**Assignment 4: Dijkstra's Algorithm and Data Structures** *Due Thu Oct 28 11:00 PM Pacific Time* [Back to Algorithms](http://cs.pomona.edu/classes/cs140/) # Learning Goals - Learn how to implement graph algorithms and use an adjacency list. - Discover properties about heaps and how they relate to other data structures. - Apply tree balancing with a Red-Black binary search tree. - Compare different methods for implementing hash tables. # 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 14 - Submit your work prior to end of day Oct 28 - You must meet with a TA for grading prior to end of day Nov 2 + **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 Nov 5 # Overview This assignment includes two parts: 1. Answer the [question in this PDF](resources/Heaps-BSTs-HashTables.pdf). See section Resources for the PDF Questions for some help. 2. Write a program for the problem described in section Dijkstra's Single Source Shortest Path Algorithm (must be compatible with Python 3.8). You may work on this assignment alone or 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 both parts to [gradescope](https://www.gradescope.com/). Three key points for the hand written part: 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://divisionii.slack.com/archives/G019H3HEXBK)**. # Resources for the PDF Questions For question `3(c)` you can use the formula found under "A simple exponentiation" at the [Wiki Page for the Birthday Problem](https://en.wikipedia.org/wiki/Birthday_problem). For question `4`, you will find the following resources helpful: - [Code Listing and Example](https://code.activestate.com/recipes/578375/) - [GitHub Code Listing](https://github.com/ActiveState/code/blob/master/recipes/Python/578375_Proofofconcept_more_spaceefficient/recipe-578375.py) - [StackOverflow Comment](https://stackoverflow.com/questions/39980323/are-dictionaries-ordered-in-python-3-6) - [Python 3.6 News](https://docs.python.org/3.6/whatsnew/3.6.html#whatsnew36-compactdict) - [Explanation in Blog Form](https://morepypy.blogspot.com/2015/01/faster-more-memory-efficient-and-more.html) - [Python-Dev Mailing List Conversation](https://mail.python.org/pipermail/python-dev/2016-September/146327.html) # 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/364437 **You can copy and past from the above animation!** # Dijkstra's Single Source Shortest Path Algorithm Your program will accept two program arguments: (1) a filename and (2) a start vertex number. Your program will output the shortest path from the start vertex to all other vertices. ## Input File The file will include all of the information needed to create a **directed** graph. The format of this file is referred to as an adjacency list. Here is an example of such a file: ~~~ 1 2,1 8,2 2 1,1 3,1 3 2,1 4,1 4 3,1 5,1 5 4,1 6,1 6 5,1 7,1 7 6,1 8,1 8 7,1 1,2 ~~~ Each line of the file contains the following information: a vertex identifier (a value from `1` through `n`) and then a list of edges where each edge contains a pair of values (the connecting vertex and an integer value for the edge weight). For example, on the third line above (`3 2,1 4,1`) we can see that vertex `3` is connected to vertex `2` with a weight of `1`, and vertex `3` is also connected to vertex `4` with a weight of `1`. The graph for the above adjacency list is shown below:  **Although the above example only shows two edges per node, there can be any number of edges.** For example, look at the adjacency list below: ~~~ 1 2,3 3,2 2 4,4 3 2,1 4,2 5,3 4 5,2 6,1 5 6,2 6 1,9 ~~~ **Additionally, the spacing between edges might not be consistent.** Your program should handle any kind of whitespace between edges (i.e., multiple spaces and tabs). ## Your program Your file must be named `dijkstras.py`. You will implement Dijkstra's Algorithm using [this implementation of a Fibonacci Heap (`fibheap.py`)](resources/fibheap.py). See [this page created by Dr. Damon Wischik](https://www.cl.cam.ac.uk/teaching/2021/Algorithms/repo2/advdata.html) for additional help using his code. You will need to follow these steps: **Step 1**. Open the input file and read in the contents. I read the data into a Python dictionary where each *key* was a vertex identifier and each *value* was a list of edges. For instance, this is what my dictionary looks like for the example pictured above: ~~~ { 1: [(2, 1), (8, 2)], 2: [(1, 1), (3, 1)], 3: [(2, 1), (4, 1)], 4: [(3, 1), (5, 1)], 5: [(4, 1), (6, 1)], 6: [(5, 1), (7, 1)], 7: [(6, 1), (8, 1)], 8: [(7, 1), (1, 2)] } ~~~ **Step 2.** Implement Dijkstra's SSSP Algorithm. **Step 3.** Print all path lengths as a comma separated list. For instance, the correct output for the example graph (pictured above) starting at vertex 1 is: ~~~ 0,1,2,3,4,4,3,2 ~~~ # 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. You will submit your Python file to gradescope. **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. 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)