...
- We need some data to use for our timing experiments. Write a function
up: nat -> (list-of nat)
which constructs a list of naturals starting with0
in ascending order or retrieve it from a previous lab. For example,(up 7)
returns(list 0 1 2 3 4 5 6)
. You can probably write it faster usingbuild-list
that you can retrieve it. Similarly, write a functiondown: nat -> (list-of nat)
that constructs a list of naturals ending in0
in descending order. For example,(nums-down 7)
returns(list 6 5 4 3 2 1 0)
.
Now write a functionCode Block rands
Wiki Markup that constructs a list of random numbers in the range from {{0}} to {{32767}}. To create a single random number in the range from {{0}} to {{_n_}}, compute {{(random _n+1_)}}. For larger numbers in the range {{\[0, 32768)}}, try:
Note:Code Block (define max-rand 32768) (random max-rand) ; random is built-in
random
is a function in the Scheme library, but it is not a mathematical function, since the output is not determined by the input.
Now, make sure you know how to usetime
. Timeisort
on a list of 200 elements. Run the exact same expression again a couple times. Note that the time varies some. We typically deal with such variation by taking the average of several runs. The variation is caused by a number of low-level hardware phenomena that are beyond the scope of this course (see ELEC 220 and COMP 221).
Continue timing, filling in the following chart. When you're done, compare results with other pairs in the lab.
|
| input size | input size | input size | |||||
---|---|---|---|---|---|---|---|---|---|
|
|
|
| 200 |
| 1000 | 5000 | ||
| up |
| up |
| up
| ||||
isort | down |
| down
| down |
| ||||
| rand |
| rand |
| rand |
| |||
| up |
| up |
| up |
| |||
qsort | down |
| down |
| down |
| |||
| rand |
| rand |
| rand |
|
COMP 280 introduces concepts of how these algorithms behave in general.
The punchline is that we can say that both insertion sort and
quicksort on lists are "_O(n
...