Analysis of Algorithms : Asymptotic Notations and its properties.

Asymptotic Notations: - 

To represents, the Growth of any algorithm three types of Asymptotic Algorithms used.

1. Big O Notation (read as "Oh")
2. Big Ω Notation (read as "omega")
3. Big θ Notation (read as "theta")

Types of Analysis: -  

1. Worst Case: - It provides Upper Bound on running time. In the worst case, the algorithm will not run for a long time period, no matter what the inputs are.
2. Best Case: -  It provides a Lower Bound on running time. Input is one for which the algorithm runs the fastest. 
3. Average Case: -  It provides a prediction about the running time and assumes that the Input is random.

Algorithm Analysis using Asymptotic Notations: -  

• Big O Notation: -  The function f(n) = O (g(n)) [read as " f of n is Big-Oh of g of n"] iff  their exist positive constants c and n0 (i.e., n not) such that f(n) <= c*g(n) for all n, n>= n0 (i.e., n not).

• Big Ω Notation: -  The function f(n) =  Ω(g(n)) [read as " f of n is Big-omega of g of n"] iff  their exist positive constants c and n0 (i.e., n not) such that f(n) >= c*g(n) for all n, n>= n0 (i.e., n not).

• Big-  θ Notation : -   The function f(n) =  θ (g(n)) [read as " f of n is Big-theta of g of n"] iff  their exist positive constants c and n0 (i.e., n not) such that c1*g(n) <= f(n) >= c2*g(n) for all n, n>= n0 (i.e., n not).