VCE Algorithmics HESS

VCE ALGORITHMICS
HESS
Distance Education Centre Victoria
(DECV)
VCE Algorithmics (HESS) 2018

VCE Algorithmics (HESS) and DECV, two interesting
and mysterious entities in the Victorian Education
Landscape.
DECV
Algorithmics
(HESS)
EARN
ATAR & University Credits

How Distance Education Works
All courses are delivered
online.
VCE Courses have live weekly
online lessons that are also
recorded for later viewing.

VCE Algorithmics (HESS) @DECV
For students and schools in 2018 DECV offers
• Unit 3
• Unit 4

About Algorithmics at DECV
VCAA Study Guide
 Unit 3
• Focus on Analysis and Modelling with Graphs
• Creating Algorithms for problem solving
 Unit 4
• Accuracy of Algorithmic Solution
• Efficiency of Solution

VCE Algorithmics: Algorithms
Predefined steps to achieve a goal.
Recipe
Flowchart
Designing Algorithms is problem solving.
Problem solving is important in human society.

VCE Algorithmics: Exploring Analysis
What do I know about this problem?
What information is available?
How can I make sense of it?
Modelling the problem – abstraction of the main
components of the problem.
Making order out of the main components of the problem.

Graphs for Modelling G=(V,E)
V={set of nodes/vertices}
E={set of edges}
G=(V,E) Road Network
V={cities}
E={roads}
G=(V,E) Novel/Movie
V={characters}
E={relationships}
G=(V,E) Circulatory System
V={organs}
E={veins/arteries}
G=(V,E) Coffee Machine
V={states}
E={transitionss}

Modelling
Conflict
G=(V,E) Map of Countries
V={Country}
E={Shared Border}
Using colour as an attribute. No two adjacent vertices have the same colour.
Neighbouring nodes have different colour.
G=(V,E) Laboratory Storage
V={chemicals}
E={forbidden shared storage}

Analysis: Water Jug Problem
Water jugs problem: We have one 3
litre jug, one 5 litre jug and an
unlimited supply of water. The goal is
to get exactly one litre of water into
either jug. Either jug can be emptied
or filled, or poured into the other.

Analysis: Airport Runways
A small but busy airport has only one runway. In each unit of
time one plane can land or one plane can take off, but not both.
Planes arrive ready to land or take off at random times, so at any
given unit of time the runway may be idle or a plane may be
landing or taking off, and there may be several planes waiting
either to land or take off.
• What model can we set up to represent this situation?
• Write a simple algorithm in pseudocode to safely handle this situation.
• How could the solution be adjusted if a second runway is built at this airport?

VCE Algorithmics: Exploring Process
Problem solving is an increasingly detailed description of
process using some information or data.
Algorithms for solving a problem, pseudocode combined
with model.

Process: Solving a Kenken
The KenKen puzzle is the trademarked name for a style of arithmetic and
logic puzzle invented by Japanese math teacher Tetsuya Miyamoto.
The puzzles require the integers 1 to 𝑛 to be placed in each row and
column of a (𝑛 × 𝑛) square grid or matrix, while satisfying each
arithmetic cage rule.
Backtracking for bad decisions
Try to minimise bad decisions

Process: Coin Change
The Classic coin change problem:
In Elbonia the coins are in denominations of: 1, 4, 5 cents. If we want to give change
using the minimum amount of coins we need to consider the following recursion
Dynamic Programming
Keeping track of subset solutions
Find the optimal solution
A Naïve algorithm for working out the minimum coins for giving
change: Exponential Time Complexity
function MC(coinValueList,change):
minCoins := change
if change in coinValueList then
return 1
else
foreach coin in coinValueList do
if (coin <= change) then
numCoins = 1 + MC(coinValueList,change-coin)
if (numCoins < minCoins) then
minCoins := numCoins
end if
endif
end do
end if
return minCoins
end function
Dynamic programming will improve run-time, use an array to hold
intermediate values. Minimum coins work out for change from 1
cent incrementing by 1 cent to the amount of change required.

VCE Algorithmics: Model and Process
• Model and Process
• Rules, States and Actions
• Turing Machine
Problem Solving
a sequence of actions that will bring the environment into a desired state.
Search
The process of looking for such a sequence, involving a systematic
exploration of alternative actions.
An algorithm is complete, if will find a solution if one
exists, optimal, if it finds the cheapest solution.

Resources for New Teachers & Students
Preview/Buy at
https://sites.google.com/site/msgvce/

VCE Algorithmics (HESS) @DECV
• If your School is not able to offer VCE Algorithmics in 2018 you can study
it at DECV.
• Enrolments for DECV in 2018 OPEN October 2017 close February 2018
• Year 10 & 11 Students who have successfully completed Math Methods
Units 1 & 2 are eligible to enrol.

WHY?
Problem solving is important in human society.
The world needs more problem solvers.

VCE Algorithmics HESS

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