HKOI 2008 FINAL EVENT Q3 STORAGE BOX Hackson Leung 2007-12-29

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

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

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

PRE-REQUISITE Data Processing Simple geometry concept Basic Recursion technique

WRONG SOLUTIONS Wrong → 0 marks They contribute to correct solutions

WRONG SOLUTIONS Hardcode Remove-all Naïve removal

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

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

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

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?

OBSERVATION (ADVANCED) Target

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?

POSSIBLE EXTREME CASE Target