Question: Problem 1. Imagine there is an algorithm, X, whose runtime follows the following recurrence equation: a. Draw a recursion tree showing the top two and

Problem 1. Imagine there is an algorithm, X, whose runtime follows the following recurrence equation:

T(n) = 9T( 3. + N T(1) = 1

a. Draw a recursion tree showing the top two and the bottom two levels of the recursion tree.

b. Solve the recurrence equation using the recursion tree exactly.

c. How many subproblems are in level j, somewhere between the top and the bottom level of the recursion tree?

d. What is the size of each subproblem at level, j?

e. What is the value of T(9)?

T(n) = 9T( 3. + N T(1) = 1

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