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#|                    Extra Credit Assignment                       |#
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This assignment is worth at most 25 percentage points on a homework
assignment.  Since this is an EXTRA credit assignment, it's going to
require EXTRA effort on your part.  You are expected to look up
information for this assignment on your own.  The built in Help Desk
is an excellent resource.  This assignment will cover a topic
that has not been and will not be discussed in lecture or recitation:
strings.  To get you started, type "hello world" (with the quotes) in
a Dr. Scheme interpreter.  That's a string.  A string is a sequence of
characters.  So what's a character?  Search for the Revised(5) Report
on the Algorithmic Language Scheme (known as R5RS) in the Help Desk,
then check out sections 6.3.4 and 6.3.5.  After reading about strings
and experimenting on your own you should see that strings are similar
to vectors in many ways.  Also, please note that THIS IS AN
INDIVIDUAL ASSIGNMENT.  YOU ARE EXPECTED TO FOLLOW THE HONOR CODE AS
IF THIS WERE A REGULAR HOMEWORK.  This assignment is due Friday, 27
July 2001 at 8:00am.  There will be NO extra credit assignments
accepted late for any reason.


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#|                           RESTRICTIONS                           |#
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For this assignment you may NOT use any libraries.  This means no
"require-library" function calls.


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#|                             Grading                              |#
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As per any assignement, you must have good style, but unlike regular
assignments, there will be no style points.  In order to get credit
for a problem you must have both correct code and good style.  One
without the other means no credit.  There will be no partial credit
for a problem; it's all or nothing--remember that this is an EXTRA
credit assignment. 


Problem one
1 point
Write a function called reverse-string.  It should take in a string as
its parameter and return a NEW string with the characters in reverse
order.  Your function must work for ANY string (that includes the
empty string).

Problem two
2 points
Write a function called reverse-in-place.  It should take in a string
as its parameter and reverse the characters of that string.  This
function should return a the changed string.  (hint: remember that
strings are pass-by-reference)

Problem three
2 points
Write a function called to-upper! (yes, include the '!').  It should
take in a string and change all of the letters to uppercase.  Leave
numbers alone.  Return a reference to the changed string.

Problem four
3 points
Write a function called number-of-vowels.  It should take in a string
and return the number of vowels in the string.  (HINT: good style
includes good abstraction)

Problem five
3 points
Write a function called is-palindrome?  It should return #t if the
string is a palindrome and #f if it is not.  If you are unsure what a
palindrome is then consult www.google.com.

Problem six
4 points
Write a function called find-substring.  It should take in two
strings.  If the first string occurs within the second string then
return the index in the second string where the first string begins.
If the first string doesn't occur within the second string then return
#f. 

Problem seven
5 points
Write a function called get-all-paths.  It will be called just like
the dfs and bfs functions from homework five, but instead of returning
one path, return a list of ALL possible paths (remember that a path
has no cycles).  You may use whatever kind of search you like.

Problem eight
5 points
Write a function called sorted-paths.  It will be called just like
get-all-paths.  It should return a list of paths, but the paths should
be sorted such that the shortest path comes first.  Once again, you
may use whichever search you feel is appropriate.