Introduction to HKOI

1. Introduction to HKOI

2. Self Introduction

3. Ice Breaking Game

4. Ice Breaking Game • Level 1 • Form a big circle • The person holding the deck of cards will start the game, by introducing himself, and then passes the deck of cards to his left. • In each preceding turn, the person holding the deck of cards will repeat what the previous person has said, and then introduces himself. After that, he will passes the deck to his left. • The game ends when the deck of cards return to the first person.

5. Ice Breaking Game • Level 2 • Form a big circle • The person holding the deck of cards will start the game, by introducing himself and drawing a card from the deck. After that, he will pass the deck of cards to the kth person on his left, where k is the number written on the card he draw. • In each preceding turn, the person holding the deck of cards will repeat what the previous person has said, and then introduces himself. After that, he will draw a card from the deck and pass the deck of cards to the kth person on his left, where k is the number written on the card he draw. • The game ends when the deck runs out of cards.

6. Problems • Just like in Final Events • Usually starts with a story or a situation in daily life. • e.g. A group of people is playing an ice-breaking game • Specifies a set of well-defined inputs, and the corresponding outputs • What can be the input and output of the ice-breaking game we played? • Sometimes, there may be more than one correct output, and the problem only requires you to output any one of the them. • Be careful of the format of the input and output! • Example: sorting

7. Algorithms • “Informally, an algorithm is any well-defined computational procedure that takes some value, or set of values, as input and produces some value, or set of values, as output. An algorithm is thus a sequence of computational steps that transform the input into the output.” [CLRS] • An algorithm (算法) is a method to solve a problem. • There may be more than one algorithms corresponding to a problem. • Take sorting as an example. Bubble sort and insertion sort are algorithms that solves the problem. • We usually regard algorithms as language independent. • An algorithm, by definition, must eventually terminates. • Many important algorithms are named after Computer Scientists.

8. NT Q WA SA NSW V T Algorithms • Tree-Search algorithms • Depth-First Search • Breath-First Search • Graph algorithms • Dijkstra’s • Floyd-Warshall • Bellman-Ford • Prim’s • Kruskal’s • Convex Hull algorithm • Graham’s scan

9. Data Structures • Data structures (數據結構) are how we organize and store the input data, or intermediate results of computation • Helps to speed up algorithms • Different data structures have different properties • different types of data • different types of operations • Examples • Array • Stack • Queue • Heap • Binary Search Tree

10. Complexity • We want to know how well an algorithm “scales” (i.e. when there is a large input). • Usually, minor improvements are not critical in competitions. • A reasonable implementation can pass. • So, we want to hide the lower order terms. • We do not know the exact time each operation takes. • So, we want to measure the time by counting the number of basic operations.

11. Complexity

12. Complexity • Big-O notation • Definition We say that f(x) is in O(g(x)) if and only if there exist numbers x0 and M such that |f(x)| ≤ M |g(x)| for x > x0

13. Complexity • Bubble sort • For i := 1 to n do For j := 2 to i do if a[j] > a[j-1] then swap(a[j], a[j-1]); • Worst case number of swaps = n(n-1)/2 • Time Complexity = O(n2) • Total space needed = size of array + space of variables • Space Complexity = 32*n +32*3 = O(n) +O(1) = O(n)

14. Complexity • Binary search • While a<=b do m=(a+b)/2 If a[m]=key, Then return m If a[m]<key, Then a=m+1 If a[m]>key, Then b=m-1 • Worst case number of iterations = lg n • Time Complexity = O(log n) • Total space needed = size of array + space of variables • Space Complexity = O(n)

15. Complexity • Usually, the time complexity of the algorithm gives us a rough estimation of the actual run time. • O(n) for n ~ 108-109 • O(n log n) for n ~ 5x105 • O(n2) for n ~ 1000-10000 • O(n3) for n ~ 100~1000 • O(n4) for n ~ 50-100 • O(kn) (k>1) or O(n!) for very small n, usually < 20 • Keep in mind • The constant hidden by Big-O notation (including the algorithm and the details implementation) • Computers vary in speeds, so the time needed will be different. In fact, computers are getting faster these days. • Read the instructions carefully for the time limit. • Test the program/computer before making assumptions!

16. Training Session • Topics are divided into two categories, such that students may master the necessary skills after two years of training • Intermediate: designed for students who have never entered training team in the past • Advanced: designed for students who are familiar with intermediate topics • All topics are open to all trainees. • We strongly recommend that students make sure they have the necessary background knowledge before they attend a training session.

17. Training Session • On Saturdays (including some public holidays) • Venue • HW312(Intermediate) and HW311(Advanced), Haking Wong Building, The University of Hong Kong • AM Session • regular training topics • 10:00am – 1:00pm • Lunch • Questions and discussions • Making friends • PM Session • 2:00pm – 5:00pm • Detailed schedule is available in the official website (http://www.hkoi.org/) • Training notes will be uploaded after each training session.

18. Training Topics • Algorithms and Data Structures • Linux • Free, popular and powerful • Competition environment • C++ • Advantage of Stardard Template Library (STL)

19. Training References • Books • “Introduction to Algorithms” by Cormen, Leiserson, Rivest, Stein [CLRS] • Heapsort, Quicksort, Sorting in Linear Time, Elementary Data Structures, Binary Search Trees, Dynamic Programming, Greedy Algorithms, Data Structures for Disjoint Sets, Elementary Graph Algorithms, Minimum Spanning Trees, Single-Source Shortest Path, All-Pairs Shortest Path • Online • Wikipedia (http://en.wikipedia.org/)

20. Online Judge • HKOI Judge (HKOJ) • https://judge.hkoi.org • After each training, some problems are open for practice. • Update your personal information. • Take attendance on your own every training. • Rank, score and attendance are for reference only.

21. Team Formation Test • 29 May 2010 • Trainees with outstanding performance can represent Hong Kong in international and national competitions • The delegation selection algorithm is based on the score of the Team Formation Test (TFT)

22. External Competitions • International Olympiad of Informatics (IOI) • http://www.ioi2010.org/ • 14-21 August 2010 @ Canada • National Olympiad of Informatics (NOI) • 全國信息學奧林匹克競賽