Algorithms and Data Structures

Algorithms and Data Structures

The course will cover basic and advanced data structures & algorithms and their analysis. Examples of data structures are cuckoo hashing, splay trees, randomized search trees, union-find structures. In terms of problem domains, we cover graphs, strings, polynomials, and geometry. Furthermore, we discuss algorithm analysis techniques such as amortization and randomization, and general algorithm design principles.

Time & Date & Format

This core course consists of two lectures per week (Tuesday + Friday, 10:15 - 12:00) plus tutorials once a week. The first lecture is on November 3. 

Registration

You must register on this website until Sunday, November 8, so that we can assign you to a tutorial. You do not need to register to attend the first two lectures.

Prerequisites

The course requires basic knowledge in algorithms and data structures as covered for example by the introductory course "Grundzüge von Algorithmen und Datenstrukturen". In particular, you should be familiar with correctness proofs of algorithms. Specific concepts that you should have basic familiarity with and should be able to apply include:

• pseudocode notation
• O-notation, running time analysis
• binary search
• basic sorting algorithms (e.g. mergesort)
• arrays, linked lists
• stacks, queues
• heaps / priority queues
• binary search trees, balanced binary search trees (e.g. AVL trees)
• definition of a graph
• graph traversal (e.g. depth first search / breadth first search)

In case you want to read up on these topics we recommend the script of the introductory course "Grundzüge von Algorithmen und Datenstrukturen".

Exercise Sheets

Exercise sheets will be handed out on Tuesday and are due on the next Tuesday before the lecture. As an experiment, this course will have optional programming content. Every exercise sheet will consist of 3-4 regular exercises and 1-2 programming exercises. This means that you may choose to ignore the programming exercises, or you may focus on the programming exercises and only do few regular exercises.

Regular Exercises

Regular exercises are theory questions that must be answered by uploading a PDF on this course website. You can produce a PDF by writing in LaTeX, writing in a common word processor like Word, or by taking a scan or a photo of your handwritten solution (if you take a photo, take special care that the PDF is readable).

An exercise that asks you to design an algorithm is to be answered by (1) your algorithm in pseudocode, (2) a correctness proof, and (3) a running time analysis.

You may collaborate on solving the regular exercises in groups of up to 4 students, but every student must hand in a write-up in their own words. You are required to state your collaborators and all sources (books, papers, course notes, web pages, etc.) that you use to arrive at your solutions.

The solutions to these exercises are presented in the tutorial. We will assign you to one of the following tutorial slots (when registering you can give your preferences): Wednesday 16-18 (Jasper), Thursday 10-12 (Hannaneh), Thursday 14-16 (Alejandro), Friday 14-16 (Sergei). Tutorials start in the week November 9-13.

Programming Exercises

Solutions to the the programming exercises will be submitted to an online judge. You are required to solve these exercises on your own.

For questions regarding programming aspects there is an office hour Monday 10-12, and you can ask questions on Discord. On November 5, 14:00-16:00 there will be a general introduction to the online judge and efficient coding in C++ given by Julian and Marian (a recording will be made available).

Exam

To be admitted to the exam, you need to achieve 50% of the points on the exercise sheets (where 100% means solving 4 exercises completely on each exercise sheet). There is no midterm exam.

There is an opportunity to obtain up to 15 % bonus points for the exam via a bonus sheet of regular and programming exercises (solutions need to be handed by 11:59 am on Sunday, February 7).

You can bring a cheat sheet to the exam (handwritten, A4 format, two-sided).

Endterm: Friday, February 26. 14:00-17:00, Günter-Hotz lecture hall E 2 2 (written, non-virtual exam)

Re-exam: Tuesday, March 30. 10:00-12:00, Günter-Hotz lecture hall E 2 2 (written, non-virtual exam)

Important: If you cannot be physically present for the exam, please contact us as soon as possible and provide proof/reason (e.g., entry into Germany from your current place of residence is not allowed).

Tentative List of Topics

03 Nov	MK	Model + O-Notation + basic data structures
06 Nov	MK	Greedy + Dynamic Programming
10 Nov	MK	Divide and Conquer I: basic examples, master theorem
13 Nov	MK	Divide and Conquer II: Karatsuba, Toom-Cook
17 Nov	MK	Divide and Conquer III: FFT
20 Nov	KB	Randomized I: model, quicksort, rank select
24 Nov	KB	Randomized II: randomized search trees, treaps
27 Nov	KB	Randomized III: hashing
01 Dec	KB	Randomized IV: more hashing + Amortization I: intro
04 Dec	KB	Amortization II: splay trees
08 Dec	KB	Amortization III: Fibonacci heaps
11 Dec	KB	Amortization IV: union find
15 Dec	MK	Strings I: longest common subsequence, intro to string matching
18 Dec	MK	Strings II: string matching: Rabin-Karp, Knuth-Morris-Pratt
05 Jan	MK	Strings III: tries, suffix trees
08 Jan	KB	Graphs I: intro, depth first search, breadth first search, shortest paths
12 Jan	KB	Graphs II: more shortest paths
15 Jan	MK	Graphs III: maxflow: intro, maxflow mincut, Ford-Fulkerson
19 Jan	MK	Graphs IV: maxflow: further algorithms
22 Jan	MK	Graphs V: maximum matching
26 Jan	KB	Geometry I: intro, degeneracies, convex hull
29 Jan	KB	Geometry II: orthogonal range searching, segment trees
02 Feb	KB	Geometry III: sweep line, linear programming
05 Feb	MK	Outlook

Literature