02110 Algorithms and Data Structures II

General Info

Teacher Professor Inge Li Gørtz, office 011, building 322, Email: inge@dtu.dk.

When Thursday 8-12. The course runs in the DTU fall semester.

Structure The class is structured as follows:

8.00-10.00 Group work. Time to work on the exercises you couldn't solve at home. The TAs will be there to help you.
10.00-12.00 Lecture

Where The exercise class from 8-10 is in building 358, room 060a, 039, 040, 065.
Lectures will be in building 358, room 060a.

OBS!! (Covid-19) Due to Covid-19 restrictions, you will be divided into groups. The group you are in determines which room you have exercise class in and which weeks you can attend the lecture in the lecture room. See more on DTU Learn.

Textbook "Algorithm Design" by Kleinberg and Tardos. (KT)

Prerequisites The course builds on 02105 Algorithms and Data Structures I. You are expected to know the curriculum for 02105, which includes

Basic algorithm analysis, asymptotic notation.
Data structures: stacks, queues, linked lists, trees, heaps, priority queues, hash tables, union-find, binary search trees.
Searching and sorting: binary search, heap sort, insertion sort, merge-sort.
Graph algorithms: single source shortest paths (Dijkstra and SSSP in DAGs), Minimum spanning trees, topological sorting, Breadth first search, Depth first search, representation of graphs.

CodeJudge Exercises marked with [CJ] are implementation exercises and can be tested in CodeJudge (CodeJudge). For each of these exercises, a detailed specification of the input/output can be found on CodeJudge.

Mandatory assignments

The course has mandatory exercises that must be passed inorder to attend the final exam. The mandatory exercises consist of written and implementation exercises:

Written assignments These are algorithmic challenges that must be answered in writing. These must be handed through DTU Learn for correction by the TA's. Each written exercise is scored depending on the quality of your solution and your writing. It is a requirement for participation in the exam that you score at least 50 points in total in these exercises.

Implementation assignments These are programming challenges that must be implemented and handed in through CodeJudge for automatic evaluation and scoring. It is a requirement for participation in the exam that you score at least 50 points in total in these exercises.

The exercises do not count in the final grade for the course. There are 10 written assignments and 5 implentation assignments. Each can give up to 20 points.

The deadline for handing in the home work must be respected.

Collaboration policy All mandatory exercises are subject to the following collaboration policy.

You may work in groups consisting of at most two students.
For the written exercises collaboration is limited to discussion of ideas, and you should write up the solutions entirely on your own. Your collaborator must be listed in your solution.
In weeks where there is both a written and a programming exercise, the group you are in has to be the same for both exercises.
It is not allowed to collaborate with people not in your group, except for discussing the text of the exercise with teachers and fellow students enrolled on the course in the same semester.
Under no circumstances is it allowed to exchange, hand-over or in any other way communicate solutions or part of solutions to the exercises.
It is not allowed to use solution from previous years, solutions from similar courses, or solutions found on the internet or elsewhere. It is not allowed to search for solutions or parts of solutions on the internet.

Programming Competition

The programming competition is now on. There will be a prize for the best three teams. The deadline is November 29th at 20.00. The description can be found at CodeJudge.

Weekplan

The weekplan is preliminary. It will be updated during the course.

Topics	Slides	Weekplan	Deadline Mandatory Written	Deadline Mandatory Programming	Material	Demos
Warmup		Warmup
Divide-and-Conquer: Recurrence relations, Mergesort (recap), integer multiplication	1x1 · 4x1	DC			KT 5.1, 5.2, 5.5
Dynamic programming I: Introduction, weighted interval scheduling, segmented least squares	1x1 · 4x1· full	DP1	X	X	KT 6.1, 6.2, 6.3
Dynamic programming II: Sequence alignment and shortest paths	1x1 · 4x1	DP2	X		KT 6.6, 6.8.	Sequence Alignment
Network Flow I: Max-cut min-flow theorem, augmenting paths, Ford-Fulkerson	1x1 · 4x1 · full	Flow1	X	X	KT 7.1, 7.2	Ford Fulkerson and min cut
Network Flow II: scaling, Edmonds-Karp, applications, maximum bipartite matching, disjoint paths	1x1 · 4x1 · full	Flow2	X		KT 7.3, 7.5, 7.6 KT 7.7, 7.8, 7.9, 7.10, 7.11
Introduction to NP-completenes	1x1 · 4x1	NP	X	X	KT 8.0, 8.1 KT 8.3 (except the proof of 8.10) KT 8.4 (only introduction and the subsection A General Strategy for Proving New Problems NP-Complete)
Data Structures I: Red-Black trees and 2-3-4 trees	1x1 · 4x1	Balanced Search Trees	X		Algorithms in Java by Sedgewick, page 572--585 (on Campusnet) (Supplementary reading: CLRS chapter 13)
Data Structures II: Partial Sums and Dynamic Arrays	1x1 · 4x1	Data Structures II	X		A New Data Structure for Cumulative Frequency Tables, P.M. Fenwick, Softw. Pract. Exp. 1994. Tiered Vectors: Efficient Dynamic Arrays for Rank-Based Sequences, M.T. Goodrich and J.G. Kloss, WADS 1999
Data Structures III: Amortized Analysis + splay trees.	1x1 · 4x1 · full	Amortised Analysis	X		Section 15 + 16.5-16.6 in notes by Jeff Erickson (can also be found on CampusNet) Chapter 17 in Algorithms from Cormen, Leiserson, Rivest, Stein (can be found on Campusnet).	Splay 0211 Trees Splay Trees Deletions
String matching	1x1 · 4x1	Strings	X	X	CLRS 32.0, 32.3, 32.4 (on Campusnet)	Automata matching and construction KMP matching and construction
Randomized Algorithms I: Contention resolution, Minimum cut.	1x1 · 4x1	Randomized Algorithms I	X		KT 13, 13.1, 13.2, 13.12
Randomized algorithms II: selection, quicksort	1x1 · 4x1	Randomized Algorithms II		X	KT 13.3, 13.5
Questions, repetition, prize for programming competition

Old Exam Sets

Here is the exam set from some of the previous years: ExamE19 ( solution (very brief)), ExamE18, ExamE17 ( solution (very brief)), ExamE16, ExamE15, ExamE14 and a solution to E14.
And an example exam: ExampleExam.

Solutions to selected exercises

Here are solutions to a couple of exam like exercises, such that you can see how a well written solution could be: Example solutions.

Frequently Asked Questions

How should I write my mandatory exercises? Here is a few tips:

Write things directly: Cut to the chase and avoid anything that is not essential. Test your own writing by answering the following question: “Is this the shortest, clearest, and most direct exposition of my ideas/analysis/etc.?”
Add structure: Don’t mix up description and analysis unless you know exactly what you are doing. For a data structure explain following things separately: The contents of the data structure, how to build it, how to query/update it, correctness, analysis of space, analysis of query/update time, and analysis of preprocessing time. For an algorithm explain separately what it does, correctness, analysis of time complexity, and analysis of space complexity.
Be concise: Convoluted explanations, excessively long sentences, fancy wording, etc. have no in place scientific writing. Do not repeat the problem statement.
Try to avoid pseudocode: Generally, aim for human readable description of algorithms that can easily and unambiguously be translated into code.
The only exception for this is dynamic programming algorithms, where pseudo code is often the best choice.
Examples for support: Use figures and examples to illustrate key points of your algorithms and data structures.

Can I write my assignments in Danish? Ja. Du er meget velkommen til at aflevere på dansk. Det samme gælder til eksamen.

What do I do if I want to do a MSc/BSc thesis or project in Algorithms? Great! Algorithms is an excellent topic to work on :-) and Algorithms for Massive Data Sets is designed to prepare you to write a strong thesis. Some basic tips and points.

Let us know well in advance: Identifying an interesting problem in algorithms that matches your interest can take time. With enough time to go over the related litterature and study up on relevant topics your project will likely be more succesful. It may also be a good idea to do an initial “warm up” project before a large thesis to test ideas or survey an area.
Join the community: It is very good idea to enter the local algorithms community at DTU and the Copenhagen area to get a feel for what kind of stuff you could work on for your thesis and what thesis work algorithms is about. Talk to other students doing thesis work in algorithms. Go to algorithms talks and thesis defenses in algorithms.
Collaborate: We strongly encourage you to do your thesis in pairs. We think that having a collaborator to discuss with greatly helps in many aspects of thesis work in algorithms. Our experience confirms this.
No strings attached. Choosing a topic for your thesis is important. You are welcome to discuss master thesis topics with us without pressure to actually write your thesis in algorithms. We encourage you to carefully select your topic.