Timetable at FEE
Students of ePAL
Upload system BRUTE
Discussion board
Practices
Problem sets with comments/solutions
Extra online consultations will be organized during semester weeks 10. - 14. to discuss presented solutions in problem set 1.-8.
Online consultations
Consultation 1
Consultation date: Tue 24.11., 16:15-17:45
The discussed topics of the consultation were topics 5. and 6. - Isomorphism and Combinatorial generation (see the documents above), those correspond to lectures 5. and 6.
Consultation 2
The discussed topics of the consultation will be topics 3. and 4. - Directed graphs and Heaps (see the documents above), those correspond to lectures 3. and 4.
Your course of action:
1. Note the consultation date: Mon 30.11., 11:00-12:30
2. Check the solutions/comments of the given topics 3. and 4. above. Mark the solutions which, in your opinion, need more explanation or corrections and which you would like to understand better.
3. Go to the poll Advanced Algorithms Consultation 2 and tick the boxes at the corresponding problems from topics 3. and 4. above, where you demand more explanation.
Complete this step before 10:00 PM Sunday 29.11.
The consultations will discuss primarily the problems in the highest demand.
The Basics
Introduction and repetitions
For more thorough or necessary basic acquaintance with the related topics consult the book
Problems on Algorithms. Student are expected to be able to solve any problem marked by one cap in chapters 2. and 3. both during the semester and at the exam. We recommend problems 64. - 66., 144. - 148., 163. - 170. as an easy start.
Upload system
An introduction to Upload system, 0-th programming optional (not graded) task, its specification can be found
here.
Write a program that solves the task. Upload it and check how the system asseses it. Follow strictly the rules specified on page
Upload System.
Training homework problem
The solution and submission is not mandatory and it is not graded if submitted. The problem itself is extremely simple, you can utilize it is to get acquainted with the.
Upload System BRUTE.
Training problem: Problem statement and public data
1st week
First homework problem
Laser Highways
Exam topics
Asymptotic notations, asymptotic complexity, graph representations.
Boruvka's, Kruskal's, Prim's algorithms. Their implementation and data structures, ie. priority queues and Union-Find.
Prim's algorithm without a queue.
Union-Find implementations.
2nd week
Note:
Supplementary problems for missing online practices are available: in pdf .
Solve problems 1-5 and one of problems 6-10 according to your choice.
Send a photo of your solutions by 6.10., to berezovs@fel.cvut.cz with cc to varhaiho@fel.cvut.cz.
Additional:
Problems for personal training: Directed graphs, strongly connected components, Eulerian graphs:
set 1, set 2.
Exam topics
Eulerian graph (directed and undirected), Eulerian path/cycle, method of finding them.
Strong and weak connectivity, strong and weak components, graph condensation. Algorithms which find strong components or produce a condensation.
Topological ordering of a graph using DFS or using gradual roots/leaves removal.
3rd week
Additional problems for training
here
Exam topics
The heap rule. Standard operations on heaps. Binary, d-ary and binomial heap.
Binary and d-ary heap implemented in an array.
Fibonacci heap, amortized complexity of its operations.
4th week
Additional problems for training
here
Exam topics
Graph isomorphism, definition, invariants, algorithm for finding all isomorphisms.
Isomorphism and certificates of undirected trees, computing the certificate for a tree and reconstructing a tree from a certificate.
5th week
Combinatorial generation of subsets, permutations and their ranks.
Example problems.
Additional problems for training
here
Kreher, Stinson: Combinatorial Algorithms, notes:
Exam topics
Combinations, variations, permutations with or without repetition, definitions, formulas. Binomial coefficients, their basic relations, Pascal triangle.
Operations(functions) Rank and UnRank for ordered permutations and k-element subsets of given set.
Gray code - definition, properties, operations Rank and UnRank.
6th week
Additional problems for training
here
Exam topics
Deterministic and non-deterministic finite automaton (DFA and NFA), definition. Languages accepted by finite automata.
Algorithm for transforming NFA to DFA, simulation of NFA work without transformation to DFA. Epsilon-transitions and their removal from an automaton.
Regular expressions. Definition, algorithm for transformation of regular expression to NFA.
7th week
Text Searching. Additional problems for training
here
Exam topics
Construction of NFA for pattern matching. Impelementation of NFA/DFA by a table or by code.
Hamming and Levenshtein distance. NFA/DFA for search of substrings which have nonzero distance from a given pattern.
8th week
Additional problems for training
here.
Exam topics
Finding dictionary entries in a text with the help of dictionary automaton.
Number of states of dictionary NFA, DFA.
Approximate text search based on previous methods.
9th week
10th week
11th week
2-3-4 trees and B+ trees, splay trees. Additional problems for training
here
Exam topics
2-3-4 trees and B+ trees. Asymptotic complexity of particular search tree operations.
12th week
Exam topics
KD trees, search for Nearest Neighbour in 2D.
13th week
In preparation
Exam topics
14th week
In preparation
* Radix trie, Patricia trie, segment tree.
Exam topics
* Radix trie, Patricia trie, segment tree.
Search Trees Interactive Animations
Problems in Czech
Week | Topics | Problems |
1. | Asymptotic complexity, graphs basics | cv01.docx |
2. | MST | |
3. | Strong connectivity, Eulerian path | |
4. | Heaps | haldy.docx |
5. | Graph isomorphism | cviso-1.doc |
6. | Ranking, combinatorial objects generators | kombi1.docx |
7. | DFA, NFA 1 | ata1.docx |
8. | DFA, NFA 2 | |
9. | DFA, NFA 3 | ata3.docx |
10. | Prime numbers and random generators | cvrndprimes.docx |
11. | Skip list, B/B+ tree | cv11_2015.docx |
12. | Splay, AVL, RB tree | opakování, AVL, splay , B, splay. |
13. | kD-trees | cv13mb.docx |
14. | Trie | cv14_2017.docx |
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