Longest Common Subsequence and Optimal BST

This lecture covers the recursive formulation of the Longest Common Subsequence (LCS) problem, discussing the naive implementation and the bottom-up approach for finding LCS. It also delves into recording optimal solutions, presenting pseudocode and analysis for LCS, and printing the solution. Furthermore, it introduces the concept of Optimal Binary Search Trees (BST), explaining how to build a BST with minimum expected search cost using probabilities. Examples are provided to illustrate the concepts, highlighting that the optimal BST may not have the smallest height or the highest-probability key at the root. The lecture concludes with discussions on the search cost of keys in an optimal BST and the optimal substructure for building a binary search tree.