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--- teaching:ads12324_lecture [2024/03/06 00:25] – Martin Koutecky
+++ teaching:ads12324_lecture [2024/05/29 20:41] (aktuální) – Martin Koutecky
@@ Řádek 13: / Řádek 13: @@
 | 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: [[https://cp-algorithms.com/graph/bridge-searching.html|notes]], [[https://syga.app/#/algorithm/detail/syga/dfs-bridges/latest|demo]].|
-| 12. 3. | //Plan: Shortest paths: BFS, Dijkstra, general relaxation algorithm, Bellman-Ford, detecting negative cycles. **[A, Chap 4]**.//|
+| 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 ([[https://ksvi.mff.cuni.cz/~dingle/2021-2/algs/notes_10.html|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. [[https://courses.cs.washington.edu/courses/cse373/19su/files/lectures/slides/lecture09.pdf|slides from U of Washington]]). **{{ :teaching:ads12122:ads_bsts.pdf |OneNote notes}}**. AVL tree rebalancing. Possible resources for AVL trees: [[https://www.programiz.com/dsa/avl-tree|1]], [[http://gtu-paper-solution.com/Paper-Solution/DataStructure-2130702/AVL%20Trees/Summer-2019/Question-4-c-OR|2]], [[https://courses.cs.washington.edu/courses/cse373/19su/files/lectures/slides/lecture09.pdf|3]]|
+| 16. 4. | $(a,b)$-trees [[https://cs.lmu.edu/~ray/notes/abtrees/|1]], [[http://www14.in.tum.de/lehre/2016WS/ea/split/sub-ab-trees-single.pdf|2]], hashing [[https://jeffe.cs.illinois.edu/teaching/algorithms/notes/05-hashing.pdf|hashing notes from Jeff E]]. **In tutorials: we showed a construction of a $1$-universal family of hashing functions, see [[https://research.koutecky.name/db/_media/teaching:ads12324:09-cv.pdf|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 $O(1)$) [[https://jeffe.cs.illinois.edu/teaching/algorithms/notes/09-amortize.pdf|JeffE]]. Brief mention of LLRB trees [[https://sedgewick.io/wp-content/themes/sedgewick/papers/2008LLRB.pdf|original paper]], [[https://sedgewick.io/wp-content/uploads/2022/03/2008-09LLRB.pdf|slides]], [[https://read.seas.harvard.edu/~kohler/notes/llrb.html|controversy]]. Divide & conquer -- Recursion tree technique, Karatsuba's algorithm for multiplication of $n$-digit numbers in time $n^{\log_2 3}$ **[JE 1]**, specifically [[https://jeffe.cs.illinois.edu/teaching/algorithms/book/01-recursion.pdf|here]]|
+| 30. 4. | Master theorem [[https://jeffe.cs.illinois.edu/teaching/algorithms/book/01-recursion.pdf|JE 1]], QuickSelect is fast in expectation, thus QuickSort is fast in expectation [[https://en.wikipedia.org/wiki/Quicksort#Average-case_analysis|Wiki]]|
+| 7. 5. | Finding the $k$-th element in $O(n)$ time by the "median of medians" technique **[JE 1]**. Sorting lower bound [[https://jeffe.cs.illinois.edu/teaching/algorithms/notes/12-lowerbounds.pdf| JeffE's notes]]. Begin dynamic programming: Longest Increasing Subsequence in $O(n^2)$ time with a table; brief mention that it can be done in $O(n \log n)$ with an enhanced balanced binary search tree [[https://jeffe.cs.illinois.edu/teaching/algorithms/book/03-dynprog.pdf|JE 3]].|
+| 14. 5. | //No lecture!//|
+| 21. 5. | dynamic programming - edit distance, Floyd-Warshall, optimal binary trees [JE 3], [A 6], specifically [[https://jeffe.cs.illinois.edu/teaching/algorithms/book/03-dynprog.pdf|here]].|
-/*
-| 9. 3. | Shortest paths: BFS, Dijkstra, general relaxation algorithm, Bellman-Ford, detecting negative cycles. **[A, Chap 4]**, [[https://stream.cuni.cz/cs/Detail/16723|recording]]. |
-| 16. 3. | Shortest paths: recap of Bellman-Ford; Floyd-Warshall for APSP. **[A 4]** //(Also see **[JE 8, 9]** but that's a lot more information than necessary.)// Beginning of Min Spanning Trees: if edge weights distinct, MST is unique. **[A 5]**, **[JE 7]**.)  [[https://stream.cuni.cz/cs/Detail/16775|recording]]|
-| 23. 3. | Minimum Spanning Trees: Cut property (the MST contains every safe edge), Borůvka, Jarník, Kruskal **[JE 7]**, Union-Find data structure **[A 5.1.4]**. [[https://stream.cuni.cz/cs/Detail/16842|recording]]|
-| 30. 3. | Union-Find Data structure **[A 5.1.4]**; Binary Search Trees ([[https://ksvi.mff.cuni.cz/~dingle/2021-2/algs/notes_10.html|intro to Algs notes]]), perfect balancing too expensive; depth-balanced trees = AVL trees. [[https://courses.cs.washington.edu/courses/cse373/19su/files/lectures/slides/lecture09.pdf|slides from U of Washington]]). **{{ :teaching:ads12122:ads_bsts.pdf |OneNote notes}}**. [[https://stream.cuni.cz/cs/Detail/16918|recording]]|
-| 6. 4. | AVL tree rebalancing, intro to $(a,b)$-trees. [[https://stream.cuni.cz/cs/Detail/16972|recording]]. Possible resources for AVL trees: [[https://www.programiz.com/dsa/avl-tree|1]], [[http://gtu-paper-solution.com/Paper-Solution/DataStructure-2130702/AVL%20Trees/Summer-2019/Question-4-c-OR|2]], [[https://courses.cs.washington.edu/courses/cse373/19su/files/lectures/slides/lecture09.pdf|3]]|
-| 13. 4. | $(a,b)$-trees [[https://cs.lmu.edu/~ray/notes/abtrees/|1]], [[http://www14.in.tum.de/lehre/2016WS/ea/split/sub-ab-trees-single.pdf|2]], LLRB trees [[https://sedgewick.io/wp-content/themes/sedgewick/papers/2008LLRB.pdf|original paper]], [[https://sedgewick.io/talks/?pdfjs_id=1281&_wpnonce=effd5be684#zoom=auto|slides]], [[https://read.seas.harvard.edu/~kohler/notes/llrb.html|controversy]]. [[https://stream.cuni.cz/cs/Detail/17028|recording]]|
-| 20. 4. | Amortized analysis, hashing [[https://stream.cuni.cz/cs/Detail/17063|recording]], [[https://jeffe.cs.illinois.edu/teaching/algorithms/notes/05-hashing.pdf|hashing notes from Jeff E]], [[https://jeffe.cs.illinois.edu/teaching/algorithms/notes/09-amortize.pdf|amortized analysis notes by Jeff E]]|
-| 27. 4. | Universal, perfect hashing [[https://jeffe.cs.illinois.edu/teaching/algorithms/notes/05-hashing.pdf|hashing notes from Jeff E]], open addressing will be done at tutorial. [[https://stream.cuni.cz/cs/Detail/17230|recording]]|
-| 4. 5. | Divide & conquer -- Karatsuba's algorithm for multiplication of $n$-digit numbers in time $n^{\log_2 3}$, finding the median (or any $k$-th element) in $O(n)$ time by the "median of median" technique. [JE 1], specifically [[https://jeffe.cs.illinois.edu/teaching/algorithms/book/01-recursion.pdf|here]]. [[https://stream.cuni.cz/cs/Detail/17289|recording]]|
-| 18. 5. | Sorting lower bound [[https://jeffe.cs.illinois.edu/teaching/algorithms/notes/12-lowerbounds.pdf| JeffE's notes]], Dynamic programming [JE 3], [A 6], specifically [[https://jeffe.cs.illinois.edu/teaching/algorithms/book/03-dynprog.pdf|here]]. [[https://stream.cuni.cz/cs/Detail/17423|recording]]|
-*/
 {{page>teaching:bits:resources_ads1}}
-{{ :teaching:ads12122:exam2122.pdf | Exam topics and format (2022) (PDF).}}
+{{ :teaching:ads12324:exam2324.pdf | Exam topics and format (PDF).}}
-/*
+====== ADS1 Exam / 2024 ======
-====== ADS1 Exam / 2022 ======
 The exam will consist of:
-  - Two questions about an algorithm or a data structure from the lecture – describing the algorithm or data structure, proving they are correct, giving the complexity analysis.
+. Two questions about an algorithm or a data structure from the lecture -- describing the algorithm or data structure, proving they are correct, giving the complexity analysis.
-  - Two tasks similar to those from the tutorial – either apply an algorithm / data structure from the lecture to some problem (need to model the problem appropriately) OR adapt the algorithm / data structure to solve some problem (need to understand how it works internally to be able to adapt it appropriately)
+. Two tasks similar to those from the tutorial -- either apply an algorithm / data structure from the lecture to some problem (need to model the problem appropriately) OR adapt the algorithm / data structure to solve some problem (need to understand how it works internally to be able to adapt it appropriately)
+The form of the exam is that you will come, get the question sheet, and work on the answers. Once you are finished with one of the answers, you hand it in, I (or one of my colleagues) will read it, point out anything which is missing / incorrect, give you hints if needed, and you can revise it.
+At some point either you will reach a correct solution, or you won't want to try to improve it again, or I will feel like I can't give you any more hints, and then we'll reach some grade.
-The form of the exam is that you will come, get the question sheet, and work on the answers. Once you are finished with one of the answers, you hand it in, I will read it, point out anything which is missing / incorrect, give you hints if needed, and you can revise it. At some point either you will reach a correct solution, or you won’t want to try to improve it again, or I will feel like I can’t give you any more hints, and then we’ll reach some grade.
 ==== Grading ====
-**To get a 3** it suffices to know definitions and algorithms / data structures and (with hints) finish at least one of the “type 2” tasks (perhaps suboptimally).
+**To get a 3** it suffices to know definitions and algorithms / data structures and (with hints) finish at least one of the "type 2" tasks (perhaps suboptimally).
-**To get a 2** you need to be able to solve the tasks with some hints, or find a suboptimal (complexity) algorithm. If we proved some intermediate claims during the lecture, and these are used in the proofs of correctness/complexity, you need to at least know the statements of these claims.
+**To get a 2** you need to be able to solve the tasks with some hints, or find a suboptimal (complexity-wise) algorithm.
+If we proved some intermediate claims during the lecture, and these are used in the proofs of correctness/complexity, you need to at least know the statements of these claims.
+**To get a 1** you need to analyze the algorithms (correctness and complexity) including the proofs, and you need to be able to solve the "type 2" tasks mostly independently. (Advice like "try dynamic programming" and similar is still fine though.)
-**To get a 1** you need to analyze the algorithms (correctness and complexity) including the proofs, and you need to be able to solve the “type 2” tasks mostly independently. (Advice like “try dynamic programming” and similar is still fine though.)
 ===== Topics =====
-**Disclaimer:** the topics below are NOT specific instances of “type 1” questions. It is clear that some topics are wider and some narrower. However, if you have a good understanding of all the topics below, you should not be surprised by anything during the lecture.
+**Disclaimer:** the topics below are NOT specific instances of “type 1” questions. It is clear that some topics are wider and some narrower. However, if you have a good understanding of all the topics below, you should not be surprised by anything during the exam.
   * BFS, DFS and their edge classifications
   * DFS applications: topological sorting, detecting strongly connected components
-  * Dijkstra’s algorithm
+  * Dijkstra's algorithm, $d$-ary heaps
-  * Bellman-Ford’s algorithm
+  * Bellman-Ford's algorithm
-  * Floyd-Warshall’s algorithm (small topic)
+  * Floyd-Warshall's algorithm (small topic)
-  * Jarník’s algorithm
+  * Jarník's algorithm; cut lemma
-  * Borůvka’s algorithm
+  * Borůvka's algorithm
-  * Kruskal’s algoritmus + Union-Find data structure using trees
+  * Kruskal's algoritmus + Union-Find data structure using trees
   * Binary Search Trees (BSTs) in general
   * AVL trees
   * $(a,b)$-trees
-  * Red-black trees – we covered these very briefly, but you should be able to describe the bijection between LLRBs and $(2,4)$-trees
+  * Hashing with chaining (each bucket is a linked list)
-  * Hashing with chaining
-  * Hashing with open addressing (warning, I did this at the tutorial; if you don’t understand it, please read JeffE’s notes)
   * Universal hashing
-  * Master theorem – analyzing the complexity of Divide & Conquer algorithms using the recursion tree
+  * Master theorem -- analyzing the complexity of Divide & Conquer algorithms using the recursion tree
-  * Integer multiplication using Karatsuba’s algorithm
+  * Integer multiplication using Karatsuba's algorithm
   * MomSelect (finding the $k$-th smallest element in an array in linear time)
+  * QuickSelect with random pivots works in expected $\mathcal{O}(n)$ time, QuickSort with random pivots in expected $\mathcal{O}(n \log n)$ time.
   * Edit Distance dynamic programming algorithm
   * Longest Increasing Subsequence dynamic programming algorithm
   * Lower bounds: searching in a sorted array is $\Omega(\log n)$, sorting is $\Omega(n \log n)$ (only applies to deterministic and comparison-based algorithms)
-*/