Programming Assignment Expert - Analysis Algorithm
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In the subject of computer science, the analysis of algorithms is the purpose of
the number of resources (such as time and storage) necessary to execute them. Most
algorithms are designed to work with inputs of arbitrary length. Usually the efficiency
or running time of an algorithm is stated as a function relating the input length
to the number of steps (time complexity) or storage locations (space complexity).
Algorithm analysis is an imperative part of a broader computational complexity theory,
which provides theoretical estimates for the resources needed by any algorithm which
solves a given computational problem. These estimates provide an insight into reasonable
directions of search for efficient algorithms.
In hypothetical analysis of algorithms it is common to approximate their complexity
in the asymptotic sense, i.e., to estimate the complexity function for arbitrarily
large input. Big O notation, Big-omega notation and Big-theta notation are used
to this end. For instance, binary search is said to run in a number of steps proportional
to the logarithm of the length of the list being searched, or in O(log(n)), colloquially
"in logarithmic time". Usually asymptotic estimates are used because different implementations
of the same algorithm may differ in efficiency. On the other hand the efficiencies
of any two "reasonable" implementations of a given algorithm are related by a constant
multiplicative factor called a concealed constant.
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