(require 2htdp/universe)
(require 2htdp/image)
; 
;  Problem 1:
;  
;  Given the following define-struct statement, name all the func-  
;  tions that are created when this line is executed, give 
;  their contracts, and identify them as constructor, accessor, 
;  mutator, and type checker.
;  
;      (define-struct animal (family genus species))
;      
; family genus and species are strings.
;  
;  


; Problem 2
; 
; Draw the binary search tree that results from inserting           
; the following numbers (as btnodes), in the order given, 
; into an initially empty binary search tree: 
;            55, 25, 89, 77, 65, 12, 5, 14, 90.
;            
; Give the numbers contained in each of the following nodes:
; 
; The root of the BST-
; 
; The internal nodes of the BST-
; 
; The leaves of the BST-
; 


; Problem 3
; 
; Write the function PREFIX-SUM that consumes a list of numbers
; and produces a list of numbers in which every number except  
; the first is replaced by the sum of the previous number (which    
; may itself be a sum) in the list added to its value.
; 
; The first number on the list should be added to the output       
; list unchanged.
; 
; Examples to help clarify the problem:
;  
;  > (prefix-sum '(9 2 4 2 8))     ==> (9 11 15 17 25)
;  
;  > (prefix-sum '(1 2 3 4 5 6 7)) ==> (1 3 6 10 15 21 28)
;  
;  > (prefix-sum '(1 2 3 4))       ==> (1 3 6 10)
;  
;  > (prefix-sum '(1 2))           ==> (1 3)
;  
;  > (prefix-sum '())              ==> ()
;  
;  > (prefix-sum '(5))             ==> (5)
; 
; 



; 
;  Problem 4:
;  
;  Develop the function swap-posn, which consumes a posn structure  
;  and swaps the values in the two fields.
;  
;  First, write a non-mutating function called swap-posn and then 
;  write a mutating function called swap-posn!.
;  


; 
;  Problem 5:
;  
;  Develop the function double-all-ohs which consumes a string 
;  and adds an extra o for each lowercase or uppercase "o" in the   
;  string.
;  
;  Examples to help clarify the problem:
;  
;  > (double-all-ohs "stop")   ==> "stoop"
;  
;  > (double-all-ohs "Onward!")  ==> "OOnward!"
;  
;  > (double-all-ohs "")   ==> ""
;  
;  > (double-all-ohs "hello world")     ==> "helloo woorld"
;  
;  > (double-all-ohs "cat")     ==> "cat"
;  


         
; 
; Problem 6
; 
; Write the function COUNT-WORDS that consumes a phrase 
; (a string) and returns the number of words in the given     
; string. You can assume that words are separated by any non-       
; alphabetic characters.
; 
; > (count-words "This is a sentence.") => 4
; 
; > (count-words "a b c d e f g h i") => 9
; 
; > (count-words "") => 0
; 
; Hint (IF YOU ARE HAVING PROBLEMS WRITING THIS 
; FUNCTION): Use the char-alphabetic? and substring 
; functions and an external helper function to search 
; for the position of the next non-alphabetic char in 
; the input string.
; 
; 



; 
; Problem 7
; 
; Write the function LIST-WORDS that consumes a phrase 
; (a string) and returns each word in the given string as
; a list of strings.
; 
; You can assume that words are separated by any non-
; alphabetic characters.
; 
; > (list-words "This is a sentence.") => 
;                            ("This" "is" "a" "sentence")
; > (list-words "") => ()
; 
; > (list-words "Four score and seven years ago") =>
;             ("Four" "score" "and" "seven" "years" "ago")
;                       
; Hint: You may be able to re-use an external helper 
; function you wrote for problem 8 in the solution for this   
; problem.
;                      


; 
;  Problem 8:
;  
;  Define a function copy-n that consumes a list of anything and a     
;  number, N,  and produces the contents of the input list appended 
;  to itself N times.
;  
;  Examples to help clarify the problem:
;  
;  > (copy-n (list 1 2 3) 4)   ==> (list 1 2 3 1 2 3 1 2 3 1 2 3)
;  
;  > (copy-n (list 1 2 3) 0)   ==> empty
;  
;  > (copy-n empty 4)   ==> empty
;  


; 
;  Problem 9: 
;  
;  Use build-list
;  
;  1. To create the lists (list 0 ... 3) and (list 1 ... 4).
;  
;  2. To define a function evens, which consumes a natural 
;     number n and creates the list of the first n even numbers.      
; 
;  Hint: Use un-named lambda style functions in your calls to 
;  build-list.
;     


; 
;  Problem 10: 
;  
;  Use map to create the function move-all, which consumes a list     
;  of posn structures and translates each by adding 3 to the x-
;  field. 
;  


; 
;  Problem 11: 
;  
;  Use filter to create the function selection, which consumes 2      
;  lists of quoted symbols and produces all the elements from the
;  second list that are also on the first.
; 
;  


; 
;  Problem 12: 
;  
;  Suppose you wanted to write a big-bang simulation that places an    
;  image of a solid maroon circle of radius 20 at the point where 
;  the mouse is clicked on the scene (i.e., a "button-down" event). 
;  At any point in time, there will be at most one circle displayed.
;  
;  (a) What constants would you need to define?
;  
;  (b) What values or structure would you use to define the state of 
;      the world and why?
;  
;  (c) Which clauses (on-draw, on-tick, on-key, on-mouse) would you 
;      need to include in the call to big bang?
;  
;  (d) Write the function used as input to each of the clauses you
;      mentioned in part (c).  Write the invocation of big-bang. 
;  


; 
;  Problem 13: 
;  
;  Evaluate the result of the following expressions:                   
;  
;  (a)  (filter cons? '(1 (2 3) 4 9 (8 7) ((2))))
;  
;  (b)  (map expt '(1 3 4) '(2 2 2))
;  
;  (c)  (apply + (map expt '(1 3 4) '(2 2 2))) 
; 
;