What is the height of the tallest possible red-black tree containing 31 values?

The height of tallest possible red-black tree having 31 values is 10.

Explanation:

The height of tallest possible red-black tree = 2㏒₂ (n+1)

here we have n=31 So substituting the value of n in the equation.

=2㏒₂ (31+1)

=2㏒₂ (32)

=2㏒₂ (2⁵) since ㏒ (aⁿ) = n㏒ (a)

=2x5㏒₂ (2)

=10㏒₂ (2) since ㏒ₙ (n) = 1.

=10.