Print the biggest K elements in a given heap in O(K*log(K))?

Question

Given the following problem , I\'m not completely sure with my current solution :

Question :

Given a maximum heap with n ele

Answer 1

This is possible in a max-heap because you are only printing elements from the tree, not extracting them.

Start by identifying the maximum element, which is located at the root node. Form a pointer to a node and add it to an otherwise empty "maximums" list. Then, for each of the k values, perform the following steps in a loop.

• Pop the maximal element from the list, taking O(1).
• Print its value, taking O(1).
• Insert each of the children of this maximal element to the list. Maintain sort when you insert them, taking O(log(size of list)) time. The maximum size of this list, since we are performing this loop k times, is branch-size*k. Therefore this step takes O(log(k)) time.

In total, then, the run time is O(klog(k)), as desired.