;; CS101, Spring 2013
;; Lab 6

;; Using the random function and higher-order functions

(display "\n         CS101 Lab 6, Spring 2013\n")
(display "\n        PLEASE WRITE YOUR NAME HERE\n\n")

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(display "Problem 1: Simulate result of rolling three n-sided dice.\n\n")
; 
; PROBLEM 1:  Function ROLL-3-DICE
; 
;    Write a function that consumes 1 positive natural number, n,
;    and that returns a possible result of rolling three n-sided dice.
;    Remember that certain numbers occur with greater probability
;    than others.
;    
;    The following is an example of what calling this function in 
;    the interactions pane might look like. You should try this a      
;    number of times for a given n after you have written the function 
;    to convince yourself that the numbers generated are sufficiently 
;    random.
;    
;    > (roll-3-dice 6)
;    7
;    > (roll-3-dice 8)
;    13
;    
;    Pre-function tests for this function will not be possible due
;    to random generation of list contents. You can, however, test
;    the range of possible numbers in your check-expect statements,
;    as shown below.
;     


; Contract: 
; Header:   
; Purpose: 

; Pre-function tests:
;(check-expect (and (>= (roll-3-dice 8) 3) (<= (roll-3-dice 8) 24)) true)
;(check-expect (or (< (roll-3-dice 8) 3) (> (roll-3-dice 8) 24)) false)

; Function definition:


; Post-function printf's:

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(display "Problem 2(a): Create a list of random numbers.\n\n")
;    
;   Problem 2(a): Function CREATE-RANDOM-LIST
; 
;    Write a recursive function that consumes 2 positive natural 
;    numbers, num and range, and that returns a list of num numbers 
;    that are chosen at random between 1 and range.
;    
;    The following is an example of what calling this function in 
;    the interactions pane might look like. The contents of the list 
;    will differ because the numbers in the list are chosen at 
;    random.   
;    
;    > (create-random-list 10 20)
;    (list 2 14 5 8 18 7 20 1 4 17)
;    
;    > (create-random-list 5 100)
;    (list 98 3 27 59 42)
;    
;    > (create-random-list 0 0)
;    empty
;    
;    Pre-function tests for this function will not be possible due
;    to random generation of list contents.
;    
;    Use recursion in this solution. 
;    
;    Warning: Calling the random function on 0 produces an error.
;    


; A list of numbers (lon) is either:
; 1. empty, or
; 2. (cons num ln), where num is a number and ln is a lon

; Contract: 
; Header:   
; Purpose:  

; Pre-function tests:


; Function definition:


; Post-function printf's:


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(display "Problem 2(b): Build a list of random numbers.\n\n")
;    
;   Problem 2(b): Function CREATE-RANDOM-BUILDLIST
; 
;    Write a function that consumes 2 positive natural numbers, 
;    num and range, and that returns a list of num numbers that are  
;    chosen at random between 1 and range.
;    
;    The following is an example of what calling this function in 
;    the interactions pane might look like. The contents of the list
;    will differ because the numbers in the list are chosen at 
;    random.   
;    
;    > (create-random-buildlist 10 20)
;    (list 2 14 5 8 18 7 20 1 4 17)
;    
;    Use a call to the function build-list in the body of your function 
;    instead of using explicit recursion.
;    
;    Hint: The unnamed lambda function that is consumed by the 
;          build-list function may ignore its input parameter.
;    
;    Contract: (build-list number (X -> Y)) -> (listof Y)
;    Header:   (define build-list (lambda (n f) ... ))
;    Purpose:  Constructs a list by applying f, a single parameter 
;              function, to the numbers between 0 and (- n 1): 
;    


; Contract: 
; Header:   
; Purpose:  

; Pre-function tests:


; Function definition:



; Post-function printf's:



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(display "Problem 3: FILTER-IF-NOT.\n\n")
;  
; Problem 3: Function FILTER-IF-NOT
; 
;   Write a function called filter-if-not that takes 2 arguments:  
;   a predicate function and a listof anything.  Filter-if-not should 
;   apply the predicate to every element on the list and return the 
;   elements for which the predicate is false.
;   
;   The recursive action of the filter-if-not function should be 
;   done using the built-in FILTER function.
;   
;   Examples of running this function:
;   
;   > (filter-if-not boolean? '(#t 4 a #f 43))
;   (list 4 'a 43)
;   > (filter-if-not number? '(#t 4 a #f 43))
;   (list #t 'a #f)
;   > (filter-if-not odd? '(1 2 3 4 5 6 7))
;   (list 2 4 6)
;   > (filter-if-not even? '(1 2 3 4 5 6 7))
;   (list 2 4 6)
;   
;   The pre-function tests and post-function printfs are provided 
;   for you...uncomment them after you have written the function.
;   


; A list of anything (lox) is either:
; 1. empty, or
; 2. (cons x lx), where x is anything and ls is a lox

; Contract: 
; Header:    
; Purpose:  

; Pre-function tests: (uncomment these check-expects after you write 
;                      the function)
;(check-expect (filter-if-not number? '(a 3 45 "hi" b c)) '(a "hi" b c))
;(check-expect (filter-if-not number? '(43 21 67 34)) '())
;(check-expect (filter-if-not number? '()) '())

; Function definition:



; Post-function printf's: (uncomment these lines after you write the
;                          function)
;(printf "(filter-if-not number? '(a a 1 1 b b)) => ~a~%" 
;        (filter-if-not number? '(a a 1 1 b b)))
;(printf "(filter-if-not number? '(a a b b c 0)) => ~a~%" 
;        (filter-if-not number? '(a a b b c 0)))
;(printf "(filter-if-not number? '(12 3 4)) => ~a~%" 
;        (filter-if-not number? '(12 3 4)))
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(display "Problem 4: Average.\n\n")
;  
; Problem 4: Function AVERAGE
; 
;      The average of the list (a_1 a_2 ... a_n) is defined
;      to be the following quantity:
;  		(a_1 + a_2 + ... + a_n) / n
;                  
;                  
;      Write a Scheme function AVERAGE that computes the average  
;      of the numbers in its input list.  
;  
;      > (average '(1 2 3 2 9 6))
;      23/6
;      > (average '(1 1 1 1))
;      1
;      > (average '(2 3 4 3 2))
;      14/5
;      > (average '())
;      0
;  
;      Use a higher-order function in your solution to this 
;      problem.
;   
;      Your function should avoid the possibility of dividing
;      by zero - an arithmetic error.
;  
 

; Contract: 
; Header:   
; Purpose:  

; Pre-function tests:


; Function definition:


; Post-function printf's:



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