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This lecture covers the concept of optimal binary search trees, where a binary search tree is built from a sequence of distinct keys with associated probabilities to minimize the expected search cost. The lecture explains the process of building optimal binary search trees, the considerations for selecting roots, and the recursive formulation for calculating the expected search cost. Examples and observations are provided to illustrate the concepts discussed, emphasizing the importance of optimal substructure and bottom-up approach in constructing efficient binary search trees.