<; office hours: Thursdays 9:30-10:30am, WWH 303
- Course Assistants: Min Jae Song (mjs1168); office hour: Wednesdays 3:00-4:00pm, 60FifthAve 402; Ishan Agarwal (ia1020)
- Recitation 1 (section 004): Ishan Agarwal (ia1020), Wednesdays 8:00-9:15am, Silv 401; office hours: Wednesdays 9:45-10:45am, WWH 805
- Recitation 2 (section 041): Aaron Zweig (az831), Wednesdays 8:00-9:15am, online; office hours: Tuesdays 11:00am-12:00pm, 60FifthAve 402
- Tutors:
- Leo Xu: Wednesdays 4:00-6:00pm, 60FifthAve 402; Fridays 3:30-5:30pm, 60FifthAve 402; Sundays 3:00-4:00pm, online
- Frank Liu: Tuesdays 1:00-4:00pm, 60FifthAve 350; Thursdays 2:00-4:00pm, WWH 805
- As this is a large class, we ask that you first try to post all questions on [Campuswire](https://campuswire.com/p/G7563B609), and/or attend the tutoring sessions. Please email your course assistants (mjs1168, ia1020) only as a last resort. The instructor and recitation leaders will not be able to respond to emails.
## Overview
Reviews a number of important algorithms, with emphasis on correctness and efficiency. The topics covered include solution of recurrence equations, sorting algorithms, binary search trees, partitioning, graphs, spanning trees, shortest paths, connectivity, depth-first and breadth-first search, dynamic programming, and divide-and-conquer techniques.
We will try to cover most of chapters 1-4, 6-8, 12, 15, 16, 22-25, 30, 31, 34 of [CLRS].
## Prerequisites
Data Structures (CSCI-UA 102); Discrete Mathematics (MATH-UA 120); and either Calculus I (MATH-UA 121) or Mathematics for Economics I (MATH-UA 211). Also at least one year of experience with a high-level language such as Python, C++, or Java; and familiarity with recursive programming methods and with data structures (arrays, pointers, stacks, queues, linked lists, binary trees).
## Resources
- **Introduction to Algorithms, 3rd Edition, by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Cliff Stein**, published by MIT Press. Our main textbook. [Available online via NYU Libraries](http://proxy.library.nyu.edu/login?url=https://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=2932690&site=ehost-live)
- [Algorithms Illuminated Omnibus Edition](http://www.algorithmsilluminated.org/) by Tim Roughgarden. Any book written by [Tim Roughgarden](http://timroughgarden.org/) is highly recommended.
- Algorithm Design by Jon Kleinberg and Eva Tardos, Published by Pearson.
- [Lecture Slides](http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/) for Algorithm Design by Kevin Wayne, distributed by Pearson.
## Summary of lectures
Class | Date | Topics | Read and watch before class | Notes | Assignments
--- | --- | --- | --- | --- | ---
1 | Jan 24 | Intro, logists, insertion sort, run time analysis | CLRS §1, §2.1, §2.2; Insertion sort [video1](https://www.youtube.com/watch?v=K4CuPzdiAIo), [video2](https://www.youtube.com/watch?v=EdIKIf9mHk0) and [demo1](https://www.lemmaplay.com/sort/insertion-sort.html) and [demo2 (click INS)](https://visualgo.net/en/sorting)| pp. 1.2-1.5 of [Lecture 1](lecture_1.pdf) | [HW1](hw1.pdf)
2 | Jan 26 | Big-O notation, merge sort | CLRS §2.3,3; Merge Sort [video](https://www.youtube.com/watch?v=Pr2Jf83_kG0) and [demo (click MER)](https://visualgo.net/en/sorting); [Big-O video](https://www.youtube.com/watch?v=v4cd1O4zkGw) | [Lectures 2-6](lectures_2_6.pdf), slides 2-11 of [KT Chapter 5a](http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/05DivideAndConquer.pdf) |
3 | Jan 31 | Analysis of merge sort, Quick Sort | CLRS §2.3, 4.3-4.6, 7; Quick Sort [video](https://www.youtube.com/watch?v=SLauY6PpjW4) and [demo (click QUI)](https://visualgo.net/en/sorting) | [Lectures 2-6](lectures_2_6.pdf), slides 2-11 of [KT Chapter 5a](http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/05DivideAndConquer.pdf) | [HW2](hw2.pdf)
4 | Feb 2 | Finishing Quick Sort; Karatsuba's algorithm | CLRS §7 | [Lectures 2-6](lectures_2_6.pdf), slides 4-12 of [KT Chapter 5b](http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/05Multiplication.pdf) |
5 | Feb 7 | Finishing Karatsuba, Closest pair in the plane | KT §5 | [Lectures 2-6](lectures_2_6.pdf), slides 21-34 of [KT Chapter 5a](http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/05DivideAndConquer.pdf) | [HW3](hw3.pdf)
6 | Feb 9 | Finishing Closest Pair | CLRS §33.4 | [Lectures 2-6](lectures_2_6.pdf) |
7 | Feb 14 | Median and order statistics in linear time | CLRS §9 | [Lectures 7-13](lectures_7_13.pdf) | [HW4](hw4.pdf)
8 | Feb 16 | Lower bound for comparison sort | CLRS §8.1 | [Lectures 7-13](lectures_7_13.pdf) |
9 | Feb 21 | Counting sort, Radix sort; Dynamic Programming: Fibonacci Numbers | CLRS §8.2, §8.3 | [Lectures 7-13](lectures_7_13.pdf) | [HW5](hw5.pdf)
10 | Feb 23 | Dynamic Programming: Rod Cutting Problem | CLRS §15.1 | [Lectures 7-13](lectures_7_13.pdf) |
11 | Feb 28 | Dynamic Programming: Longest Common Subsequence| CLRS §15.4, [visualization](http://lcs-demo.sourceforge.net/) | [Lectures 7-13](lectures_7_13.pdf) | [HW6](hw6.pdf)
12 | Mar 2 | Dynamic Programming: LCS, Knapsack | CLRS §15.3-4; Demaine's [video lecture](https://youtu.be/ocZMDMZwhCY?t=2592)| [Lectures 7-13](lectures_7_13.pdf), slides 23-28 of [KT Chapter 6](http://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/06DynamicProgramming.pdf) |
13 | Mar 7 | Greedy: Interval scheduling (aka activity selection) | CLRS §16.1-2 | [Lectures 7-13](lectures_7_13.pdf), [Slides 1-10](http://athena.nitc.ac.in/~kmurali/Courses/Algos15A/interval.pdf) | [HW7](hw7.pdf)
14 | Mar 9 | Greedy - Huffman Code | 6 first minutes of video on [priority queues](https://youtu.be/B7hVxCmfPtM); CLRS §16.3 | [Lectures 16-22](lectures_16_22.pdf); Slides 1-17 of [KT Chapter 4.8](https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/04Huffman.pdf) | [Practice Midterm](practice_midterm.pdf)
15 | Mar 21 | Review of practice midterm and HW | | |
16 | **Mar 23** | Midterm | | |
17 | Mar 28 | Greedy - Huffman Code | CLRS §16.3 | [Lectures 16-22](lectures_16_22.pdf); [KT Chapter 4.8](https://www.cs.princeton.edu/~wayne/kleinberg-tardos/pearson/04Huffman.pdf), and [advanced notes for further reading](https://cs.nyu.edu/~roweis/csc310-2005/notes/lec2x.pdf) | [HW8](hw8.pdf)
18 | Mar 30 | Graphs, BFS | CLRS §22.1-22.2, [adj list and adj matrix visualization](https://visualgo.net/en/graphds), [visualization](https://visualgo.net/en/dfsbfs) | [Lectures 16-22](lectures_16_22.pdf) |
19 | Apr 4 | DFS | CLRS §22.3; [video](https://youtu.be/AfSk24UTFS8) |[Lectures 16-22](lectures_16_22.pdf) | [HW9](hw9.pdf)
20 | Apr 6 | DFS, edge classification, detecting acyclic graphs | CLRS §22.3 | [Lectures 16-22](lectures_16_22.pdf) |
21 | Apr 11 | Topological sort, strongly connected components | CLRS §22.4,22.5 | [Lectures 16-22](lectures_16_22.pdf) | [HW10](hw10.pdf)
22 | Apr 13 | Finishing SCC; Minimum Spanning Tree | CLRS §23.1; [demo](https://visualgo.net/en/mst?slide=1) | [Lectures 16-22](lectures_16_22.pdf) |
23 | Apr 18 | MST safe edge theorem, Kruskal's algorithm | CLRS §23.2 | [Lectures 23-28](lectures_23_28.pdf) | [HW11](hw11.pdf)
24 | Apr 20 | Prim's algorithm | CLRS §23.2 | [Lectures 23-28](lectures_23_28.pdf) |
25 | Apr 25 | Dijkstra's SSSP algorithm | CLRS §24.3 and [video](https://www.youtube.com/watch?v=_qX5mIrAjtU) | [Lectures 23-28](lectures_23_28.pdf); [Prof. Shoup's demo](dijkstra_demo.pdf) | [HW12](hw12.pdf)
26 | Apr 27 | Floyd-Warshall APSP algorithm | CLRS §25.2 | [Lectures 23-28](lectures_23_28.pdf) | [Practice Final](practice_final.pdf)
27| May 2 | Computability, Wang tiling, the halting problem is uncomputable | CLRS §34 | [Lectures 23-28](lectures_23_28.pdf) |
28| May 4 | P vs. NP, NP completeness, Vertex Cover, Independent set, 3SAT, reductions, approximating Vertex Cover | CLRS §34, 35 | [Lectures 23-28](lectures_23_28.pdf) |
| **May 15** | **Final - Good Luck! May 15 (Monday), 8am - 9:50am, loc: Silv 411** |||
## Course Policies
### Homework
There will be weekly homework assignments.
We prefer homework submissions typeset in LaTeX (you might want to use the [Overleaf templates](https://www.overleaf.com/read/pzrwfyzkfyqq)) or Word. You are encouraged to insert scanned figures or illustrations. Scanned handwritten submissions will only be graded if **neatly written and perfectly legible**. Honors questions will be graded, but will not affect your grade in any way.
Submission is through Gradescope.
### Grading
Tentative grade split is 5% participation, 20% homework, 30% midterm, and 45% final exam.
### Late Submission Policy
**Late submissions will NOT be graded. No exceptions.** Instead, the lowest 3 HW scores will be dropped.
### Academic Integrity
Please review the departmental [academic integrity policy](http://www.cs.nyu.edu/web/Academic/Graduate/academic_integrity.html).
### Collaboration
We strongly encourage you to discuss assignments with your peers. However, all work that you submit must be written by you alone and be
completely your own. In other words, you can *discuss* homework with others but not *write it up together*. You must list all discussions you had.
You **should not** consult previous years' students, code, assignments, etc. You may help other students and groups on specific technical issues but you must acknowledge such interactions.
Interactions must be limited to groups of at most 3.
### Plagiarism
**Anything** you use from other sources (other students, web, etc.) must be clearly acknowledged.
Failure to do so will result in a zero grade for the submitted work and, except in cases of obvious mistakes, a University investigation.
### Laptops and Tablets
We discourage the use of laptops. Pen and paper are more efficient for taking notes, and less distracting to students around you. Tablets are also OK for taking notes.
If you do decide to bring a laptop, we ask that you use it for taking notes only, and not browsing the web (even if it is
related to the course). If you cannot follow this rule, we ask that you sit in the back row, so there are no students behind you to get distracted by the monitor.
### Participation
Students are expected to attend all lectures (we'll check using PollEverywhere) and recitations.
Students are also expected to attend at least 2 tutoring sessions or office hours, and participate actively in course discussion, either in person or on Campuswire. Participation will be taken into account in the final grade.
## Applicable University Policies
### Academic Integrity
Work you submit should be your own. Please consult the [CAS academic integrity policy](https://cas.nyu.edu/content/nyu-as/cas/academic-integrity.html) for more information. Penalties for violations of academic integrity may include failure of the course, suspension from the University, or even expulsion.
### Religious Observance
As a nonsectarian, inclusive institution, NYU policy permits members of any religious group to absent themselves from classes without penalty when required for compliance with their religious obligations. The policy and principles to be followed by students and faculty may be found in the [University Calendar Policy on Religious Holidays](http://www.nyu.edu/about/policies-guidelines-compliance/policies-and-guidelines/university-calendar-policy-on-religious-holidays.html)
### Disability Disclosure Statement
Academic accommodations are available to any student with a chronic, psychological, visual, mobility, learning disability, or who is deaf or hard of hearing. Students should please register with the Moses Center for Students with Disabilities at 212-998-4980.
> NYU's Henry and Lucy Moses Center for Students with Disabilities
> 726 Broadway, 2nd Floor
> New York, NY 10003-6675
> Telephone: 212-998-4980
> Voice/TTY Fax: 212-995-4114
> Web site: http://www.nyu.edu/csd
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