The height of any rooted tree is defined as the maximum number of edges in the path from the root node to any leaf node. Suppose a Min-Heap $T$ stores 32 keys. The height of $T$ is ____________. (Answer in integer)

A binary min-heap with $n$ elements is a complete binary tree.

The height $h$ (defined as the number of edges on the longest path from the root to any leaf) of a complete binary tree with $n$ nodes is given by:

For $n = 32$:

Alternatively, considering levels:

• Level 0: $2^0 = 1$ node

• Level 1: $2^1 = 2$ nodes

• Level 2: $2^2 = 4$ nodes

• Level 3: $2^3 = 8$ nodes

• Level 4: $2^4 = 16$ nodes

Total nodes up to level 4 = $1 + 2 + 4 + 8 + 16 = 31$ nodes.

The $32^{\text{nd}}$ node is located at level 5. Thus, the maximum path from the root to a leaf node consists of 5 edges.