HKOI 2005 Training

1. HKOI 2005 Training New Problem Types: Interactive and Open Test Data

2. Roadmap • Interactive Tasks • Partial Scoring • Open Test Data Tasks

3. The Traditional Problem Type • Read input, write output • Input is static • It does not change according to your output • Program’s output is compared with judge’s output, or another program (judging program) is used to check its correctness • That’s a must, what else can it be?

4. Interactive Tasks • Input is dynamic • Successive input items depend on your previous output items • Forced to make output before you can continue reading from input • “Interactive” doesn’t mean the process of programming is interactive!

5. Example: Guess-the-number • My lucky number is an integer between 1 to 5, guess it • Each time you make a guess (an integer), I will reply with either one of: • Too big • Too small • Correct

6. Example: Guess-the-number • You: 1? Me: Too small. • You: 2? Me: Too small. • You: 4? Me: Too big. • You: 5? Me: Too big. • You: 3? Me: Correct.

7. Interactive Tasks • In the judging environment, you are the submitted program • Note that input varies to suit your output • How can the judge achieves this effect? • Another program! • In fact there is another way to achieve interactivity • A library!

8. Roadmap • Interactive Tasks • Interactivity via Standard I/O • Interactivity via Libraries • Partial Scoring • Open Test Data Tasks

9. Interactivity via Standard I/O • Your program reads from standard I/O as in a traditional tasks • However, at some points, your program must stop reading, produce output, and go on to read • Just keep on reading may lead to errors • A judging program reads your output and produces suitable input for you

10. Interactivity via Standard I/O Too small Too small Correct Submitted program Judging program Standard input 1 2 3 Standard output

11. Interactivity via Standard I/O • This type of interactivity first appeared in IOI1995 • I/O are much like the traditional way, but pay attention to the order of input and output • When to read? When to write? Read the problem description carefully

12. Interactivity via Libraries • A library is a collection of subprograms used to develop software (Wikipedia) • To use a library, • In Pascal: uses somelib; • In C/C++: #include “somelib.h” • The problem description should contain instructions on using the provided library • But you should learn it now

13. Function Declarations • Pascal examples: • procedure myproc(x: integer, var c: char); • function myfunc(x, y: integer): integer; • C++ examples: • void myproc(int x, char &c); (Not in C) • int myfunc(int x, int y); • The declaration and meaning of each library functions provided to you will be shown in the problem description

14. Interactivity via Libraries • Recall the game of Guess-the-number • Suppose we are given a library guesslib with one function: • Pascal: function guess(x: integer): integer; • C/C++: int guess(int x); • guess takes an integer parameter, your guess, and returns 1 for “Too big”, -1 for “Too small”, 0 for “Correct”

15. Interactivity via Libraries • The implementations of the library functions will NOT be given to you • Sometimes you are also required to read from standard input or an input file for initial data • Always read the problem description carefully • For your information, this type of interactivity first appeared in IOI1996

16. Hands-on • Guess-the-number • Celebrity

17. Interactive Tasks • We have discussed two methods to achieve interactivity • Those are just I/O stuff, may not be related to the problem itself at all • Interactivity gave rise to three new major classes of contest problems • Detection • Two-person games • Online problems

18. Roadmap • Interactive Tasks • Detection • Two-person Games • Online Problems • Partial Scoring • Open Test Data Tasks

19. Detection • Uncover facts using a specialized detector • Examples: • Celebrity • Guess-the-number • Usually the detector can be used for a very limited number of times, otherwise the problem will become easy

20. Detection: Strategies • Bisection or Binary Search • It makes the worst case better • Application: Guess-the-number • Any other?

21. Two-person Games • The judging program (or the library) and your program play a two player game • Examples: • Tic-tac-toe • Nim • Your score depends on how well your program plays against the opponent (judge)

22. Two-person Games • Unfortunately, your opponent is usually optimal, that is, you are destined to lose once you make a single wrong move • Common strategies and techniques • Minimax • Something from Game Theory • Ad-hoc • Some well-known or easy-to-derive strategies • Application: Nim

23. Online Problems • “Online” does not mean “being connected to the Internet”! • A part of the input data is not available until some later time • Usually an online problem has its offline counterpart

24. Example: Online Sorting • Sort some given integers • Some integers may arrive late • Initially • We have 7, 4, 2, 5 • Bubble-sort them: 2, 4, 5, 7 • Then 3, 8 arrives • We have 7, 4, 2, 5, 3, 8 • Bubble-sort them: 2, 3, 4, 5, 7, 8

25. Example: Online Sorting • If we use bubble sort, every time some new integers arrive, we need O(N2) time to re-sort the numbers • If we use insertion sort, every time some new integers arrive, we need O(N) time per new integer to re-sort the number • So you can see insertion sort is more “online” than bubble sort

26. Online Problems • Most of the time an online problem is much harder to solve that its offline counterpart • Examples of online problems: • Mobile Phones (IOI2001) • Path Maintenance (IOI2003)

27. Roadmap • Interactive Tasks • Partial Scoring • Open Test Data Tasks

28. The Traditional Scoring Method • For a task, there are some test cases • If your program passes a certain test case, marks for that test case will be awarded to you • For each test case, you either get all or nothing

29. Partial Scoring • For each test case, you may get something between 0% and 100% exclusive • Why partial scoring? • The output consists of several parts • Sub-optimal solutions • The closer to the optimum, the more marks you can get

30. Partial Scoring • Measurements of optimality • How close is your answer to the optimal solution • How many queries (detections) have been made before your program produces the correct answer • Sometimes the optimal solution is not even known to the judge • Relative scoring

31. Relative Scoring • You score depends on how close your answer is to the best known solution • The best known solution may be • The judge’s official solution (which may not be optimal) • The best solution among all submitted solutions

32. Examples of Partial Scoring • Example problem • Guess-two-numbers: I have two lucky integers 1 ≤ A < B ≤ 100, guess them • You may ask me questions in the form “Is it true that A ≤ X ≤ B?”, where X is an integer. • Maximum score per test case is 10 marks • Partial scoring 1 • 5 marks for each correctly guessed lucky integer

33. Examples of Partial Scoring • Partial scoring 2 • Let a, b be your output integers and A, B be the correct answer • Your score = max(10-|A-a|-|B-b|, 0) • Partial scoring 3 • If your answer is wrong, 0 marks; else • if number of queries ≤ 10, 10 marks; else • If number of queries ≤ 50, 5 marks; else • 0 marks

34. Partial Scoring: Gallery • Berry (NOI2003) • Zenith Protected Linked Hybrid Zone (NOI2003)

35. Roadmap • Interactive Tasks • Partial Scoring • Open Test Data Tasks

36. Open Test Data Tasks • Official judging test cases must be kept confidential until the end of the contest • The above rule no longer holds after the introduction of open test data tasks • Given a number of test cases, you should submit, for each test case, an output file • First appeared in IOI2001

37. Characteristics of OTD Tasks • NP-Hard • No fast algorithms have yet been found • Relative scoring • Your solution is compared with an optimal or, more probably, a near-optimal solution • Special cases • Some test cases are actually special cases of the problem which is hard in general

38. Open Test Data Tasks: Strategies • Manually solve the first cases • Usually the first few test cases are easy enough to solve manually • Look at all test cases • There may be wicked but trivial test cases • Keep the CPU busy • Let your exhaustive search program run in the background

39. Open Test Data Tasks: Strategies • Make good use of what you have • OS, image editing program, other compilers, etc. • Identify the special cases • Special cases may be easier to deal with • Greedy, randomization, heuristics • Relative scoring does not require an optimal solution!

40. Open Test Data Tasks • Double Crypt (IOI2001) • XOR (IOI2002) • Reverse (IOI2003) • Polygon (IOI2004) • Another Game of Tetris (NOI2002) • Berry (NOI2003) • Graduate (NOI2004)

41. Last Words • Interactive and open test data tasks are now quite common in IOI and NOI • They may appear in the coming Team Formation Tests

42. New Problem Types? • ROBOT (IOI2002 proposed task) • From the contest report: However, ROBOT was in the end rejected… we hope this innovative type of task will be accepted in future IOIs to broaden the IOI task repertoire even further. • Multiple Choice Questions (NOI) • Much like doing school exams... • Question papers and technical terms in Simplified Chinese…