Yet another Way to Explain Algorithms

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Yet another Way to Explain Algorithms

• Tomasz Müldner, Elhadi Shakshuki and Joe Merrill
  
• Jodrey School of Computer Science, Acadia
  University, Wolfville, NS, Canada
• presenting

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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.

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Contents of the Talk

• Introduction to Algorithm Visualization
• Description of Algorithm Explanation
• Example Selection Sort (Proceedings
  Insertion Sort)
• Conclusions
• Future Work

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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

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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

learners conceptions of these entities and events
the domain consisting of the algorithm entities
and temporal events
?
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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.

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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.

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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.

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Example Selection Sort

• Abstraction tree

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Top Level of Abstraction

• ADT consists of sequences of elements of type T,
  denoted by SeqltTgt, 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

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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(seqltTgt t, Comparator comp), which
  finds the smallest element in t (using comp)
• swap(T el1, T el2), which swaps el1 and el2.

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Top Level Code Text
void selection(SeqltTgt t, Comparator comp)
for(prefix(t) NULL prefix(t) ! t
inc(prefix(t))) swap( smallest(suffix(t),
comp), first(suffix(t)))
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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
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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.

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Low Level Code Text
T smallest(SeqltTgt t, Comparator comp) small
current first(t) while((currentnext(curre
nt,t))!NULL) if(comp(small, current) lt 0)
small current return small
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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.
• Whats the last step of the algorithm?

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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

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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.

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Correction