CATE, August 18, 2004
1
Yet another Way to Explain
Algorithms
Tomasz Müldner*,
Elhadi Shakshuki and Joe Merrill
Jodrey School of Computer Science, Acadia University,
Wolfville, NS, Canada
* presenting
CATE, August 18, 2004
2
Standard approach
The user has to
map the problem
domain to the
graphical domain
and then looking
at the animation
they have to
retrieve essential
properties of the
algorithm.
CATE, August 18, 2004
3
Contents of the Talk
•
Introduction to Algorithm Visualization
•
Description of Algorithm Explanation
•
Example: Selection Sort
(Proceedings: Insertion Sort)
•
Conclusions
•
Future Work
CATE, August 18, 2004
4
Standard Algorithm Visualization
1.
take the
description
of the algorithm (usually
the code in a programming language, e.g. C)
2.
graphically represent
data
in the code using
bars, points, etc.
3.
use animation to represent the
flow of control
4.
show the animated algorithm
5.
hope that the learner will now
understand
the
algorithm
CATE, August 18, 2004
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Algorithm Explanation (AE)
•
To make algorithm explanation possible,
the learner has to build a
mapping
:
•
AE uses a variety of tools to help the
students to learn algorithms, including
textual and visual representation
learner’s conceptions of
these entities and events
the domain consisting of the
algorithm entities and temporal
events
CATE, August 18, 2004
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Goals of AE
•
Understanding of both,
what
the algorithm
is doing and
how
it works.
•
Ability to justify the algorithm correctness
(
why
the algorithm works).
•
Ability to
program
the algorithm in any
programming language.
•
Understanding the
time complexity
of the
algorithm.
CATE, August 18, 2004
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Requirements of AE
•
the algorithm is presented at several
levels of abstraction
•
each level of abstraction is represented
by the text and optionally by visualization
•
active learning is supported
•
the design helps to understand time
complexity
•
presentations are designed by experts.
CATE, August 18, 2004
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AE Explanations
An explanation of a single algorithm consists of the
following four parts:
•
Hierarchical Abstract Algorithm Model
•
Example of an abstract implementation of the
Abstract Algorithm Model
•
Tools to help predicting the algorithm
complexity.
•
Questions for students, including “do it yourself”
mode for each level of abstraction.
CATE, August 18, 2004
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Example: Selection Sort
Abstraction tree
selection
smallest
swap
CATE, August 18, 2004
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Top Level of Abstra
ction
•
ADT consists of sequences of elements of
type T, denoted by
Seq<T>
, with a
linear
order.
•
There is a function (or a type)
int comparator(const T x, const T y)
which returns

1 if x is less than y, 0 if they
are equal and +1 otherwise
CATE, August 18, 2004
11
Operations from top

level ADT
•
prefix(t)
, possibly empty (NULL), which can be
incremented by one element;
•
inc(prefix(t))
, which increments a prefix by one
element;
•
suffix(t)
, where a prefix followed by the suffix is
equal to the entire sequence
t
;
•
first(suffix)
, which returns the first element of the
suffix;
•
T smallest(seq<T> t, Comparator comp)
, which
finds the smallest element in
t
(using
comp
);
•
swap(T el1, T el2)
, which swaps
el1
and
el2
.
CATE, August 18, 2004
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Top Level Code: Text
void selection(Seq<T> t, Comparator comp)
{
for(prefix(t) = NULL; prefix(t) != t; inc(prefix(t)))
swap( smallest(suffix(t), comp), first(suffix(t)));
}
CATE, August 18, 2004
13
Visualization shows Invariants
INVARIANT 1
All elements in the prefix are smaller
(according to the “comp” relation)
than all elements in the suffix.
In the visualization, the prefix box is
smaller than the suffix box
INVARIANT 2
The prefix is sorted.
In the visualization, elements in the
prefix are growing
CATE, August 18, 2004
14
ADT: Low Level
The ADT consists of data described before,
and the following operations:
•
first(t)
, which returns the first element of
the sequence
t
;
•
next(current, t)
, which returns the element
of the sequence
t
, following current, or
NULL if there is no such element.
CATE, August 18, 2004
15
Low Level Code: Text
T smallest(Seq<T> t, Comparator comp)
{
small = current = first(t);
while((current=next(current,t))!=NULL)
if(comp(small, current) < 0)
small = current;
return small;
}
CATE, August 18, 2004
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Post Test
•
What is the number of comparisons and swaps
performed when selection sort is executed for a sorted
sequence and a sequence sorted in reverse.
•
What is the time complexity of the function isSorted(t),
which checks if t is a sorted sequence?
•
Hand

execute the algorithm for a sample set of input
data of size 4.
•
Hand

execute the next step of the algorithm for the
current state.
•
What’s the last step of the algorithm?
CATE, August 18, 2004
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Conclusions
A new approach for learning algorithms:
•
an algorithm is explained at various levels of
abstraction
•
each level is designed to present a single
operation used in the algorithm
•
all operations are shown in a textual and visual
form
•
the visualization system presented in this work is
implemented using Macromedia Flash MX
CATE, August 18, 2004
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Future Work
•
Generic visualizations for various classes
of algorithms such as iterative and
recursive
•
A complete system with a student model
to provide an intelligent and adaptive
learning system.
CATE, August 18, 2004
19
Correction
Kruskal
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