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This notation gives an upper bound for a function to within a constant factor. Given Figure illustrates the plot of f(n) = O(g(n)) depend on big O notation. We write f(n) = O(g(n)) if there are positive constants n0 & c such that to the right of n0, the value of f(n) always lies on or below cg(n).
Figure: Plot of f(n) = O(g(n))
Mathematically specking, for a given function g(n), we specified a set of functions through O(g(n)) by the following notation:
O(g(n)) = {f(n) : There exists a positive constant c and n0 such that 0 ≤ f(n) ≤ cg(n)
for all n ≥ n0 }
Obviously, we employ O-notation to describe the upper bound onto a function using a constant factor c.
We can view from the earlier definition of Θ that Θ is a tighter notation in comparison of big-O notation. f(n) = an + c is O(n) is also O(n2), but O (n) is asymptotically tight while O(n2) is notation.
While in terms of Θ notation, the above function f(n) is Θ (n). Because of the reason big-O notation is upper bound of function, it is frequently used to define the worst case running time of algorithms.
Program of sun series
The smallest element of an array's index is called its Lower bound.
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