If key₁ < key₂ < key₃, and p₁ = 0.3, p₂ = 0.2, p₃ = 0.5 Then answer the following questions:

(Note: pi is the probability that keyi is the search key)

a)draw all possible binary search tree that can be formed using the four keys

b) find the optimal binary search tree (show the calculations)