CSC151.02 2016S, Review Session 2 (2016-02-04) ============================================== * Thank you to the many people who showed up, so that we were able to have a review session. _Overview_ * Quiz topics and structure. * Your questions. * Sample quiz questions. * More questions. Quiz Topics and Structure ------------------------- Topics * Scheme's order of evaluation and sequencing. * Definitions (in Scheme). * Arithmetic operations, including things like `max`, `min`, `floor`, `ceiling`, `round`, `quotient`, and `remainder`. * You do NOT have to understand the difference between `remainder` and `modulo`. * RGB colors, and the operations on integer-encoded RGB colors. * Basic RGB transforms (although we will remind you of what they do): `irgb-redder`, `irgb-greener`, `irgb-bluer`, `irgb-darker`, `irgb-lighter`, `irgb-complement`, `irgb-rotate`, `irgb->string` * Function composition. E.g., `(compose irgb-redder irgb-darker)`. * NOT sectioning. * NOT `image-load`, `image-save`, `image-variant` Form * "evaluate this expression (or series of expressions)" * "using composition, write a procedure to compute ..." * "given this definition, what does this procedure do?" Your Questions -------------- _I can't do math in my head. Are calculators okay?_ > Probably not; I don't think we have anything particularly complicated on the quiz. Mostly addition and subtraction. Plus, you have paper! _Do we have to memorize how much each transform changes things?_ > No. We'll tell you. We may be cruel enough that we will give you different definitions (e.g., "assume `irgb-redder` adds 11 to the red component, bounding at 255 ...") _Do we have to be able to convert RGB triples to those unreadable numbers?_ > NO! _What transformations can't be undone? It seems like most of the time we are adding and subtracting, so you just do the inverse._ > You can't do the inverse when we "cap" the value. E.g., `(irgb-lighter (irgb-darker (irgb 0 10 15)))` gives us `(irgb 16 16 16)`, which is not the same. If the result of `(irgb-darker x)` is black, we can't tell which of the 8000 or so fairly dark colors `x` was. > Similar issues for `irgb-redder`, `irgb-bluer`, `irgb-greener`, `irgb-lighter`. _Is there a way to add 3 to the red component, assuming `color` is already an integer-encoded IRGB color?_ > `(irgb-add color (irgb 3 0 0))` _Do we get extra credit for catching typos in your quizzes?_ > Not usually. Sometimes typos affect solvability, in which case yes. Sample Quiz Questions --------------------- Given that * `irgb-redder` adds 32 to the red component (bounding at 255) * `irgb-greener` adds 32 to the green component (bounding at 255) * `irgb-bluer` adds 32 to the blue component (bounding at 255) * `irgb-complement` subtracts each component from 255 * `irgb-darker` subtracts 16 from each component (bounding at 0) * `irgb-lighter` adds 16 to each component (bounding at 255) ### Evaluate These Expressions (Show Your Work) #### Colors (irgb->string (irgb-darker (irgb-lighter (irgb 16 192 240)))) (irgb->string (irgb-lighter (irgb-darker (irgb 16 192 240)))) ##### A Solution (irgb-lighter (irgb 16 192 240)) -> (irgb 32 208 255) (irgb-darker (irgb 32 208 255)) -> (irgb 16 192 239) "16/192/239" (irgb-darker (irgb 16 192 240)) -> (irgb 0 176 224) (irgb-lighter (irgb 0 176 224)) -> (irgb 16 192 240) "16/192/240" #### Floors and Ceilings (floor (+ 1/2 (ceiling (- 1/2 (round 2.5))))) (ceiling (+ 1/2 (truncate (- 1/2 (floor 2.5))))) ##### Solutions (round 2.5) -> 2 (- 1/2 2) -> -3/2 (ceiling -3/2) -> -1 (+ 1/2 -1) -> -1/2 (floor -1/2) = -1 (floor 2.5) -> 2 (- 1/2 2) -> -3/2 (truncate -3/2) -> -1 (+ 1/2 -1) -> -1/2 (ceiling -1/2) -> 0 ### Write a Procedure #### Much Darker Without using `section`, `lambda`, or `irgb-darker`, write a procedure, `irgb-much-darker`, that takes an integer-encoded RGB color as input and subtracts 32 from each component (bounding at 0). ##### A Solution (define irgb-much-darker (irgb-complement irgb-lighter irgb-lighter irgb-complement)) For a component, `c` 255 - (16 + (16 + (255 - c))) 255 - (16 + 16 + 255 - c) 255 - (16 + 16 + 255) + c 255 - 32 - 255 + c -32 + c If we were allowed to use `section` (define irgb-much-darker (section irgb-subtract <> (irgb 32 32 32))) #### Less Blue Without using `section`, or `lambda` write a procedure, `irgb-less-blue`, that takes an integer-encoded RGB color as input and subtracts 32 from the blue component (bounding at 0). ##### A Solution ### Quad Without using `section` or `lambda`, write a procedure, `quad`, that takes a number is input and computes the number to the fourth power. #### A Solution (define quad (compose square square)) ### Interpret a Procedure or Expression #### A Color Transformation Consider this definition (define fun (compose irgb-darker irgb-redder irgb-greener)) What is (irgb->string (fun (irgb 16 192 210))) Explain *concisely* what `fun` computes. #### Another Color Transformation Consider this definition (define fun (compose irgb-complement irgb-darker irgb-bluer irgb-greener irgb-complement)) What is (irgb->string (fun (irgb 16 192 210))) Explain *concisely* what `fun` computes. > `fun` subtracts 16 from the green and blue components and adds 16 to the red component. > _No, I probably wouldn't ask something quite that complex on a quiz, but maybe on an exam._ #### Fun with Numbers Assume that `(square x)` computes `(* x x)`. Consider this definition (define fun (compose floor square)) What is (fun 3.9) #### A Strange Expression Explain what the result of the following expression is in terms of `x`. (- x (remainder x 5)) ##### A Solution > The difference between x and the remainder of x/5. (No; just a translation into English.) > The nearest multiple of 5 to x. #### Potential Values What values can the following expression take on? (- (floor x) (round x)) More of Your Questions ---------------------- _What does `truncate` do?_ > Cuts off everything after the whole part. > Rounds down for positive, rounds up for negative. _What does "explain concisely" mean?_ > Talk about the apparent purpose, rather than the steps involved. > Give a "high level" overview.