How many different binary search trees can be constructed, Computer Engineering

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How many different binary search trees can be constructed

Problem

1. Write an efficient algorithm that will find an optimal order for multiplying n matrices A₁ × A₂ × · · · × Aⁿ, where the dimension of each matrix is 1 × 1, 1 × d, d × 1, or d × d for some positive integer d. Analyze your algorithm and show the results using order notation.

2. How many different binary search trees can be constructed using six distinct keys?

3. Create the optimal binary search tree for the following items, where the probability occurrence of each word is given in parentheses: CASE (.05), ELSE (.15), END (.05), IF (.35), OF (.05), THEN (.35).

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