Problem 1 (Marroquin Pattern)
The Marroquin pattern of order n is formed by superimposing three square arrays of points of size 2n + 1. Consequently, each array has an odd number of rows and columns. The arrays are rotated about the center (i.e., n + 1) point. The orientations of the arrays (relative to the x-axis) are 0, 60, and 120 degrees. You will write a function called marroquin which takes a single integer argument, n, and returns the Marroquin pattern of order n. Example:>(marroquin 9) #<struct:graphic> >
Problem 2 (Tail-Recursive Spiral)
The following program draws a spiral:
(define spiral
(lambda (angle len n)
(if (= n 0)
(adjoin)
(adjoin (bend angle)
(straight len)
(spiral angle (add1 len) (sub1 n))))))
Rewrite spiral so that it is tail-recursive. You are free to
use any helper functions you may require.
Problem 3 (S-expression Tree)
Write a Scheme function, draw-sexpr, which, given an s-expression, sexpr, draws the corresponding pair tree. Hint: This is a typical tree-recursion on pairs, i.e., the same recursion on car and cdr. You might find a function similiar to the following helpful for assembling the tree:
(define tree-step
(lambda (trunk left-branch right-branch)
(adjoin trunk
(adorn (adjoin (bend -20) left-branch)
(adjoin (bend 20) right-branch)))))
Use the Plumbing Graphics function, text, to label the leaves
of the tree. Here is what a good (i.e., B letter grade) solution
looks like:
> (draw-sexpr (cons 1 (cons 2 0))) #<struct:graphic> >
Here is what an excellent (i.e., A letter grade) solution looks like:
> (draw-sexpr '((1) ((2)) 3)) #<struct:graphic> >
