Aspire Faculty ID #18764 · Topic: UGC NET Computer Science Sep 2022 (Paper II) · Just now
UGC NET Computer Science Sep 2022 (Paper II)

The number of nodes of height $h$ in any $n$-element heap is atmost:

Solution

In a heap, height of a node means the number of edges on the longest downward path from that node to a leaf.

Leaves have height $0$.

In an $n$-element heap, the number of nodes at height $h$ decreases as $h$ increases.

Standard result:

Number of nodes of height $h$ in an $n$-element heap is at most

$\left\lceil \frac{n}{2^{h+1}}\right\rceil$

Ignoring the ceiling value, it is written as:

$\frac{n}{2^{h+1}}$

So, the required expression is:

$\frac{n}{2^{h+1}}$

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