K1 < K2 < K3 < K4 < K5 are five search keys. They are searched with probabilities 0.05, 0.4, 0.15, 0.3, 0.1 respectively.

5.1 Use the dynamic programming method to create an optimal binary search tree for the five keys. Show the calculation details for cell (1,5) in the main table.

5.2 Design a greedy algorithm for creating optimal binary search trees. Represent the algorithm in pseudocode. Show how your algorithm creates a tree for the five keys.