Use the {{Intermediate Student with lambda}} language level. You can choose to use {{lambda}}, as appropriate, in any of the assigned problems. \[For 2011: You may _not_ use {{local}} to define functions; all program functions (including helpers) must be defined at the top level.\] |
Book Problems:
(define (my-max lon) (cond [(empty? lon) (error 'my-max "applied to no arguments")] [(empty? (rest lon)) (first lon)] [else (local [(define head (first lon)) (define max-tail (my-max (rest lon)))] (if (>= head max-tail) head max-tail))])) |
(define (my-max1 lon1) (cond [(empty? lon1) (error 'my-max "applied to no arguments")] [(empty? (rest lon1)) (first lon1)] [else (local [(define head2 (first lon1)) (define max-tail2 (my-max1 (rest lon1)))] (if (>= head2 max-tail2) head2 max-tail2))])) |
22.2.2 (10 pts) \[For 2011: 12 pts\] |
make-sort
.make-sort
produces functions. Test these results by applying them to a few different arguments.23.3.9 (10 pts) \[For 2011: 8 pts\] |
greg
is (4, -4/3, 4/5, -4/7, ...).(lambda (f g x) (f x (lambda (x) (g (g x))))) |
(lambda (f1 g1 x1) (f1 x1 (lambda (x2) (g1 (g1 x2))))) |
; compose : ? ; Purpose: (compose f g) returns the result of composing functions f and g: x |-> f(g(x)) (define (compose f g) (lambda (x) (f (g x)))) |
mergesort
function as described in exercise 26.1.2, except decompose the problem "top-down" rather than "bottom-up". You will need to define a function split: (list-of number) -> 2-element-structure-of-lists-of-number)
that partitions its input into two lists of approximately (+/- 1) the same length in O(n) time where n is the length of the input list. (split l)
returns a 2-element structure containing two lists of numbers. See below for hints in defining a 2-element structure. After splitting the list in half, mergesort
recursively sorts each half and then merges them together. Be careful about attempting to split a one-element list!Hints for writing the "split" function:
A 2-element structure can be defined (you MUST do this somewhere!) in one of two ways:
a) Define your own structure. The CS term for a pair of elements is "dyad", so for instance, one could define a structure as
(define-struct dyad (first second)) |
Review your notes on how "define-struct" automatically creates constructor and accessor functions. You will still need to, in words, define what types the "first" and "second" elements are supposed to be (note: there are several ways to do this).
b) Use Scheme's built-in functions. First, you must explicitly define that you are going to use a list of exactly two elements, i.e. (list a b)
. Scheme already provides functions to access the first and second elements of such a list, called, oddly enough, "first" and "second":
(first (list a b)) ==> a (second (list a b)) ==> b |
Again, you will still need to define exactly what types the first and second elements are supposed to be.
Think simple!
Follow these important rules whenever you write function on a list using structural recursion (note that the generative recursion that mergesort uses follows slightly different rules):
(first aList)
and the recursive result, (myFunction (rest aList))
.local
definition to keep you from repeating the recursive call.