Consider the recurrence T(n) = n²/3 . T(n²/3) +n with base case T (n) = 1 for n<2. Find an asymptotic solution using the method of recursion trees, presenting your answer as follows: (a) How deep is the recursion tree for T(n)? (b) What is the size of the subproblems at level d? (considering the root node to be at depth d = 0) (c) How many nodes does the tree have at level d? (Hint: you may find the geometric series formula helpful.) (d) What is the total “non-recursive work" (i.e., the sum of the non-recursive terms) at level d? (e) What is the asymptotic growth rate of T(n)? Give a precise answer using the O notation.

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Binomial Heap

A binomial heap is a group of binomial trees. This data structure acts as a priority queue and implements the merge operation faster.