What is the minimum number of nodes in a red-black tree of height 8?

Expert Solution

Minimum number of nodes in a red-block tree: h + 1 on the right path and necessary nodes on the left sub trees.

For a tree with height h, the black –height is greater than or equal to h/s.

Therefore for n internal nodes the height will be,

h ≤ 2 lg(n + 1)

To find minimum n:

h ≤ 2 lg(n + 1)

8/2 ≤ 2lg(n + 1)

4 ≤ log2(n + 1)

4 = log2(n + 1)

n + 1 = 2^4

n + 1 = 16

n = 15

Thus the minimum number of nodes is 15.

Junaid answered 2 years ago

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