that takes in a list of employees and returns a list of the same employees, each earning 10% more than before.
  Hint: Use do-to-each on a function that operates on a single employee.

• Modify the animation from homework 9 to use do-to-each wherever possible. The result should be much shorter and simpler than what you did for homework 9.

• Develop a function do-twice that takes in a function with contract "X -> X", and returns a function with the same contract which applies the given function twice. For example,

  (define add2 (do-twice add1))
  (check-expect (add2 3) 5)

  What does (do-twice sqr) do?

  Generalize this to a function iterate that takes a natural number and a function with contract "X -> X", and returns a function with the same contract which applies the given function the specified number of times. For example, (iterate 2 f) should be equivalent to (do-twice f), and

  (define add5 (iterate 5 add1))
  (check-expect (add5 3) 8)

  What does (iterate 3 sqr) do? What about (iterate 5 sqr)? (iterate 3 (iterate 3 sqr))? (iterate 3 do-twice)?

Problems using mutation, covered Dec 3

For these problems, you'll need to be in DrScheme's Advanced language.

• Develop a function named next that takes no arguments, but each time you call it, it returns how many times it has been called. Example:

  > (next)
  1
  > (next)
  2
  > (next)
  3
  

• Develop a function named next-color that takes no arguments, but each time you call it, it returns the next element in the list (list "red" "orange" "yellow" "green" "blue" "violet"). If you call it more than six times, it returns false.

  Example:

  > (next-color)
  "red"
  > (next-color)
  "orange"
  > (next-color)
  "yellow"
  > (next-color)
  "green"
  > (next-color)
  "blue"
  > (next-color)
  "violet"
  > (next-color)
  false
  

What to turn in and how

The essay should be written individually and turned in with one name at the top. The programming problems should not be turned in. You are free to work with anybody you wish in solving them. Call it a study group.