Sorting Properties

• We have looked at two sorts, merge and quick.
• There are many sorts and they have been studied extensively.
• We can identify a number of properties
  • In place vs requires extra memory.
    • Merge sort requires two copies of the data at each level. It is not in place.
    • Quicksort does not, it is in place.
  • Stable
    • If two elements have the same key, will their relative position be maintained.
    • This is useful if you sort on multiple keys
      • Sort by first name, then by last name.
      • The list will be ordered by last names, but ordered within groups of last names by first name.
    • Merge sort can be implemented as stable (normal implementation)
    • Quick sort can not.
      • Why not?
• We also consider performance
  • Merge sort is $\Omega(n \log n)$
  • Quicksort is $O(n \log n$ on average but $O(n^2)$ in the worst case.
• But we saw, quicksort outperforms merge sort in most cases.