Toto je starší verze dokumentu!

Algorithms and Data Structures I 2023/24 -- Lecture

I teach Algorithms and Data Structures I (NTIN060) every Tuesday at 12:20 at S9 (Malá strana). I have taught this class last year and there are some (somewhat problematic) recordings from then (see the link).

I also teach a tutorial for this class on Monday at 15:40, and another one is taught on Tuesday at 17:20 by Todor Antić. Both tutorials will cover the same content and have the same criteria for obtaining credit.

If you want to talk to me, schedule a meeting with me. You can e-mail me at koutecky+ads1@iuuk.mff.cuni.cz and/or include the text [ADS1] in the email subject.

data	what was taught [resources]
19. 2.	The Random Access Machine (RAM) model of computation, instruction cost (unit, logarithmic, relative logarithmic) [A Chapter 0], Wiki: Random Access Machine, Big-Oh notation ($\mathcal{O}, \Omega, \Theta$)
27. 2.	Graph problems, DFS: identifying connected components, pre- and post-orderings, cycle detection. [A, up to 3.3.2]
5. 3.	DFS: topological ordering, detecting strongly connected components. [A, remainder of Chap 3]. Also learn the $\mathcal{O}(n+m)$ algorithm to find all bridges of an undirected graph: notes, demo.
12. 3.	Finish SCC algorithm [A, Chap 3]; begin shortest paths: BFS, Dijkstra. [A, Chap 4]
19. 3.	$d$-ary heaps for Dijkstra; general relaxation algorithm, start Bellman-Ford [A, Chap 4].
26. 3.	Bellman-Ford [A 4] (Also see [JE 8, 9]* but that's a lot more information than necessary.)* Beginning of Min Spanning Trees: cut lemma, if edge weights distinct, MST is unique; Jarník's algorithm; Borůvka's algorithm [A 5], [JE 7].)
2. 4.	Finish Borůvka's algorithm; Kruskal's algorithm for MSTs, Union-Find problem and data structure. [A 5.1.4]. Intro to Data structures. Binary Search Trees (intro to Algs notes)
9. 4.	Perfectly balanced trees (balancing turns out to be too expensive, this is a dead-end); depth-balanced trees = AVL trees. slides from U of Washington). OneNote notes. AVL tree rebalancing. Possible resources for AVL trees: 1, 2, 3
16. 4.	$(a,b)$-trees 1, 2, hashing hashing notes from Jeff E. In tutorials: we showed a construction of a $1$-universal family of hashing functions, see here. This theorem may appear at the exam.
23. 4.	Brief mention of amortized analysis: expanding arrays can do $n$ INSERT / DELETE operations in time $O(n)$ (but not each operation is $O(1)$) JeffE. Brief mention of LLRB trees original paper, slides, controversy. Divide & conquer – Recursion tree technique, Karatsuba's algorithm for multiplication of $n$-digit numbers in time $n^{\log_2 3}$ [JE 1], specifically here
30. 4.	Plan: Master theorem, finding the median (or any $k$-th element) in $O(n)$ time by the „median of medians“ technique [JE 1], quicksort in the average case

Useful Resources

[A] Algorithms by Dasgupta, Papadimitriou, and Vazirani
[JE] Algorithms by Jeff Erickson (the page contains various PDFs suitable for screen, printing etc.)
[CLRS] Introduction to Algorithms by Cormen, Leiserson, Rivest, and Stein. Find it on libgen

Exam topics and format (2022) (PDF).