Note: The functions cross, filter-in, filter-out and comes-before? you define in problems 3,4 and 5 are really useful!
(max-sin-r L)
and
(max-sin-f L)
that both take a list
L = (x1 x2 ... xn)
and return the largest
number amongst sin(x1), sin(x2), ..., sin(xn)
.
The function (max-sin-r L)
must be defined
recursively, without the aid of map and apply. The function
(max-sin-f L)
may not use recursion or call any
recursive function you write, it must use map and apply instead.
Examples:
> (max-sin-r '(3 4 7 8 10 12)) 0.9893582466233818 > (max-sin-f '(3 4 7 8 10 12)) 0.9893582466233818 > (max-sin-f '(5.5)) -0.7055403255703919 > (max-sin-r '(5.5)) -0.7055403255703919
(sin-max L)
that takes a
non-empty list of numbers L and returns the element of
that list whose sin is the largest. For example:
> (sin-max '(2.5 2.0 1.5 1.0)) 1.5... because the sin(1.5) = 0.9974949866040544, which is larger than the sines of all the other values. You already know how to write this kind of function recursively. However, think about whether map and apply are much help for this problem ... more specifically, why are they not much help? What else do you need for them to be useful? (To turn in: write a comment in your scheme file, under "Problem 2", that answers this question.)
(cross A B)
that
takes two lists, A and B, and returns the list of all
pairs of elements whose first component comes from A and
second componant comes from B.
For example:
> (cross '(1 2 3) '(a b)) ((1 a) (1 b) (2 a) (2 b) (3 a) (3 b)) > (cross '(hi) '(bye there)) ((hi bye) (hi there))
Here are some words of wisdom: Wouldn't it be
useful to have a function (pair-with x L)
that
takes an object x
and a list
L = (l1 l2 ... lk)
and returns
the list ((x l1) (x l2) (x l3) ... (x lk))
?
Both in defining this function and in using it, you have a
choice of map/apply and recursion. Think about; what are the tradeoffs?
(filter-in keep? L)
and
(filter-out reject? L)
that take a predicate and
a list and return a list that either keeps only elements that
the predicate keep? evaluates to true on or keeps everything
except what reject? evaluates to true on.
Here are some examples:
> (filter-in even? '(10 9 8 7 6 5 4 3 2 1)) (10 8 6 4 2) > (filter-out even? '(10 9 8 7 6 5 4 3 2 1)) (9 7 5 3 1) > (filter-out null? '( (a b) () (1 2 3) ("the" "end") () (x y z))) ((a b) (1 2 3) ("the" "end") (x y z)) >Note: You'll need to do this by recursion ... at least one of them. However, a clever person could use these to solve the
sin-max
problem.
member
function in scheme is pretty
useful. The call (member x L)
searches for x
in the list L by taking the cdr of L repeatedly until it
either runs out, in which case #f is returned, or until it
gets to a point where x is the car of whatever's left of
L, in which case this remaining sublist is what's returned.
For example:
> (member 'd '(a b c d e f)) (d e f) > (member 'x '(a b c d e f)) #fUsing
member
, write a function
comes-before?
that takes a
list L, and two objects a and b, and returns #t if a comes
before b in the list, and #f otherwise. For example:
> (comes-before? 'mon 'wed '(sun mon tue wed thu fri sat)) #t > (comes-before? 'fri 'wed '(sun mon tue wed thu fri sat)) #f >