17: B Trees¶
Asymptotics for tree height¶
Which statement gives you more information about a hotel?
A) The most expensive room in the hotel is $639 per night. B) Every room in the hotel is less than or equal to $639 per night.
The answer is
A, since we know for sure that there is atleast one room in the
hotel that costs $639, whereas there is no guarantee of that in
B. Moreover, a
large number of hotels, (or motels) would fulfill the statement in
B (ie, have
rooms that cost a 100 bucks, but would still fulfill the statement).
In the same vein, the one of the following statements about tree height is more informative:
A) Worst case BST height is Θ(N). B) BST height is O(N).
In this case, it's
Which leads to the question, why is Big O useful? It's because of the following:
- Allows us to make simple blanket statements, e.g. can just say “binary search is O(log N)” instead of “binary search is Θ(log N) in the worst case”.
- Sometimes don’t know the exact runtime, so use O to give an upper bound.