;;Practice exam:  CMPU 101 Exam 2 Practice exam, Spring 2013

; 
; Problem 1:
; 
;    Write a function PR-SQR that takes a string (str) and a number 
;    (n) as input and prints a n x n square of the str.  This 
;    function should not return anything, it should just have side-
;    effect printing.  Examples of running the function are given
;    below:
;    
;    > (pr-sqr "X" 4)
;    XXXX
;    XXXX
;    XXXX
;    XXXX
;    
;    > (pr-sqr "X " 5)
;    X X X X X
;    X X X X X
;    X X X X X
;    X X X X X
;    X X X X X
;    
;    Hint: You may want to break the function down into a main
;    and a helper function as you did in the printURtriangle
;    function in lab 5.
;    

; 
; Problem 2:
; 
; (a) The sum of the squares of the natural numbers from 0 to n is  
;     given as 
;    
;              1^2 + 2^2 + 3^2 +...+ n^2
;              
;     Write a recursive function that takes a natural number n and
;     computes the sum of the squares up to n.
;     
; (b) Write the same function as in part (a), but use an accumula-
;     tor.
;     
; (c) Write another version of the function that uses higher
;     order functions instead of explicit recursion.   
;    
; (d) The value computed in part (a) is equal to the following:
;     
;                    (n(n+1)(2n+1))/6
;                    
;     Write a function that computes the equation given above and
;     use check-expect statements to show the equality of the 
;     expressions from parts (a) and (b).
;    

; 
; Problem 3:
; 
;    Write a predicate function called SMALL-VALUE? that takes in a 
;    data item (any valid Racket entity) as input and that returns
;    #t if the input is a Boolean value or a number between 0 and 
;    20 (including 0 and 20).  For full credit, your solution 
;    should not use an if or a cond.  If you have trouble writing
;    a solution with no decision statement, try writing the 
;    function with a decision statement first and it might give 
;    you some insight into writing it without if or cond.
;    
;    > (small-value? 7)
;    #t
;    
;    > (small-value? #f) 
;    #t
;    
;    > (small-value? 'foo)
;    #f
;    

; 
; Problem 4:
; 
;    Write a function called KEEP-SYMBOLS that takes a list of any  
;    length and containing any valid Racket types and returns a
;    list containing only the quoted symbols found in the input 
;    list.
;    
;    > (keep-symbols '(a b c))
;    (list 'a 'b 'c)
;    
;    > (keep-symbols empty)
;    empty
;    
;    > (keep-symbols '(3 4 6 a))
;    (list 'a)
;    
;    Write this function using both a higher-order function and
;    using explicit recursion.
;    

;  
; Problem 5:
; 
; (a) Write a function called NAME-TO-DIGIT that consumes a quoted  
;     symbol and, if the input symbol is the name of a digit ('zero
;     through 'nine, in lowercase letters), the corresponding digit
;     is returned.  Otherwise, the input value is returned 
;     unchanged.
; 
;       > (name-to-digit 'zero)
;       0
; 
;       > (name-to-digit 'eighty-two)
;       eighty-two
; 
;       > (name-to-digit 'four)
;       4
;       
;       > (name-to-digit 'SIX)
;       SIX
;       
;       
; (b) Write a function called SUM-ALL that takes a list as its
;     input.  This function computes the sum of the values 
;     specified in the list, and your solution should use the
;     NAME-TO-DIGIT function from part (a).  The list given as
;     input can contain any valid Racket entities, but should
;     only sum the items that are either numbers or quoted
;     symbols representing digits as specified in part (a).
;     
;     > (sum-all '(1 2 3 4))
;     10
;     
;     > (sum-all (list 'three 'two 'six 9))
;     20
;     
;     > (sum-all (list "three" "two" 'seven))
;     7
;     
;     > (sum-all empty)
;     0
;   

; 
;  Problem 6:
;  
;  Write down the value of each of the following Racket 
;  expressions, assuming that each expression is evaluated after    
;  the definition of the constant FOOD-GROUPS, shown below. If 
;  the evaluation of an expression results in an error, give a 
;  brief description of the cause of the error:
;  
;  (define FOOD-GROUPS '(sugar fat coffee chocolate))
;  
;  a) (cons (first (rest FOOD-GROUPS)) 
;           (list (first (rest (rest FOOD-GROUPS)))))
; 
;  b) (first (rest (rest (rest FOOD-GROUPS))))
; 
;  c) (first (rest (rest (rest (rest FOOD-GROUPS)))))
; 
;  d) (append (list (first (rest (rest FOOD-GROUPS)))) '(salt))
; 
;  e) (cons (first FOOD-GROUPS) (cons (first (rest FOOD-GROUPS))
;           (cons 'oreos (rest (rest FOOD-GROUPS)))))
; 
;  f) (rest (first FOOD-GROUPS))
; 


;  
;  Problem 7:
; 
; (a) Write a string-reverse function using explicit recursion over the 
;     input string.
; 
;     Do not use any list functions in your solution.
;     
; (b) Write a string-reverse function that uses list functions to
;     reverse the input string.
; 
;