Work Note 10, DM803, fall 2016

Exercises November 17

  1. In the lecture on van Emde Boas trees, we claimed that a time complexity of T(n) = 2 T(√n) + 1 was not good enough to get a result better than O(log n). Prove that.
  2. On the other hand, T(n) = T(√n) + 1 should give us O(log log n). Prove that.
  3. What is the base case of findsucc?
  4. For insertions and deletions, clarify exactly how size, min, and max should be updated.
  5. Review red-black trees, and consider how to merge two red-black trees in time O(log n), provided that the keys in one tree are all smaller than the keys in the other.
  6. Given a key k, consider how to split two red-black trees in time O(log n) such that all keys smaller than k go into one tree and the rest go into the other.
  7. How can one split a red-black tree in two parts or equal size (±1) in time O(log n)?

Lecture November 21


Last modified: Fri Nov 18 10:37:02 CET 2016
Kim Skak Larsen (kslarsen@imada.sdu.dk)