Question: Solve the recurrence equation T(n) = 9T(n/3) + n^2 with T(1) = 1 with a recurrence tree but do not show the recurrence tree. Answer

Solve the recurrence equation T(n) = 9T(n/3) + n^2 with T(1) = 1 with a recurrence tree but do not show the recurrence tree. Answer the following questions: - What is the mathematical formula that describes the cost of any node that is not a leave? - What is the mathematical formula that describes the sum of the sibling nodes at each level of the recurrence tree that is not the level of the leaves? - How many leaves does the tree have? and what is the sum of their cost? - Compute the running-time of T(n) by simplifying the formula that sums all the levels of the recurrence tree, and provide it in asymptotic notation.

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