Construct an optimal binary search tree for five keys A, B, C, D, E with probabilities p1 = 0.1, p2 = 0.3, p3 = 0.1, p4 = 0.4, p5 = 0.1.

Show(1) the main table;

(2) the root table;

(3) all computations to fill in the main table and the root table;

(4) the optimal binary search tree based on the root table;

(5) that the average number of comparisons of your optimal binary search tree is indeed C(1,5).