**Assignment 1: Loop Invariants, Asymptotic Notation, and Total Running Time** [Back to Algorithms](http://cs.pomona.edu/classes/cs140/) # Learning Goals - Perform a proof by loop invariant. - Analyze code and proof its asymptotic complexity. - Convert pseudocode to Python. - Identify differences in code performance from data. # Grading This assignment will be graded as pass/no-pass by a TA. To pass the assignment, you must 1. Complete every question in the PDF and submit your answers to gradescope. 2. Complete the programming component and submit your answers to gradescope. 3. Schedule a time to meet with a TA (see section Important Dates for deadlines). 4. Walk the TA through your answers. 5. The TA will then either - mark your assignment as 100% on gradescope, or - inform you that you have some corrections to make. 6. If corrections are needed, then you will need to complete them and then schedule a new time to meet with the TA. If you have concerns about the grading walk-through, you can meet with me after you've first met with a TA. # Walk-Through Guidelines - Walk-through should take no more than 20 minutes. You should be well prepared to walk a TA through your answers. - You may not make any significant corrections during the walk-through. You should plan on making corrections afterward and scheduling a new walk-through time. Mistakes are expected--nobody is perfect. - We will use the Google Sheet found on Slack to schedule your walk-through. This helps TAs manage their time and balance the grading load. - You must be prepared to explain your answers and justify your assumptions. TAs do not need to lead you to the correct answer during a walk-through--this is best left to a mentor session. # Important Dates - You should start this assignment Sep 2 - Submit your work prior to end of day Sep 9 - You must meet with a TA for grading prior to end of day Sep 14 + **It is a good idea to complete the assignment as early as possible** + **You must book a time to meet with a TA** - You should complete corrections by end of day Sep 16 # Overview This assignment includes two parts: 1. Answer the [question in this PDF](resources/time-complexity-loops.pdf). 2. Code the Insertion Sort algorithm in Python (must be compatible with Python 3.8). You may work on this assignment alone or with a partner (**I much prefer you to work with a partner**). Please send me a message on Slack if you want me to assign you to work with a random partner. Whether you work alone or with a partner, only one partner will submit a both parts to [gradescope](https://www.gradescope.com/). Three key points: 1. you should either print the PDF and write your answers directly on the printed sheet, or add annotations to the PDF with Edge (Windows) or Preview (OSX) (using the correct format and spacing will help us grade), 2. ensure that the uploading partner adds the other partners after submission, and 3. **if you have any questions please ask them on [Slack](https://pomona-division-ii.slack.com/archives/C02DGGLQBUG)**. # Example Execution I always like to start by showing you the end result. If you do not see an animation above this line (or if you see the animation but you don't see the progress bar), you will need to refresh the page (sometimes more than once). Or you can go directly to the player: https://asciinema.org/a/433623 **You can copy and past from the above animation!** # Insertion Sort Since this is more of a warm-up algorithm, all you need to do is convert the pseudocode below into a proper Python function. ~~~text linenumbers # Sort the given array into nondecreasing order. # # Args # array : an input array of numbers # # Return # the original array in nondecreasing order # FUNCTION InsertionSort(array)    FOR j IN [1 ..< array.length]       key = array[j]       i = j - 1       WHILE i ≥ 0 && array[i] > key          array[i + 1] = array[i]          i = i - 1       array[i + 1] = key    RETURN array ~~~ I'd encourage you to watch the example execution above and imagine how you would write a program to replicate the command line interaction. After you've had a chance to think about it (or an attempt at coding it up) feel free to fill in this skeleton code with your `insertion_sort` function: [`insertion_sort_skeleton.py`](resources/insertion_sort_skeleton.py). Note that you will need to rename this file to `insertion_sort.py`. You will run your program with the following command: ~~~bash python3 insertion_sort.py ~~~ where `` is one of the following inputs files that you will need to download ([click here to download a zip file with all input files](resources/input-files.zip)): - [decreasing10.txt](resources/decreasing10.txt) - [decreasing1000.txt](resources/decreasing1000.txt) - [decreasing10000.txt](resources/decreasing10000.txt) - [increasing10.txt](resources/increasing10.txt) - [increasing1000.txt](resources/increasing1000.txt) - [increasing10000.txt](resources/increasing10000.txt) - [random10.txt](resources/random10.txt) - [random1000.txt](resources/random1000.txt) - [random10000.txt](resources/random10000.txt) # Code for Merge Sort Instead of asking you to implement both `insertion_sort` and `merge_sort` I am providing you with a [completed implementation of `merge_sort`](resources/merge_sort.py). Note that this is not an efficient implementation, just a simple one implemented by converting pseudocode from my slides. You will run this program similar to how you ran `insertion_sort.py`: ~~~bash python3 merge_sort.py ~~~ # Submitting Your Assignment You will submit your PDF assignment on [gradescope](https://gradescope.com/). **Only one partner should submit your PDF.** The submitter will add the other partner through the gradescope interface. You will also submit your code to gradescope. Your file must be named `insertion_sort.py`. **Only one partner should submit your code.** The submitter will add the other partner through the gradescope interface. Please add your names in comments at the top of the file. To pass the autograder, your output must exactly match the expected output. Your program output should be similar to the example execution above, and the autograder on gradescope will show you the correct output if yours is not formatted properly. You can use [text-compare](https://text-compare.com/) to compare your output to the expected output and that should give you an idea if you have a misspelled word or extra space (or if I do). I've enabled a leaderboard for the assignment. You do not need to worry about it affecting your grade. I just thought it looked like a cute feature. Feel free to give yourself (your group) any name you'd like for the leaderboard. Additional details for using gradescope can be found here: - [Submitting an Assignment](https://help.gradescope.com/article/ccbpppziu9-student-submit-work) - [Scanning Work on a Mobile Device](https://help.gradescope.com/article/0chl25eed3-student-scan-mobile-device) - [Adding Group Members](https://help.gradescope.com/article/m5qz2xsnjy-student-add-group-members) - [gradescope Student Help Center](https://help.gradescope.com/category/cyk4ij2dwi-student-workflow)