.ipynb file).This homework assignment must be submitted in Gradescope by Noon central time on Tuesday February 6, 2024.
Collaboration is prohibited, and you may only access resources (books, online, etc.) listed below.
This assignment corresponds to Worksheet 4, which involves the Python notebook interface, context managers, and recursion.
The materials you may refer to for this homework are:
This homework assignment has 3 problems, numbered 2, 3, and 4. Problem 2 merely requies you to follow some formatting rules, while problems 3 and 4 are based on mastery of content. The grading breakdown is:
| Points | Item |
|---|---|
| 4 | Autograder (Problem 1) |
| 5 | Notebook formatting (Problem 2) |
| 5 | Problem 3 |
| 5 | Problem 4 |
| 19 | Total |
Ask your instructor or TA a question by email, in office hours, or on discord.
.ipynb)¶To demonstrate your proficiency with the Python notebook interface, put all of your work on this assignment in a Python notebook named hwk4 and submit the notebook file (hwk4.ipynb) to Gradescope.
Your score on this problem will reflect whether or not you submitted a valid notebook file containing all your work on the problems below, and whether it followed the formatting guidelines below.
MCS 275 Spring 2024 Homework 4. In the same cell, include your name as a subheading. Put the authorship statement you would usually include in a homework Python script in this cell, too.Problem 3If you work in Jupyter (as installed with python3 -m pip install notebook), just name the notebook hwk4 and it will be saved with the .ipynb extension in the directory where you started Jupyter.
If you work in Colab, you can download the .ipynb file to your computer using the menu bar that Colab displays at the top of the notebook. Select File, then Download, and in the submenu, Download .ipynb.
Sure, though you'll need to delete a lot of stuff in order to make it conform to the formatting requirements above. I'm not sure if that's easier than starting a notebook from scratch.
First of all, in this problem you'll need to
import time
so that you can use time.time() for timing calculations.
Now, create a class TimedBlock that is a context manager which keeps track of the total amount of time between the start and end of the with-block. It should print a message upon the start of the with-block, and then another upon exit which includes the timing information. The constructor should accept an argument title which specifies a string used to identify the block in the output messages, as shown below.
Make sure your solution behaves exactly as in these examples:
# Sample usage to time a bunch of calculations
with TimedBlock("Gigantic integer arithmetic"):
digits = 0
for k in range(5000):
x = 3**k - 2**k
digits += len(str(x))
print("Total of {} digits".format(digits))
# Sample usage showing we still get timing data if the with-block
# raises an exception
with TimedBlock("Float arithmetic that eventually fails"):
for k in range(5000):
x = 1 / (3**(4000-k) - 2**(4000-k))
# Sample usage showing output is only printed when we enter the with-block
# and NOT when the class is instantiated
B = TimedBlock("Notice the constructor doesn't print anything")
# Sample usage showing that timing begins when the with-block begins
# and NOT whent he TimedBlock constructor is called.
B = TimedBlock("Should take about 0.5 seconds")
# The next delay isn't part of the timing
time.sleep(1.5)
with B:
# This delay IS part of the timing
time.sleep(0.5)
Define a sequence of integers $R_n$ as follows:
$$ \begin{split} R_0 &= 1\\ R_1 &= 1\\ R_2 &= 1\\ R_n &= R_{n-1} + R_{n-2} + \cdots + R_{n-(d+2)} \text{ if }n>2\text{ and }n\text{ has }d\text{ decimal digits.} \end{split} $$In other words, for $n>2$ the $n^{\mathrm{th}}$ term is the sum of the $d+2$ preceding terms where $d$ is the number of decimal digits in $n$.
For example, since the number $3$ has a single digit ($d=1$), the term $R_3$ is the sum of $d+2=3$ previous terms: $$ R_3 = R_2 + R_1 + R_0 = 3$$
Similarly, since the number $42$ has two digits ($d=2$), the term $R_{42}$ is the sum of $d+2=4$ previous terms: $$ R_{42} = R_{41} + R_{40} + R_{39} + R_{38}$$
The sequence thus begins $$1, 1, 1, 3, 5, 9, 17, 31, 57, 105, 210, 403, \ldots $$
with $R_{10} = 210 = 105 + 57 + 31 + 17$ being the first case where the sum includes four previous terms.
Write a function DRB(n) that calculates and returns $R_n$ using recursion.
Write a function DRB_iterative(n) that calculates and returns $R_n$ using iteration.
Verify (by including a code cell and its output in your notebook) that the values returned by these two functions agree for $0 \leq n < 20$.