# 2.11. Programming Exercises

- Devise an experiment to verify that the vector index operator is
\(O(1)\)
- Devise an experiment to verify that find and insert are
\(O(1)\) for hash tables.
- Devise an experiment that compares the performance of the
`erase()`

operator on vectors and hash tables.
- Given an array of numbers in random order, write an algorithm that works in \(O(n\log(n))\)
to find the kth smallest number in the array.
- Can you improve the algorithm from the previous problem to be linear? Explain.

Next Section - 3. Basic Data Structures