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The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources for free. To make a donation or view additional materials from hundreds of MIT courses, visit MIT OpenCourseWare at ocw.mit.edu. PROFESSOR: Today were going to solve three problems, a problem called Parenthesization, a problem called Edit Distance, which is used in practice a lot, for things like comparing two strings of DNA, and a problem called Knapsack, just about how to pack your bags. And were going to get a couple of general ideas, one is about how to deal with string problems in general with dynamic programming. The first two and our previous lecture are all about strings, certain sense or sequences, and were going to introduce a new concept, kind of like polynomial time, but only kind of, sort of-- pseudo polynomial time. Remember, dynamic programming in five easy steps. You define what your sub problems are and co