Exercises

1. The following are some growth-rate functional forms. Can you arrange them in the order of slower to faster performance?
   • 10n³
   • 3(log _e n)²
   • 10n
   • 100n
   • Log₂n²
   • Log₂n³
   • Log₃n²
   • Log₃n³
   • n^1.5
2. Answer the following questions:
   • How can we evaluate the total memory currently being used by a given R environment? What is the purpose of garbage collection (GC) in the context of R?
   • Which occupies more size-a matrix with 10 numbers of categorical attributes, or a dataframe with 10 numbers of corresponding factors?
   • Can you evaluate and plot the memory allocation for dataframes and matrices with an increment of five observations for a fixed number of attributes (15 columns)?
   • Why does data.table occupy more memory than data.frame?
3. Is data.table scalable in terms of performance (faster execution of operations) related to data pre-processing and transformations?

   (Hint: microbenchmark using large number of variables and observations with a higher number of iterations for each scenario).

4. What are the best, worst, and average...