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Submit your .ss
file via OWL-Space. You will need to use the "Intermediate Student" language to do Problem 18.1.15. If you want to use explicit lambda
notation (anywhere the right hand side of a define
statement), you will need to use the "Intermediate Student with lambda" language. You may use either intermediate level language for the entire assignment if you choose.
Required problems:
14.2.4 \ [20 pts.\] *Wiki Markup
Note*: Be sure to compare list searching with tree searching, as the problem states.Wiki Markup - 16.3.3 \ [20 pts.\]
*
Notes*:- 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 bookkeeping overhead is in addition to the size of its data.
17.1.2 \ [20 pts.\]Wiki Markup 17.6.1 \ [20 pts.\]Wiki Markup
Do the problem as specified in the book. *
Extra Credit* \ [10 pts.\]: 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 directly or indirectly) and it may need to deviate slightly from the structural recursion template. The top level {{merge
}} function is _not_ recursive. *
Note* If you do the extra credit version of this problem, you do not need to write a solution as specified in the book.unmigrated-wiki-markup- 17.7.1 \ [10 pts.\]
Note: Make sure you understand section 14.4 before working on this problem. Use this data definition as a starting point:Code Block ; 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
Be sure to include a function template with your solution.unmigrated-wiki-markupCode Block (* (f (+ 15 x)) (g x))
- 18.1.5, parts 1, 4, & 5 \ [5 pts.\]
18.1.15 \ [5 pts.\]Wiki Markup
*Optional problem for extra credit:* \ [50 pts\]
Wiki Markup
The fibonacci function fib is defined by the following rules (in Scheme notation):
Code Block |
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(fib 0) = 0 ;; formerly (fib 0) = 1; revised to match the prevailing mathematical conventions for defining fib (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 fib 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
.
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