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The algorithm presented in Figure 4.8 retains no information between invocations of FIRST. As a result, the solution for a given nonterminal might be computed multiple times.
(a) Modify the algorithm so it remembers and references valid previous computations of First(A), A N
(b) Frequently an algorithm needs First sets computed for all X N. Devise an algorithm that efficiently computes First sets for all nonterminals in a grammar. Analyze the efficiency of your algorithm.
(c) Repeat this exercise for the Follow sets.
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Find the profit Pr6 both when the policyholder is healthy at the end of 5 years and when the policy holder is unhealthy at the end of 5 years.
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