Coordinate Transformation

;; Top-level definitions are global-scope
(def dozen 12)

;; Functions create a new scope.
;; Referencing the outer variable here is a closure.
(fn [n] (* dozen n))

;; This function closure increments the counter's state
;; in the outer lexical context.
;; This way the counter can be shared between many calling contexts.

(def increment
  (let [counter (atom 0)]
    (fn [] (swap! counter inc))))

(increment)
;;=> 1
(increment)
;;=> 2

Instructions

Your design company has primarily been working with CSS transformations to build web pages. After some discussion, a decision is made to start using Clojure to perform some calculations dynamically. Some of your teammates are less experienced with Clojure, so you decide to use a function closure to create reusable transformations for {x, y} coordinate pairs.

1. Translate the coordinates

Implement the translate2d function that returns a function making use of a closure to perform a repeatable 2d translation of a coordinate pair.

(def move-coordinates-right-2px (translate2d 2 0))
(def result (move-coordinates-right-2px 4 8))
;; result => [6 8]

2. Scale the coordinates

Implement the scale2d function that returns a function making use of a closure to perform a repeatable 2d scale of a coordinate pair.

For this exercise, assume only positive scaling values.

(def double-scale (scale2d 2 2))
(def result (double-scale 6 -3))
;; result => [12 -6]

3. Compose transformation functions

Combine two transformation functions to perform a repeatable transformation. This is often called function composition, where the result of the first function 'f(x)' is used as the input to the second function 'g(x)'.

(def move-coordinates-right-2px (translate2d 2 0))
(def double-coordinates (scale2d 2 2))
(def composed-transformations 
  (compose-transform move-coordinates-right-2px 
                     double-coordinates))
(def result (composed-transformations 0 1))
;; result => [4 2]

4. Save the results of functions

Implement the memoize-transform function. It takes a function to memoize, then returns a new function that remembers the inputs to the supplied function so that the last return value can be "remembered" and only calculated once if it is called again with the same arguments.

Memoizing is sometimes called dynamic programming, it allows for expensive operations to be done only once since their result is remembered.

(def triple-scale (scale2d 3 3))
(def memoized-scale (memoize-transform triple-scale))

(memoized-scale 4 3)
;; => [12, 9], this is computed since it hasn't been computed before for the arguments

(memoized-scale 4 3)
;; => [12, 9], this is remembered, since it was computed already