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Problems from the book (HTDP) with some customization

• 11.2.4 (20 pts.)
  
  • Copy the definition of deep-list from the text. Be sure to provide your own function template for deep-list and to write template instantiations for depth and make-deep.
• 11.4.7 (20 pts.)
  
  • Include a data definition (following the text) of natural>=1. In addition to the constructors, accessors, recognizers, and equal?, you may use the library functions remainder and * . Hint: define an auxiliary function is-divisible-by of two inputs p and q (using the remainder library function) that determines if p is divisible by q (i.e., p/q is a whole number).
  • Note that the problem as stated in the book has TWO parts; the second, writing prime? is easy after doing the first. Do not worry about optimizing the search for a divisor for n by bounding the search to numbers less or equal to (integer-sqrt n); for simplicity, the integer-sqrt and sqrt library functions are forbidden in this exercise.
• 12.2.2 (20 pts.)
• 12.4.2 (30 pts.)
  [In Second Edition, exercises 171 & 172]
  
  • Do this problem followed by developing the function arrangements that returns a list containing all of the arrangements (permutations) of the input word. This function is described in detail in the text and the code for it is given to you in the statement of problem 12.4.1. You are expected to present this answer in your program file as if you developed it, including supporting test data.
  • The Hintfor this problem should include the following:
    
    • Your program must distinguish between the types word and list-of-word and process them separately. The data-driven approach to program design preached in this course naturally leads to this distinction.

    • The behavior of the function insert-everywhere/in-all-wordsis more easily understood given the following examples:

      Code Block
      (insert-everywhere/in-all-words 'd (list (list 'e 'r))) = (list (list 'd 'e 'r) (list 'e 'd 'r) (list 'e 'r 'd)) (insert-everywhere/in-all-words 'd (list (list 'e 'r) (list 'r 'e))) = (list (list 'd 'e 'r) (list 'e 'd 'r) (list 'e 'r 'd) (list 'd 'r 'e) (list 'r 'd 'e) (list 'r 'e 'd))

    • You will need to write a help function insert-everywhere where (insert-everywhere s w) inserts the letter s in each possible position in the word w, including before and after all letters of w. Note the difference in the type contracts for insert-everywhere and insert-everywhere/in-all-words.
  • Notes: the function arrangements computes all of the permutations of the input word. Permutation is an important concept in basic probability theory. For some reason, the authors of the book chose to avoid using the relevant mathematical terminology. This problem includes writing the arrangements function because it is cool and developing insert-everywhere/in-all-words is the bulk of the work involved in developing arrangements .
• 13.0.5 (part 4 only) (5 pts.)
• 13.0.8 (part 2 only) (5 pts.)