Kth largest element in a max-heap

Question

I\'m trying to come up with something to solve the following:

Given a max-heap represented as an array, return the kth largest element without modifyi

Answer 1

No, there's no O(log n)-time algorithm, by a simple cell probe lower bound. Suppose that k is a power of two (without loss of generality) and that the heap looks like (min-heap incoming because it's easier to label, but there's no real difference)

      1
   2     3
  4 5   6 7
.............
permutation of [k, 2k).

In the worst case, we have to read the entire permutation, because there are no order relations imposed by the heap, and as long as k is not found, it could be in any location not yet examined. This takes time Omega(k), matching the (complicated!) algorithm posted by templatetypedef.