Present an algorithm that returns the largest k elements in a binary max-heap with n elements in 0(k lg k) time. Here, k can be some number that is much smaller than n, so your algorithm should not depend on the size of the heap.

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3.
Present an algorithm that returns the largest k elements in a binary max-heap with n elements in 0(k lg k)
time. Here, k can be some number that is much smaller than n, so your algorithm should not depend on the
size of the heap.
Hint: you need to consider who are the candidates for the ith largest element. It is easy to see that the root
contains the only candidate for the 1st largest element, then who are the candidates for the 2nd largest
element after the 1st largest element is determined? Who are the candidates for the 3rd largest element after
the 2nd largest element is determined? And so on. Eventually, you will find that there are i candidates for the
ith largest element after the (i-1)th largest element is determined. Next, you need to consider how to use
another data structure to maintain these candidates.
Transcribed Image Text:3. Present an algorithm that returns the largest k elements in a binary max-heap with n elements in 0(k lg k) time. Here, k can be some number that is much smaller than n, so your algorithm should not depend on the size of the heap. Hint: you need to consider who are the candidates for the ith largest element. It is easy to see that the root contains the only candidate for the 1st largest element, then who are the candidates for the 2nd largest element after the 1st largest element is determined? Who are the candidates for the 3rd largest element after the 2nd largest element is determined? And so on. Eventually, you will find that there are i candidates for the ith largest element after the (i-1)th largest element is determined. Next, you need to consider how to use another data structure to maintain these candidates.
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