CS 257 (Spring 2006) Homework 5*

• Problem 1 (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 2 (Bacterial Chemotaxis)

• Problem 3 (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 4 (Pig Latin)

  The following description of Pig Latin is taken directly from Wikipedia:
  • For words that begin with consonants, move the leading consonants to the end of the word and add "ay." Thus, "ball" becomes "all-bay"; "button" becomes "utton-bay"; "star" becomes "ar-stay"; "three" becomes "ee-thray";
  • For words beginning with "qu," move the "qu" to the end of the word and add ay. Thus "question" becomes "estion-quay"; and
  • For words that begin with vowels, simply add "way" to the end of the word. Thus, "a" becomes "a-way"; "at" becomes "at-way"; "ermine" becomes "ermine-way."
  Write a Scheme function which will take an English word and returns the translation of the word into Pig Latin (both represented as strings).

• Problem 5 (Polynomial Arithmetic)

  Get the code for polynomial arithmetic from the class homepage. Re-write the function, p*, which multiplies two polynomials, so that it is completely tail-recursive. Hint: This should be done in two parts. First, re-write the subroutine, t*, which multiplies a polynomial by a term so that it is tail-recursive. After you have tested p* and verified that it works correctly with the tail-recursive t*, then re-write p* itself, so that the entire function is tail-recursive. You will need to add tail-recursive subroutines to the letrec (e.g., t*-it and p*-it) to do this.

What You Should Hand In

• Listings of all your code.
• Representative graphic output (where applicable).

When You Should Hand It In

* This webpage is located at http://cs.unm.edu/~williams/cs257/homework5s06.html