Problem 3. Longest increasing subsequence problem Given a string ₁... n we wish to find the length of its longest increasing subsequence, that is, the largest k for which there exist indices i₁ <...< ik such that Xi1 < xiz <...< Xik Show how to do this in time O(n²).

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Linear Programming Concepts

Linear programming is a famous mathematical modeling tool for determining the best distribution of scarce resources among competing demands. Machinery, time, personnel, raw materials, money, and space are all resources. It is used to find the most optimal solution to a problem with given constraints. The real-life situations can be formulated using linear programming concepts into a mathematical model. Linear programming problems consist of an objective function and linear equalities subjected to constraints.