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where n means the nth &nbsp;fibonacci number?<br />
If you can do additions in O(1) then yes.<br />

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where n means the nth  fibonacci number?
If you can do additions in O(1) then yes.


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= get yourself a really, really big ALU chip :)
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= get yourself a really, really big ALU chip :)

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that's O(n) as long as f(n) is small enough to fit in an int<br />
if adding large numbers is O(log(f(n)) then this method becomes O(n^2)<br />

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that's O(n) as long as f(n) is small enough to fit in an int
if adding large numbers is O(log(f(n)) then this method becomes O(n^2)


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Is there a way to calculate the fibonacci series in linear time instead of O(n^2)?
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Is there a way to calculate the fibonacci series in linear time instead of O(n^2)?

Calculate fibonacci series in linear time

An algorithm is a self-contained step-by-step set of operations to be performed. Algorithms exist that perform calculation, data processing, and automated reasoning. Starting from an initial state and initial input (perhaps empty), the instructions describe a computation that, when executed, proceeds through a finite number of well-defined successive states, eventually producing "output" and terminating at a final ending state. The transition from one state to the next is not necessarily deterministic; some algorithms, known as randomized algorithms, incorporate random input.

Algorithms

A programming language is a formal constructed language designed to communicate instructions to a machine, particularly a computer. Thousands of different programming languages have been created, mainly in the computer field, and many more still are being created every year. The description of a programming language is usually split into the two components of syntax (form) and semantics (meaning). Some languages are defined by a specification document (for example, the C programming language is specified by an ISO Standard), while other languages (such as Perl) have a dominant implementation that is treated as a reference. Some languages have both, with the basic language defined by a standard and extensions taken from the dominant implementation being common.