Department of Computer Science | Institute of Theoretical Computer Science

CADMO - Center for Algorithms, Discrete Mathematics and Optimization

Algorithmen und Datenstrukturen

This is a web page related to Fall semester 2020. It is NOT relevant for Fall semester 2021.

Fall semester 2020, ETH Zürich

Lecturers: Markus Püschel
David Steurer
Organisation: Johannes Lengler
Gleb Novikov
Lectures: Thursday, 14:15 - 17:00
Exercises: Monday, 9:15 - 12:00

If you have any questions about organisation of the course (NOT related to the content of lectures or exercises), you can send us an email to the following address: Additional information about the course can be found in the course catalogue.

Information for students of the "Computational Biology and Bioinformatics Master" programme.


  • Lectures
  • Exercises
  • Exam information
  • Information about the Moodle forum
  • News:


    General information

    The lectures take place on Thursday, 14:15 - 17:00.

    From 02.11.20 the lectures take place online (via Zoom) and they are recorded (but the chat is not recorded). Links, passwords and recordings can be found in Moodle.

    The on-site lectures (all lectures before 02.11.20) were also recorded, the recordings of on-site lectures can be found here.

    Lecture notes

    Date Covered topics Notes
    17.09.2020 Introduction.
    • Introduction
    • Grade school multiplication and Karatsuba algorithm
    • Induction
    • O-notation
    Lecture 1
    Optional references Script: 1.2.1, 1.3.1

    Induction and Recursion.

    • Pasture Break
    • Induction
    • Find the Star
    Lecture 2
    Optional References Skript: 1.2.2,1.4.1
    01.10.2020 Maximum Subarray Sum Problem.
    • Problemdefinition
    • Naiver Algorithmus, Präfixsummen vorberechnen, Divide-and-Conquer-Algorithmus, induktiver Algorithmus
    • Untere Schranken, Problemkomplexität
    Lecture 3
    Optional References Skript: 1.5
    08.10.2020 Suchen.
    • Lineare Suche
    • Interpolationssuche
    • Binäre Suche
    • Untere Schranke.
    Elementare Sortierverfahren.
    • Bubblesort
    • Sortieren durch Auswahl (Selection Sort)
    • Sortieren durch Einfügen (Insertion Sort)
    • Konzept Invariante
    Lecture 4
    Optional References Skript: 2.1, 2.2, 2.3

    15.10.2020 Sortieren II
    • Heapsort, Heaps
    • Mergesort
    • Quicksort
    • Lower Bound for Sorting
    Lecture 5
    Optional References Skript: 2.4 bis 2.7

    22.10.2020 Dynamic Programming I
    • Longest increasing subsequence
    • Longest common subsequence
    • Edit distance
    • Matrix chain multiplication
    Lecture 6
    Optional References Skript: 3.1 bis 3.5

    29.10.2020 Dynamic Programming II
    • Subset Sum problem
    • Knapsack problem
    • Approximation Algorithm for Knapsack
    Lecture 7
    Optional References Skript: 3.6, 3.7

    05.11.2020 Data Structures and Abstract Data Types
    • Stacks, Queues
    • Priority Queues
    • Search Trees, AVL Trees
    Lecture 8
    Optional References Skript: 4.1, 4.4, 4.5

    12.11.2020 Graphs
    • Introduction to Graphs
    • Euler tours
    • Data Structures for Graphs
    Lecture 9
    Optional References script on graph theory,
    Skript: 5.1.1, 5.1.2, notes from previous year


    Graph algorithms

    • Directed graphs
    • Topological sorting
    • Depth First Search
    Lecture 10
    Optional References script on graph theory,
    Skript: 5.2.1., 5.4

    Graph algorithms II

    • Depth First Search (continued)
    • Pre-/post-ordering
    • Forward/backwards/cross edges, finding cycles
    • Breadth First Search
    Lecture 11
    Optional References Skript: 5.2

    Shortest Paths

    • Shortest Paths
    • Dijkstra's algorithm
    • Bellman-Ford algorithm
    Lecture 12
    Optional References (Skript): 5.5.2, 5.5.3

    Minimum spanning trees

    • Minimum spanning trees
    • Boruvka's algorithm
    • Prim's algorithm, connection with Dijkstra's algorithm
    • Kruskal's algorithm
    • Data structure: Union-Find
    Lecture 13
    Optional References Book: Chapter 9.6

    Shortest paths 2

    • Floyd-Warshall algorithm
    • Johnson's algorithm
    • Finding number of walks using matrix multiplications
    • Strassen algorithm
    Lecture 14
    Optional References Skript: 5.5.4


    • Auswahlproblem, Mediane
    Lecture 15

    Study and reference material

    Primary study material are the handwritten notes for the individual lectures. You can use the scripts and books as optional reference material, however the presentation of some consepts there might differ significantly from the presentation in class.

    There are several scripts which cover parts of the course. They are additional material, and not per se exam-relevant. You can download the script for algorithms as a PDF-file within the ETH network. Note that the script does not exactly match the course material. In particular, it is more extensive than the course material. For the graph theory part, you can find a script as html or pdf. There is also an older (more extensive, but less adapted to the lecture) script on graph theory here. More additional materials (e.g. old exercises) can also be found on the web page of the previous year.

    For further reading, the book ``Algorithmen und Datenstruktur'', T. Ottmann and P. Widmayer, 6th edition, Spektrum Verlag, 2017, is recommended. You can find it in the ETH Store or download it as a PDF-file within the ETH network. Note, however, that the notions of the book do not always match those of the lecture, e.g. the book uses a different definition of the O notation.

    Additional Literature


    Exercise sheets

    Exercise sheets Solutions
    Exercise Sheet 0 Solutions for sheet 0
    Exercise Sheet 1 Solutions for sheet 1
    Exercise Sheet 2 Solutions for sheet 2
    Exercise Sheet 3 Solutions for sheet 3
    Exercise Sheet 4 Solutions for sheet 4
    Exercise Sheet 5 Solutions for sheet 5
    Exercise Sheet 6 Solutions for sheet 6
    Exercise Sheet 7 Solutions for sheet 7
    Exercise Sheet 8 Solutions for sheet 8
    Exercise Sheet 9 Solutions for sheet 9
    Exercise Sheet 10 Solutions for sheet 10
    Exercise Sheet 11 Solutions for sheet 11
    Exercise Sheet 12 Solutions for sheet 12
    Exercise Sheet 13 Solutions for sheet 13

    Exercise classes

    The exercises take place on Mondays from 9:15 to 12:00.

    From 02.11.20 all exercise classes take place online (via Zoom). The link should be sent to you by your TA. You should send your solutions for theory exercises to your TA and your peer graders (your TA informs you in advance who are your peer graders) by email between 09:00 and 09:15 Monday morning. Please use a pdf file of size at most 5MB and an informative title (containing the number of the sheet and all members of your working group).

    Every Monday (starting from September 21) we will publish a new theory exercise sheet on the webpage, and you have one week to solve the exercises from this sheet.

    The first exercise class takes place on Monday, September 21. It is important to attend it, since your teaching assistant (TA) will partition you into working groups of 2 (or 3) people, and then you solve exercises from the current sheet together within the working group. The solutions (one solution per working group) should be handed in at the beginning of the exercise class next Monday (for example, the first exercise sheet is published on September 21, and the solutions should be submitted in the beginning of the exercise class on September 28). The working groups are reassigned every 3 weeks (by the TA).

    During the last hour of the exercise class you will peer-grade the solutions of your fellow students: the TA distributes the solutions among working groups (each working group gets the solution of some other working group), and then asks students to read the solutions and write their comments if they think that they are incorrect or incomplete (comments should contain a clear explanation). After peer grading, you should send your comments to your TA by email.

    All exercise sheets are written in English. You can hand in your solutions either in English or in German. Chris Wendler and Ulysse Schaller are responsible for the content of theoretical exercises. If you have any content-related questions about theory exercises, please send an email to the following address:

    Programming exercises

    The online judging system for programming exercises is Code Expert ( You have two warm-up exercises in the Code Expert website to test the environment ('Welcome' and 'Median of Three'). These warm-up exercises do not give any bonus points.

    The first programming assignment with bonus points will be published in the Code Expert website on October 12.

    You can find the online documentation on Code Expert here. The following things are different to what is stated in the documentation:


    Programming exercises are created by Chih-Hung Liu. They are NOT related to the exercise classes and your TAs are not supposed to answer any questions about programming exercises. Questions regarding programming exercises can and should be submitted through the messaging system of Code Expert. This will be the only way of asking questions during the computer part of the exam.

    Bonus points

    During the semester, the students can get bonus points for

  • solving the designated parts of the theoretical exercise sheets (in working groups);
  • peer grading the specified part of the theory sheets during the class (in working groups);
  • solving the programming problems (individually).
  • At the end of the term, the bonus points are translated into a bonus grade between 0 and 0.25. The final grade is then the sum of the exam grade and the bonus grade (rounded and capped at 6.0). The students already get the maximal bonus grade (0.25) for 80% of the bonus points. This compensates for possible absences, e.g. due to illness or military service.

    Participation in the bonus system is voluntary. It is possible to get a 6.0 without participating in the bonus system.

    Each working group must hand in their own, independent solution. Likewise, programming exercises must be handed in with self-written code. We recommend solving all tasks without the help of external sources (books, internet, solutions from fellow students), as otherwise the learning effect of the tasks is largely lost. Even if you seek advice from an outside source, plagiarism (partial or complete) is not allowed. In this case, we recommend that you put this source aside after reading it and then formulate your solution (on your own!) the next day. Correspondingly, copying third-party code (in whole or in part, also from the Internet) to solve programming tasks is not permitted. The regulation on external sources also applies here by analogy. You are of course allowed to use Java documentation when programming, and in particular to search for syntax. You are not allowed to make your own solutions (whether theory or programming) available for copying. In case of copying, both involved working groups/students lose their points, regardless of whose solution was the original. Moreover, it can lead to further consequences for both working groups/students.

    Exam information

    The exam takes place in the exam session. It consists of two parts, a written theory part and a programming part.

    The exercises (theoretical and programming) that we suggest you to solve during the semester are designed to optimally prepare for the exam.

    You can find a list of some exams from previous years here.

    Technical details on the written exam like allowed aids can be found here. More information will be sent by email in the week before the exam.

    Further details will be provided later, additional information relevant for the exam can be found in the course catalogue.


    The Moodle-Forum is supposed to be used for discussions among the students, but we will check the forum at least twice a week to ensure that it does not contain wrong information. Please follow the following no-spoiler policy: If your answer directly or indirectly contains tips or solution hints for an exercise, then put a clear spoiler warning at the beginning of your post and write the critical part of the post (the possible Spoiler) in white text color. In this way, you enable your fellow students to solve the tasks independently, without accidentally reading your post or the possible hints. Please provide your fellow students with a spoiler-free learning environment by following a corresponding policy in private communication channels (Telegram groups etc.)!

    Formulated solutions (partial or complete) must not be published in the forum or in a Telegram group! This applies to both theory and programming tasks.

    Important note for students of the "Computational Biology and Bioinformatics Master" programme: If your study administration has made the course "Data Structures and Algorithms" mandatory, you will not be able to participate in this course. Instead, you must take the course Nr. 252-0002-AAL. Further information can be found in the course catalogue.