Consider the following recurrence: if i = 1 A(i, j) = A(i-1,j+1)+ A(i 1, j)...

 

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Consider the following recurrence: if i = 1 A(i, j) = A(i-1,j+1)+ A(i − 1, j) otherwise CLARIFICATION: It is possible to substantially simplify this recurrence. Do not do so. Work with the recurrence as given instead. 1. Give naïve recursive code that computes the value of A(n, 1) for n ≥ 1. 2. Give an asymptotic bound on the runtime and memory use of a memoized version of this algorithm. (Assume that storing one value of A takes constant space.) 3. Write clear (pseudocode) nested loops to specify an order could solve the subproblems to convert this to a dynamic programming solution. (There is no need to write the initialization code for the functione Win or the body that would actually solve the problem.) Go to Settings to Consider the following recurrence: if i = 1 A(i, j) = A(i-1,j+1)+ A(i − 1, j) otherwise CLARIFICATION: It is possible to substantially simplify this recurrence. Do not do so. Work with the recurrence as given instead. 1. Give naïve recursive code that computes the value of A(n, 1) for n ≥ 1. 2. Give an asymptotic bound on the runtime and memory use of a memoized version of this algorithm. (Assume that storing one value of A takes constant space.) 3. Write clear (pseudocode) nested loops to specify an order could solve the subproblems to convert this to a dynamic programming solution. (There is no need to write the initialization code for the functione Win or the body that would actually solve the problem.) Go to Settings to

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