HKOI 2008 FINAL EVENT Q3STORAGE BOXHackson 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

Target

Intersect

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 Kth bookThe Pth 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