# Analysis of Algorithm Assignment Help

Knuth in mid-1960’s coined and founded Analysis of Algorithm. An algorithm is a finite step-by-step procedure for processing of data, calculations and automated reasoning. The algorithm starts from first step to final step, processing all the steps in between, to get the desired results. The algorithm takes inputs as strings of any length and is designed to work with it.

The analysis of algorithms in computer science is the need to find out how much resources such as time and storage are required to execute the algorithm. The efficiency of an algorithm is calculated by a function relating the input length to the number of steps in the algorithm, called as time complexity or input length to the storage location called as space complexity.

The complexity of an algorithm is calculated by the complexity function for input of very large length and is also called estimating it in the asymptotic sense. Three notations used for calculation the complexity in asymptotic sense are Big O notation, omega notation, and theta notation. The asymptotic estimates are popular because same algorithms in different times may differ in efficiency. For exact calculation of the complexities of algorithms i.e. not asymptotic it requires a certain number of assumptions regarding the algorithm and is called Model of Computation. For the calculation of complexities there are 2 cost models which are generally used:

• A uniform cost model assigns a constant cost irrespective of the size of the number to every machine operation
• The logarithmic cost model  assigns a cost to every machine operation proportional to the numbers of bits involved

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