Lecture 5
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Attributes of Algorithms
• First, it must be correct!
• Other factors include:
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Efficiency of Algorithms
(S&G, ch.3)
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Three Values Common to Many
Technological Activities
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Efficiency
• Deals with the amount of resources used
• The Three E’s:
– e.g., computer time, memory space
– how to trade off one against another?
– Efficiency
– Economy
– Elegance
• Basic criteria are correctness & security
• Related to the
Three S’s:
– correct results
– resilient to operator error
– error recovery
– Scientific
– Social
– Symbolic
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efficiency
understandability
maintainability
usability
• Issues are scientific
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Elegance and the
Limitations of Analysis
Economy
• Deals with social benefit relative to costs
• Basic criteria are costs & benefits
– not all costs are monetary (e.g. human dissatisfaction,
frustration, fear, suffering; environmental impact)
– costs change in time & are hard to predict
– similarly benefits come in many forms
• Tacoma Narrows
Bridge, Puget Sound
• Basic issues are social
• Opened July 1, 1940
– usefulness of software in social context
– monetary costs depend on market forces
– social expectations affect costs & benefits
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Elegance
The Result
• Incompleteness of analytical approaches
• Under-determination of design space
• Restrict attention to designs for which
correct, efficient, economical designs are
obviously so
• Aesthetic sense guides design
• “When the form is well chosen, its analysis
becomes astonishingly simple” — Billington
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Learning Elegant Design
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Multiple Algorithms
• For some problems there are several wellknown algorithms
• A given algorithm may be chosen because:
• A sense of elegance
is acquired through
experience in
design, criticism,
revision
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It works well for small (large) data sets
It works well for data sets of a given nature
It is easy to program
A program for it is available
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slide courtesy of S. Levy
Data Cleanup:
Example of Multiple Algorithms
• Given: n and N 1, N2, …, Nn
• Want: k and M1, M2, …, Mk where M1, …,
Mk represent the valid (non-zero) items of
the original list
• The focus will be on:
• Sometimes we have a large list of data,
some items of which are not legitimate
items for the work at hand
– No responses
– Invalid values
– Not relevant for current analysis
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slide courtesy of S. Levy
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Data Cleanup (2)
– the number of copying operations
– the extra temporary space required
– both relative to problem size
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slide courtesy of S. Levy
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A New Primitive Operation
Data cleanup - Shuffle Left
• To examine or change the item at position i
in the list M, in addition to Mi we use the
expression
• Strategy:
 Move through list from left to right.
 When we encounter a zero, shuffle everything
to the right of the zero to the left one position.
M [i]
• Examples:
• Variables:
Set i to 10
Set M [i] to 35
Set M [i] to M [i] + 1
Output M [i]
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 Legit - number of legitimate items
 Left - current item inspected
 Right - current item to shuffle left
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slide courtesy of S. Levy
Shuffle Left - The Algorithm
Data cleanup - Copy Over
Set Legit to n
Set Left to 1
Set Right to 2
While Left ≤ Legit do
If N [Left] ≠ 0 then
Set Left to Left + 1
Set Right to Right + 1
Else
Set Legit to Legit – 1
While Right ≤ n do
Set N [Right – 1] to N [Right]
Set Right to Right + 1
Set Right to Left + 1
End of loop
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• Strategy:
 Make a new list with the valid items
 Move through original list from left and copy
valid items to new list.
• Variables:
 OldPos - Position in original list
 NewPos - Position in new list
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Data cleanup - Converging Pointers
• Strategy:
 Have “pointers” marking left and right ends of list
still to be processed.
 Everything to left of left pointer is good data.
 Everything to right of right pointer is bad.
 Pointers converge to one another as we proceed
Set OldPos to 1
Set NewPos to 0
While OldPos ≤ n do
If N [OldPos] ≠ 0 then
Set NewPos to NewPos + 1
Set M [NewPos] to N [OldPos]
Set OldPos to OldPos + 1
End of loop
Stop
slide courtesy of S. Levy
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Copy Over - The Algorithm
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• Variables:
 Legit - number of good items
 Left - the left hand pointer
 Right - the right hand pointer
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Comparison of
Data Cleanup Algorithms
Converging Pointers - The Algorithm
Set Legit to n
Set Left to 1
Set Right to n
While Left < Right do
If N [Left] = 0 then
Set Legit to Legit – 1
Set N [Left] to N [Right]
Set Right to Right – 1
Else
Set Left to Left + 1
End of loop
If N [Left] = 0 then
Set Legit to Legit – 1
Stop
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• Shuffle-Left requires:
– fixed working space (4, independent of problem size)
– 19 copies for a particular list of 10 elements
• Copy-Over requires:
– fewer copies (7)
– an extra copy of the list
• Converging-Pointers requires:
– fewest copies (3)
– fixed extra space (4)
– but it reorders elements (Do we care?)
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slide courtesy of S. Levy
Performance Evaluation
• We compared performance of the
algorithms on a specific problem instance
– Typical? Unusual? We don’t know
• Empirical approach: measure performance
on representative variety of test cases
• Analytical approach: use mathematics to
analyze performance on all possible inputs
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