1. HKOI 2008 FINAL EVENT Q3 STORAGE BOX
Hackson Leung

2. AGENDA Statistics Problem Descriptions Pre-requisite Wrong Solutions
“Correct” Solutions
Correct Solution(s)
Discussion

3. STATISTICS
Min = 0
Max = 100
#Max = 3
Mode = 0

4. PROBLEM DESCRIPTIONS Given N books (by means of their co-ordinates)
Find the optimal way to remove books such that the Kth book is not covered by any book
The sequence of removal is important
Target

5. PRE-REQUISITE Data Processing Simple geometry concept
Basic Recursion technique

6. WRONG SOLUTIONS
Wrong → 0 marks
They contribute to correct solutions

7. WRONG SOLUTIONS
Hardcode
Remove-all
Naïve removal

8. NAÏVE REMOVAL Project two vertical lines from two sides of the book
Whenever the lines intersect (not touch) any book that is higher than the target, it should be removed
Intersect
Target

9. NAÏVE REMOVAL Can pass sample I/O
Can correctly determine no-removal-case
Problem(s)
Easy to construct the sequence?
Always correct?
Target

10. OBSERVATIONS The books covering the Kth book are also removed
Suppose one of them is the Pth book
If the Pth book is optimally removed, then the Kth book is also removed optimally
The problem becomes: how to remove the Pth book in the optimal way?
The Pth book
The Kth book

11. CORRECT SOLUTION
From previous slide, it seems that we are doing the same job again and again
Unless the top objects are not removed, the one below should remain stationary
First-In-Last-Out (FILO) property holds
Why not use recursion to solve?
Θ(N2), fast enough for N < 1,000
Way to improve?

12. OBSERVATION (ADVANCED)
Target

13. COMMON MISTAKES Correct source, wrong executable
Wrong determination of “covering”
Poor implementation skills in recursion
Wrong concept in local / global variables
Wrong output sequence
Does the sequence always follow FILO property?

14. POSSIBLE EXTREME CASE
Target