Competitive Programming and Contests
- Teacher:Â Rossano Venturini
- CFU: 6
- Period: First semester
- Language: English
- Classroom: here. Code is d77kira
- Lectures schedule:Â Monday 9-11 Room C1 and Thursday 9-11 Room C1 -- (Google Meet, link on our classroom)
- Question time: After lectures or by appointment
Goals and opportunities
The goal of the course is to improve programming and problem solving skills of the students by facing them with difficult problems and by presenting the techniques that help their reasoning in the implementation of correct and efficient solutions. The importance of these skills has been recognized by the most important software companies worldwide, which evaluate candidates in their job interviews mostly by the ability in addressing such difficult problems (e.g., see here).
A natural goal is to involve the students in the intellectual pleasure of programming and problem solving, also preparing them for the most important international online contests, such as Topcoder, Codeforces, HackerRank, CodeChef, Facebook Hacker Cup, Google Code Jam and so on, for internships in most important companies and their interviews. A desirable side-effect of the course could be to organize and prepare teams of students for online contests.
The course will provide the opportunity of
- facing with challenging algorithmic problems;
- improving problem solving and programming skills;
- getting in touch with some big companies for internships, scholarships, or thesis proposals.
Exam
See these slides. Mandatory exercises for homeworks are in bold.
Extra points for
- active participation
- serious participation to online contests, e.g., CodeForces, TopCoder, Hacker Rank, Google Code Jam, ...
- successful interview with a big company
Implementing solutions for the problems of each lecture is strongly recommended to improve your problem solving skill and to practice with Rust.
I recommend you to create a github repository to collect all your solutions and their descriptions. The repository can be either private or public. In both cases I should be able to access it. Please send me a link to your repository and keep the repository updated. I should be able to monitor your progresses.
Upcoming Exams
| Type | Date | Room |
|---|---|---|
| Written/Lab | 03/02/2022 9:00 | Google Meet |
Old Exams
| Type | Date | Text |
|---|---|---|
| Written/Lab | 23/01/2018 9:30 | Text, TestSet, and Solution |
| Written/Lab | 14/02/2018 9:30 | Text, TestSet, and Quadratic solution |
| Written/Lab | 12/06/2018 14:00 | Text, TestSet, and Solution |
| Written/Lab | 06/07/2018 9:30 | Text and TestSet |
| Written/Lab | 14/01/2019 14:00 | Text and TestSet |
How to solve a problem
- Read carefully the description of the problem.
- Make sure you understand the problem by checking the examples.
- Design a first trivial solution.
- Think about a more efficient solution. The use of some running examples usually helps a lot in finding a better solution. If your are not able to find such solution, try to find some hints by discussing with other students, by asking questions on the group, by looking at the solution in our Web page, or by searching on internet. This is perfectly fine for the first problems and for most difficult ones. In any case, make sure you really understand the solution and the properties it is exploiting!
- Write a brief description of your solution in English. Provide an analysis of its time and space complexity.
- Implement your own solution.
- Submit your implementation to the problem's site. Fix it until it passes all the tests.
- Always compare your solution and your implementation with existing ones.
Background
If you wish to refresh your mind on basic Algorithms and Data Structures, IÂ suggest you to look at the well-known book Introduction to Algorithms, 3rd Edition by Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein.
I strongly suggest you to watch the following video lectures as soon as possible.
- Insertion Sort and Merge Sort
- Heaps and Heap Sort
- Counting Sort, Radix Sort, Lower Bounds for Sorting
- Binary Search Trees
- AVL trees
- Hashing with Chaining
References
- Introduction to Algorithms, Â 3rd Edition, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, Clifford Stein, The MIT Press, 2009 (Amazon) [CCLR]
- Algorithms, 4th Edition, Robert Sedgewick, Kevin Wayne, Addison-Wesley Professional, 2011 (Amazon) [RS]
- Algorithms, Sanjoy Dasgupta, Christos Papadimitriou, Umesh Vazirani, McGraw-Hill, 2006. (Amazon) [DPZ]
- Programming Challenges: The Programming Contest Training Manual, Steven S. Skiena, Miguel A. Revilla, Springer, 2003 (Amazon) [SR]
- Competitive Programming 4: The New Lower Bound of Programming Contests, Steven Halim, Felix Halim, (here) [HH]
- Guide to Competitive Programming: Learning and Improving Algorithms Through Contests. Second Edition, Antti Laaksonen, Springer, 2020 (here) [L]
Rust
- The Rust Programming Language
- The Rust Reference
- The Rust Standard Library
- Rust users forum
- Rustlings
C++
- The C++ Programming Language, 4th Edition, Bjarne Stroustrup, Addison-Wesley Professional, 2013Â (Amazon)
- A Tour of C++, 2nd Edition, Bjarne Stroustrup, Addison-Wesley Professional, 2018Â (Amazon)
- The C++ Standard Library: A Tutorial and Reference, 2nd Edition, Nicolai M. Josuttis, Addison-Wesley Professional, 2012Â (Amazon)
Useful links
- Erik D Demaine, Srini Devadas, Nancy Ann Lynch, "MIT Design and Analysis of Algorithms", MIT Algorithm course which includes video lectures
- Tim Roughgarden, "Algorithm specialization", Coursera
- Visualgo:Â visualising data structures and algorithms through animation
- Geeks for Geeks: Company interviews preparation
- Interviews common coding questions
- How to: Work at Google — Example Coding/Engineering Interview Video
- Google's Code Jam
- Topcoder
- Codeforces
- LeetCode
- HackerRank
- Geeks for Geeks
- LeetCode
- CodeChef - Data Structures and Algorithms links
- Geeks for Geeks: Top 10 Algorithms and Data Structures for Competitive Programming
- List of resources for competitive programming
Lectures
| Date | Lecture | References | Problems |
|---|---|---|---|
| 15/09/2022 | Introduction | Slides | Leaders in array (solution), Kadane's algorithm (solution), and Missing number in array (solution) |
| 19/09/2022 | Solutions of Trapping rain water and Sliding window maximum | Rossano's notes* | Trapping rain water (solution), and Sliding window maximum (solution) |
| 22/09/2022 | Analysis and correctness of Sliding window maximum. Brief introduction to Rust. | Next greater element and Towers (solution) | |
| 29/09/2022 | Searching and Sorting: Binary Search, Merge Sort, QuickSort, Counting Sort, and Radix Sort | Rossano's notes*. [CCLR] Chapters 2.3, 7, and 8. Binary search. Exponential search. Interpolation search (optional) | The Monkey and the Oiled Bamboo |
| 03/10/2022 | Searching and Sorting: Binary Search, Merge Sort, QuickSort, Counting Sort, and Radix Sort | Inversion count and Two Types of Spells | |
| 05/10/2022 | Hands-On 1. Deadline: 19/10/2022 | ||
| 10/10/2022 | Trees: representation, traversals, and Binary Search Tree | Rossano's notes*. [CCLR] Chapters 10.4 and 12. | Frogs and Mosquitoes |
| 13/10/2022 | Lecture Cancelled! | ||
| 17/10/2022 | Trees: representation, traversals, and Binary Search Tree | Rossano's notes*. Tree traversals. | Maximum path sum (solution) and Longest k-Good Segment |
| 20/10/2022 | Trees: representation, traversals, and Binary Search Tree | Euler Tour. Two pointers technique. | |
| 24/10/2022 | (Static) Prefix sum | Rossano's notes* | Ilya and Queries (solution), Number of ways (solution), and  Little girl and maximum sum (solution) |
| 27/10/2022 | Segment Trees | Segment Tree: description, tutorial 1, tutorial 2, tutorial 3, video, visualgo, slides and code. | Solve Nested segments with Segment trees. |
| 31/10/2022 | Segment trees: Applications | ||
| 03/11/2022 | Segment Trees: Lazy Propagation and Persistency | Segment Tree: description, tutorial 1, tutorial 2, tutorial 3, video, visualgo, slides and code. Lazy propagation: tutorial and video. | Circular RMQ |
| 07/11/2022 | Exercises | Triplets (Text and TestSet) and Smaller Values (Text and TestSet) | |
| 10/11/2022 | Hands-On 2. Deadline: 23/11/2022 | ||
| 14/11/2022 | Static RMQ with sparse table | RMQ and sparse table: tutorial 1, tutorial 2, paper, and code. Static RMQ in 2n + o(n) bits and constant time(optional). | |
| 17/11/2022 | Mo's algorithm on sequences and trees | Rossano's notes*. Mo's Algorithm: Sequences and Trees | Powerful array and Tree and queries |
| 21/11/2022 | Dynamic Programming: Fibonacci numbers, Rod cutting, and Shortest path on a DAG | Rossano's notes* (or pdf). [CCLR] Chapter 15. | |
| 24/11/2022 | Dynamic Programming: Minimum cost path and Longest common subsequence | Rossano's notes* (or pdf). Martin Gardner on Minimum cost path. | Longest common subsequence and Minimum number of jumps |
| 28/11/2022 | Dynamic Programming: 0/1 Knapsack, Fractional knapsack, and Subset sum. | Rossano's notes* (or pdf). 0/1 Knapsack problem: tutorial | Subset sum and 0-1 knapsack |
| 01/12/2022 | Dynamic Programming: Longest increasing subsequence and Coin change | Rossano's notes* (or pdf) | Longest increasing subsequence |
| 05/12/2022 | Dynamic Programming: Longest increasing subsequence, Longest bitonic subsequence, and Largest independent set on trees | Rossano's notes* (or pdf) | Longest bitonic subsequence |
| 09/12/2022 | Hands-On 3. Deadline: 23/12/2022 |
Lectures from past years
| Date | Lecture | References | Problems |
|---|---|---|---|
| 2021 | Prefix sum: Binary Indexed Tree (aka BIT or Fenwick tree) | Rossano's notes*. BIT: description, tutorial, video, visualgo, and code. | Update the array (solution) |
| 2021 | Applications of BIT and Range update with BIT. | Rossano's notes*. Range updates on BIT. Tutorial. RMQ with BIT (optional) | Nested segments (solution) and Pashmak and Parmida's problem (solution) |
| 2017 | Simulation of the exam | Misha and forest | |
| 2017 | Centroid Decomposition of trees | Centroid Decomposition of trees: here, here, here, and here | |
| 2017 | String algorithms: Knuth-Morris-Pratt and Suffix array | Knuth-Morris-Pratt from [CLRS] Chapter 32.3. Knuth-Morris-Pratt. Optional: Rabin-Karp here from Algorithms on strings, trees, and sequences, D. Gusfield, Cambridge university press, here, and here. Suffix Array: Tutorial and implementation: here and here. Optional: Suffix Array in linear time here | Longest prefix suffix and Shift the string |
| 2017 | String algorithms: LCP array, trie and ternary search trie | Computing LCP array: Kasai et al.'s algorithm and here. Ternary search trie and a video. | |
| 2018 | Standard Template Library (STL) | Slides. Tutorial and STL algorithms | Megacity (solution), Find pair (solution), and Two heaps (solution) |
| 2018 | Standard Template Library (STL). Coding | Slides | |
| 2018 | Heavy-light Decomposition of trees. This lecture is not mandatory. | Heavy-light Decomposition of trees: here, here, and here. | QTREE, QTREE2, QTREE3, GOT, and Chef and the tree. |
| 2021 | Greedy algorithms: Activity Selection, Job sequencing, and Fractional knapsack problem | Rossano's notes*. Notes by Jeff Erickson. Job sequencing. Fractional Knapsack Problem | N meetings in one room, Magic numbers, Wilbur and array, and Alternative thinking |
| 2019 | Greedy Algorithms: Boxes and Hero | Rossano's notes*. Boxes and Hero. Huffman code: Section 7.4 in Notes by Jeff Erickson (optional). | Lexicographically maximum subsequence, Woodcutters, and Queue |
| 2021 | Dynamic Programming: Edit distance, Longest palindromic subsequence, and Weighted job scheduling | Rossano's notes* (or pdf) | Edit distance, Vertex cover, and Longest palindromic subsequence |
| 2021 | Graph algorithms: BFS, DFS, and Topological Sort | Rossano's notes*. [CCLR] Chapter 22 | X total shapes, IsBipartite, and Fox and names |
| 2021 | Graph algorithms: Strongly Connected Components and Single-Source Shortest Path | Rossano's notes*. [CCLR] Chapters 22 and 23 | Learning languages and Checkposts |
| 2019 | Graph algorithms: Minimum Spanning Tree (and Disjoint Sets data structures) | Rossano's notes*. [CCLR] Chapters 21 and 23. Kruskal: code, Disjoint Set: tutorial | Minimum spanning tree |
* Notes marked with "Rossano's notes" are rough and non-exhaustive notes that I used while lecturing. Please use them just to have a list of the topics of each lecture and use other reported references to study these arguments.
Further (optional) topics
- Aho-Corasick String Matching Algorithm
- Convex Hull
- Interval tree
- Merge Sort Tree
- Manacher's Algorithm: here and here
- Maximum flow
- Splay trees
- Sweep line algorithm