Definition of Advanced algorithm:
Step by step procedure design
to perform an operation,
and which (like a map
or flowchart)
will lead
to the sought result
if followed correctly. Algorithms have a definite
beginning and a definite end, and a finite number of steps. An algorithm produces
the same output information
given the same input information, and several short algorithms can be combined to perform complex tasks such as writing a computer program.
Example
of advanced algorithm in real world application:
There is lot of examples in this
real world application using an advanced algorithm. Here I consider the electronic usage in real
world application.
1)
Electronic usage:
By using advanced algorithm method we build
electronic chips in present days by implement for various
integer and floating-point sizes in computer hardware or in microcode. In arbitrary pricision, it's
common to use long multiplication with the base set to 2w,
where w is the number of bits in a word, for multiplying relatively
small numbers.
To multiply two numbers with n
digits using this method, one needs about n2 operations. More
formally: using a natural size metric of number of digits, the time complexity
of multiplying two n-digit numbers using long multiplication is Θ(n2).
By using this advanced technology of algorithm
we can easily solve the problem facing of
*overflow
*time complexity of multiplying
n-digit
*memory usage
*Reduce the complexity
When implemented in software,
long multiplication algorithms have to deal with overflow during additions,
which can be expensive. For this reason, a typical approach is to represent the
number in a small base b such that, for example, 8b2
is a representable machine integer (for example Richard Brent used this
approach in his Fort-ran package MP); we can then perform several additions
before having to deal with overflow. When the number becomes too large, we add
part of it to the result or carry and map the remaining part back to a number
less than b; this process is called normalization.
http://en.wikipedia.org/wiki/Multiplication_algorithm
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