Purpose This problem set concerns trees and the design of functions on s-expression data.
;;; An Atom is one of:
;;; - Number
;;; - Symbol
;;; - String
;;; An SExp is one of:
;;; - Atom
;;; - [List-of SExp]
A number is represented as a base-ten numeral: "107", "-92".
A symbol is represented with the characters of the symbol: "foo", "bar". (You may assume that symbols don’t have odd characters, such as space, parentheses, quote characters, etc.)
A string is represented with the characters of the string, delimited by a pair of double-quote characters: "\"foo\"", "\"bar\"". (Note that backslash-doublequote is how you put a doublequote character in a string. You may assume that strings don’t have odd characters, such as double-quote characters themselves.)
A list of s-expressions is represented by (1) a left parenthesis; (2) the items of the list, separated by one or more spaces; (3) a close parenthesis. For example, "(a (37 \"foo\") c)" is the string encoding of a three-element list, whose first element is the symbol "a", whose second element is a two-element list (a number and a string), and whose third element is the symbol "c".
(check-expect (sexp->string '(a (37 "foo") c)) "(a (37 \"foo\") c)")
Your function can add a bit of extra whitespace before/after list elements if it makes it simpler; that’s fine. For example, this is a fine three-element list of symbols: "(a b c )".
If you raise the language level to "Advanced Student", you can use the display function to make DrRacket print out data in the interaction window.
(define-struct lego (label color width)) ; A Lego is a structure: ; (make-lego Number Symbol Number) ; interpretation: (make-lego l c w) is the lego brick ; with label l, color c, and width w (in pixels). (define-struct bigger (lego left right)) ; A LegoBldg (lego building) is one of: ; - Lego ; - (make-bigger Lego LegoBldg LegoBldg) ; interpretation: (make-bigger l lft rgt) makes a bigger ; lego building by putting a lego brick l on top of two lego ; buildings lft (left) and rgt (right).
Problem 2 Design a function, count-bricks, that takes a lego building and produces the total number of lego bricks in that building.
Problem 3 Each lego brick is 10 pixels tall. Design a function, how-high, that takes a lego building and produces the total height of the lego building (in pixels).
Problem 4 Design a function, contains-colored-brick?, that takes a lego building and a color, and determines whether the building contains a lego brick of the given color.
Problem 5 Design a function, find-colored-brick?, that takes a lego building and a color and finds any lego with the given color in the building, or returns false if there are no such legos.
; A MaybeLego is one of: ; - false ; - Lego
Your function should not use contains-colored-brick?, it should not traverse/examine parts of the building more than once, and it should stop searching once any brick of the given color is found.
Problem 6 Design a function, lb->image, that takes a lego building and produces an image of the building.
Hints: You may want to look up above and beside/align in Help Desk. Also, you may want to design a helper function, lego->image, that takes a lego and produces an image of the lego. All legos are rectangular and 10 pixels tall.
(make-bigger (make-lego 4 'purple 80) (make-bigger (make-lego 2 'blue 60) (make-lego 1 'yellow 40) (make-lego 3 'red 40)) (make-bigger (make-lego 6 'orange 60) (make-lego 5 'green 40) (make-lego 7 'red 40)))
(make-bigger (make-lego 4 'purple 80) (make-bigger (make-lego 2 'blue 60) (make-lego 1 'yellow 40) (make-lego 3 'red 40)) (make-lego 6 'orange 60))