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

Max-heap in an array: element at i is larger than elements at 2*i+1 and 2*i+2 (i is 0-based)

You'll need another max heap (insert, pop, empty) with element pairs (value, index) sorted by value. Pseudocode (without boundary checks):

input: k
1. insert (at(0), 0)
2. (v, i) <- pop and k <- k - 1
3. if k == 0 return v
4. insert (at(2*i+1), 2*i+1) and insert (at(2*+2), 2*+2)
5. goto 2

Runtime evaluation

• array access at(i): O(1)
• insertion into heap: O(log n)
• insert at 4. takes at most log(k) since the size of heap of pairs is at most k + 1
• statement 3. is reached at most k times
• total runtime: O(k log k)