One of the most useful life skills that you can gain from your
computer science training is the ability to perform quick estimates.
This is sometimes known as “back of the napkin” or
“back of the envelope” calculation.
Both nicknames suggest that only a rough estimate is produced.
Estimation techniques are a standard part of engineering
curricula but are often neglected in computer science.
Estimation is no substitute for rigorous, detailed analysis
of a problem, but it can help to decide when a rigorous
analysis is warranted:
If the initial estimate indicates that the solution
is unworkable, then further analysis is probably unnecessary.
Estimation can be formalized by the following three-step process:
Determine the major parameters that affect the problem.
Derive an equation that relates the parameters to the problem.
Select values for the parameters, and apply the equation to yield an
estimated solution.
When doing estimations, a good way to reassure yourself that the
estimate is reasonable is to do it in two different ways.
In general, if you want to know what comes out of a system, you can
either try to estimate that directly, or you can estimate what goes
into the system (assuming that what goes in must later come out).
If both approaches (independently) give similar answers, then this
should build confidence in the estimate.
When calculating, be sure that your units match.
For example, do not add feet and pounds.
Verify that the result is in the correct units.
Always keep in mind that the output of a calculation is only
as good as its input.
The more uncertain your valuation for the input parameters in Step 3,
the more uncertain the output value.
However, back of the envelope calculations are often meant only to get
an answer within an order of magnitude, or perhaps within a factor of
two.
Before doing an estimate, you should decide on acceptable error
bounds, such as within 25%, within a factor of two, and so forth.
Once you are confident that an estimate falls within your error
bounds, leave it alone!
Do not try to get a more precise estimate than necessary for your
purpose.
