Determination of time complexity, Data Structure & Algorithms

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Determination of Time Complexity

The RAM Model

The random access model (RAM) of computation was devised through John von Neumann to study algorithms. In computer science, Algorithms are studied since they are independent of machine & language.

We will do all our design & analysis of algorithms depend on RAM model of computation:

Each "simple" operation (+, -, =, if, call) takes 1 step exactly.
Loops & subroutine calls are not easy operations, but based upon the size of the data and the contents of a subroutine.
Each of the memory access takes 1 step exactly.

The complexity of algorithms by using big-O notation can be described in the following way for a problem of size n:

Constant-time method is "order 1" : O(1). The time that needed is constant independent of the input size.
Linear-time method is "order n": O(n). The time needed is proportional to the input size. If input size doubles, then, the time to run the algorithm also will be doubles.
Quadratic-time method is "order N squared": O(n²). The time that needed is proportional to the square of input size. If the input size doubles, then, the time needed will enhance by four times.

The procedure of analysis of algorithm (program) involves analyzing each of the step of the algorithm. It based on the kinds of statements utilized in the program.

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