1. Lecture 5 Efficiency of Algorithms (S&G, ch.3)
2/16/2019 9:43 AM
Lecture 5
Efficiency of Algorithms
(S&G, ch.3)
2/16/2019
CS Lecture 5
CS 100

2. Attributes of Algorithms
Lecture 5
2/16/2019 9:43 AM
Attributes of Algorithms
First, it must be correct!
Other factors include:
efficiency
understandability
maintainability
usability
2/16/2019
CS Lecture 5
CS 100

3. Three Values Common to Many Technological Activities
Lecture 5
2/16/2019 9:43 AM
Three Values Common to Many Technological Activities
The Three E’s:
Efficiency
Economy
Elegance
Related to the Three S’s:
Scientific
Social
Symbolic
Call the S’s three dimensions
2/16/2019
CS Lecture 5
CS 100

4. Efficiency Deals with the amount of resources used
Lecture 5
2/16/2019 9:43 AM
Efficiency
Deals with the amount of resources used
e.g., computer time, memory space
how to trade off one against another?
Basic criteria are correctness & security
correct results
resilient to operator error
error recovery
Issues are scientific
In other words, what resources are required to get correct results
Also, what resources are required to deal with errors, provide recovery, etc.
2/16/2019
CS Lecture 5
CS 100

5. Economy Deals with social benefit relative to costs
Lecture 5
2/16/2019 9:43 AM
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
Basic issues are social
usefulness of software in social context
monetary costs depend on market forces
social expectations affect costs & benefits
Note program maintenance cost
Monetary costs may depend on litigation & its expected outcome
Note that many people don’t expect their PC software to be reliable
2/16/2019
CS Lecture 5
CS 100

6. Elegance and the Limitations of Analysis
Lecture 5
2/16/2019 9:43 AM
Elegance and the Limitations of Analysis
Tacoma Narrows Bridge, Puget Sound
Opened July 1, 1940
Opened July 1, 1940
Took 2 years to construct
Almost 6000 ft long (5939)
42 MPH wind
Collapsed Nov 7, 1940
"Just as I drove past the towers, the bridge began to sway violently from side to side. Before I realized it, the tilt became so violent that I lost control of the car... I jammed on the brakes and got out, only to be thrown onto my face against the curb.
"Around me I could hear concrete cracking. I started to get my dog Tubby, but was thrown again before I could reach the car. The car itself began to slide from side to side of the roadway.
"On hands and knees most of the time, I crawled 500 yards or more to the towers... My breath was coming in gasps; my knees were raw and bleeding, my hands bruised and swollen from gripping the concrete curb... Toward the last, I risked rising to my feet and running a few yards at a time... Safely back at the toll plaza, I saw the bridge in its final collapse and saw my car plunge into the Narrows."
2/16/2019
CS Lecture 5
CS 100

7. The Result
2/16/2019
CS Lecture 5

8. Elegance Incompleteness of analytical approaches
Lecture 5
2/16/2019 9:43 AM
Elegance
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
2/16/2019
CS Lecture 5
CS 100

9. Learning Elegant Design
Lecture 5
2/16/2019 9:43 AM
Learning Elegant Design
A sense of elegance is acquired through experience in design, criticism, revision
2/16/2019
CS Lecture 5
CS 100

10. slide courtesy of S. Levy
Lecture 5
2/16/2019 9:43 AM
Multiple Algorithms
For some problems there are several well-known algorithms
A given algorithm may be chosen because:
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
E.g. working well for given data set: sorting almost sorted list
Dealing with English text (with its statistical properties)
Note that some of these reasons pertain to different of the Three E’s
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

11. Data Cleanup: Example of Multiple Algorithms
Lecture 5
2/16/2019 9:43 AM
Data Cleanup: Example of Multiple Algorithms
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
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

12. slide courtesy of S. Levy
Lecture 5
2/16/2019 9:43 AM
Data Cleanup (2)
Given: n and N1, 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:
the number of copying operations
the extra temporary space required
both relative to problem size
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

13. A New Primitive Operation
Lecture 5
2/16/2019 9:43 AM
A New Primitive Operation
To examine or change the item at position i in the list M, in addition to Mi we use the expression
M [i]
Examples:
Set i to 10
Set M [i] to 35
Set M [i] to M [i] + 1
Output M [i]
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

14. Data cleanup - Shuffle Left
Lecture 5
2/16/2019 9:43 AM
Data cleanup - Shuffle Left
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.
Variables:
Legit - number of legitimate items
Left - current item inspected
Right - current item to shuffle left
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

15. Shuffle Left - The Algorithm
Lecture 5
2/16/2019 9:43 AM
Shuffle Left - The Algorithm
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 Left + 1
End of loop
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

16. Data cleanup - Copy Over
Lecture 5
2/16/2019 9:43 AM
Data cleanup - Copy Over
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
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

17. Copy Over - The Algorithm
Lecture 5
2/16/2019 9:43 AM
Copy Over - The Algorithm
Set OldPos to 1
Set NewPos to 0
While OldPos  n do
If N [OldPos]  0 then
Set NewPos to NewPos Set M [NewPos] to N [OldPos]
Set OldPos to OldPos + 1
End of loop
Stop
Note that this algorithm is much easier to understand
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

18. Data cleanup - Converging Pointers
Lecture 5
2/16/2019 9:43 AM
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
Variables:
Legit - number of good items
Left - the left hand pointer
Right - the right hand pointer
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

19. Converging Pointers - The Algorithm
Lecture 5
2/16/2019 9:43 AM
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
Stop
Note that we do not advance Left on a zero item, because we don’t know if N[Right] = 0
Will this algorithm terminate?
Yes, because either Left is incremented or Right is decremented, so will eventually converge
The final If handles the case when Left = Right
We know that everything to the left of Left is good,
but we do not know about what’s under Left
2/16/2019
CS Lecture 5
slide courtesy of S. Levy
CS 100

20. Comparison of Data Cleanup Algorithms
Lecture 5
2/16/2019 9:43 AM
Comparison of Data Cleanup Algorithms
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?)
Shuffle-Left uses n, Legit, Left, Right
Converging-Pointers uses n, Legit, Left, Right
2/16/2019
CS Lecture 5
CS 100

21. Performance Evaluation
Lecture 5
2/16/2019 9:43 AM
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
2/16/2019
CS Lecture 5
CS 100