35 lines
1.1 KiB
Markdown
35 lines
1.1 KiB
Markdown
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<!-- vim: set ts=2 sw=2 et tw=80: -->
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# Complexity
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General way to describe efficiency algorithms (linear vs exponential)
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indipendent from the computer architecture/speed.
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## The RAM - random-access machine
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Model of computer used in this course.
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Has random-access memory.
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### Basic types and basic operations
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Has basic types (like int, float, 64bit words). A basic step is an operation on
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a basic type (load, store, add, sub, ...). A branch is a basic step. Invoking a
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function and returning is a basic step as well, but the entire execution takes
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longer.
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Complexity is not measured by the input value but by the input size in bits.
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`Fibonacci(10)` in linear in `n` (size of the value) but exponential in `l`
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(number of bits in `n`, or size of the input).
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By default, WORST complexity is considered.
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## Donald Knuth's A-notation
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A(c) indicates a quantity that is absolutely at most c
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Antonio's weight = (pronounced "is") A(100)
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## (big-) O-notation
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f(n) = O(g(n))
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*Definition:* if f(n) is such that f(n) = k * A(g(n)) for all _n_ sufficiently
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large and for some constant k > 0, then we say that
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