Homework 3 (Due Friday 2/5/2010 at 10:00am)
Submit your .ss and .txt files via OWL-Space. You will need to use the "Intermediate Language Level" to do Problem 18.1.15. You may use this language for the entire assignment if you choose.
Required problems:
- 14.2.4
Note: Be sure to compare list searching with tree searching, as the problem states. - 16.3.3
- Test every function thoroughly (5+ examples)
- Be sure to include definitions for both variations of
du-dir
. - The final sentence should read "storing a file or a directory in a dir
structure costs 1 storage unit." In other words, given a dir structure, each
directory entry (a file or a directory) contained therein costs 1 unit of
storage for the bookkeeping data. For a file, this is in addition to the size
of its data.
- 17.1.2
- 17.6.1
Do the problem as specified in the book.
*Extra Credit: This problem can be solved more elegantly than the solution
implied in the
book. For the extra credit solution ignore the book's guidance on "writing
functions that consume two
complex inputs" in 17.5 and follow the guidance given in class on how to write a
function that processes multiple inputs. Select one input as primary (the
choice may be arbitrary in some cases). If you need to deconstruct a second
argument, do it in a auxiliary function. Use only one design template in
each function. Hint for solving this problem: only your auxiliary function,
which has a contract and purpose statement almost identical to merge
should be recursive (call itself) and it may need to deviate slightly from
the structural recursion template.
- 17.7.1
Note: Make sure you understand section 14.4 before working on this problem. Use
this data definition as a starting point:You are required to extend this definition to include applications (that is,; expression ; An expression is one of: ; - a number ; - a symbol ; - (make-mul e1 e2) where e1 and e2 are expressions ; - (make-add e1 e2) where e1 and e2 are expressions
expressions like). Be sure to include a function(* (f (+ 15 x)) (g x))
template with your solution.
- 18.1.5, parts 1, 4, & 5
- 18.1.15
Optional problem for extra credit:
- The fibonacci function fib is defined by the following rules (in Scheme notation):
- (fib 0) = 1
- (fib 1) = 1
- (fib (+ n 1)) = (+ (fib n) (fib (- n 1)))
- A naive program for computing fib (lifted directly from the definition) runs in
exponential time, i.e. the running time for (fib n) is proportional to K*b**n
for some constants K and b)
It is easy to write a program that computes (fib n) in time proportional to n.
Your challenge is to write a program that computes (fib n) in log time assuming
that all multiplications and additions take constant time,
which is unrealistic for large n. More precisely, your program should compute
(fib n) using only O(log n) addition and multiplication operations (less
than K * log n operations for some constant K).
- Hints: assume n = 2*m. Derive a recurrence for fib 2*(m + 1) in terms of
fib 2*m and 2*m - 1. Initially write a program that works when n is a power
of 2. Then refine it to a program that works for all n.
Access Permissions: (Please don't edit)
- Set ALLOWTOPICCHANGE = Main.TeachersComp210Group