Heap problem

Consider a binary heap containing n numbers (the root stores the greatest number). You are given a positive integer k < n and a number x . You have to determine whether the kth largest element of the heap is greater than x or not. Your algorithm must take O(k) time. You may use O(k) extra storage.

Solution:

The Heap has n elements,

n n-1 n-2 .....k....3 2 1
               ^^^^^^^^^^
               The Kth largest element happens somewhere in this range, 
               because it is a heap, and every parent >= child.

Possible solution, copy the last k elements to the temporary structure,
and build a heap which will take O(k) time and compare the root with the number x.