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Part 0:
The file palindrome.py contains two functions.
Each function checks whether the input container is a palindrome,
and each function works correctly no matter whether the input container is a str, list, or deque.
Run the doctests to verify that all functions are correct:
$ python3 -m doctest palindrome.py
Now open the palindrome.py file in vim and verify that the doctests are testing all both functions using all three data types.
Read through the implementation of the functions,
and make sure you understand how they work.
Take a guess at which one will be faster,
and tell the person sitting next to you what your guess is.
Complete the following table, where each entry is the runtime of the corresponding function when the input container is of the corresponding type.
Write the runtimes in terms of n=len(container) using big-O notation.
str |
list |
deque |
|
|---|---|---|---|
check_palindrome_1 |
O(n) | O(n) | O(n^2) |
check_palindrome_2 |
O(n) | O(n) | O(n) |
HINT: The runtimes for indexing into a string are the same as those for indexing a list, which is O(1). The runtime for indexing into a deque is O(n).
HINT: One of these entries should be asymptotically larger than the others.
Part 1:
Now you will use the timeit module in python to measure the runtimes of the palendrome functions. This module is used in the terminal in the following way:
$ python3 -m timeit -s "$SETUP_CODE" "$CODE_TO_TIME"
where $SETUP_CODE is python code whose runtime we don't want to measure (but need to run to setup the problem),
and $CODE_TO_TIME is python code whose runtime we will measure.
The $CODE_TO_TIME will get run many times,
and timeit will report the average runtime.
For example, in order to measure the runtime of the check_palindrome_1 function on a list and deque of length 5, we could run the commands:
$ CODE_TO_TIME='palindrome.check_palindrome_1(xs)'
$ python3 -m timeit -s 'import palindrome; xs=[1,2,3,2,1]' "$CODE_TO_TIME"
$ python3 -m timeit -s 'import palindrome; from collections import deque; xs=deque([1,2,3,2,1])' "$CODE_TO_TIME"
Because these containers are so small,
the runtimes are insignificant.
(I get about 0.7 microseconds for both examples).
It is common to use the letter
What we're really interested in, however, is when [1]*65536 will give us a container of length one hundred thousand with all ones.
(65536 is
$ python3
>>> [1]*65536
Now time the check_palindrome_1 function on a deque of that size:
$ python3 -m timeit -s 'import palindrome; from collections import deque; xs=deque([1]*65536)' 'palindrome.check_palindrome_1(xs)'
Complete the following table with actual measured runtimes by substituting the values for xs and the function in the command above.
xs=("1"*65536) |
xs=([1]*65536) |
xs=deque([1]*65536) |
|
|---|---|---|---|
check_palindrome_1 |
4.33 msec per loop | 4.07 msec per loop | 62.2 msec per loop |
check_palindrome_2 |
3.04 msec per loop | 3.18 msec per loop | 3.21 msec per loop |
You should observe that one of these entries is significantly slower than the others. This tells us that the runtime of a function depends on: (1) the algorithm that it is implemented with, and (2) the data types it is run on.
An good programmer can easily predict which combination above would be slow without running it, and we'll cover in class next week how you can make this same prediction.