Complexity - Data Structures - Lecture Slides, Slides of Data Structures and Algorithms

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What is complexity^
^ Consider a sorting program that runs on a data set^
^ Try multiplying the size of the data set and continue toexperiment^
^ What happens??^
^ Demo

What Factors Determine theruntime of a program?

Among all those factors^
^ Size of the data set is one factor that we can analyze^
^ That is, we can describe the runtime as a function of n(size of the data set)^
^ Example:^
^ for (int i=0; i<n ; i++)^
^ Do_something^
^ for (int i=0; i<n ; i=i/2)^
^ Do_something

Definition of Big O^
^ Formal Definition:

f(n) = O(g(n)) means there are positive constants c and k, such that 0 ≤ f(n) ≤ cg(n)for all n ≥ k. The values of c and k must be fixed for thefunction f and must not depend on n.

Complexity of basic algorithms^
^ Finding an element in an unsorted array of size n^
^ Finding an element in a sorted array of size n^
^ Reversing an array of size n^
^ Sorting an array of size n

Determining big O

Final Thoughts^
^ Asymptotic analysis is a way to determine theperformance of an algorithm^
^ However, it is not the only factor that affectsperformance^
^ For the most part other factors also have a significantimpact on performance of systems^
^ Network latency^
^ Language efficiency^
^ Data Structures^
^ Many many other factors