Lambda Functions
Accumulators
======= Due to the unexpected closure of Rice and the subsequent disruption of our lecture schedule the following topics will be covered in a future lab ==========
Generative Recursion
Students should use DrScheme, following the design recipe, on the exercises at their own pace, while labbies wander among the students, answering questions, bringing the more important ones to the lab's attention.
...
- 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 function
that constructs a list of random numbers in the range from {{Code Block rands
Wiki Markup 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. - Make sure you know how to use
time
by using it to 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). - Use the
time
operation to fill in the following chart.When you are done, compare your results with those generated by other pairs in the lab.input size
input size
input size
200
1000
5000
up
isort
down
rand
up
qsort
down
rand
...