Question

1. Analysis of the time complexity of a recursive algorithm has resulted in the following recurrence equations. $\qquad T(1) = 1$ $\qquad T(n) = n^2 + 4T(\frac{n}{2}) \quad for \quad n > 1$ (a) Use the top-down method to find a closed-form solution for $T(n)$. (Recap: the top-down method is one in which you use the recurrence equations to rewrite $T(n)$ in terms of $T(x)$ where $x < n$ and repeat the process until you reach the base case.) (b) Draw a recursion tree to get a closed-form solution for $T(n)$. Use the notation in the class (show the input size within each node, annotate it with the the non-recursive time, indicate the number of nodes at each level, the non-recursive time for each level near the right margin, and the grand total vertically below). Your tree must include at least three topmost levels including the root and two bottom-most levels including the leaf.

          1. Analysis of the time complexity of a recursive algorithm has resulted in the following recurrence equations.
$\qquad T(1) = 1$
$\qquad T(n) = n^2 + 4T(\frac{n}{2}) \quad for \quad n > 1$

(a) Use the top-down method to find a closed-form solution for $T(n)$. (Recap: the top-down method is one in which you use the recurrence equations to rewrite $T(n)$ in terms of $T(x)$ where $x < n$ and repeat the process until you reach the base case.)

(b) Draw a recursion tree to get a closed-form solution for $T(n)$. Use the notation in the class (show the input size within each node, annotate it with the the non-recursive time, indicate the number of nodes at each level, the non-recursive time for each level near the right margin, and the grand total vertically below). Your tree must include at least three topmost levels including the root and two bottom-most levels including the leaf.

1. Analysis of the time complexity of a recursive algorithm has resulted in the following recurrence equations.
T(1) = 1
T(n) = n^2 + 4T((n)/(2)) for n > 1

(a) Use the top-down method to find a closed-form solution for T(n). (Recap: the top-down method is one in which you use the recurrence equations to rewrite T(n) in terms of T(x) where x < n and repeat the process until you reach the base case.)

(b) Draw a recursion tree to get a closed-form solution for T(n). Use the notation in the class (show the input size within each node, annotate it with the the non-recursive time, indicate the number of nodes at each level, the non-recursive time for each level near the right margin, and the grand total vertically below). Your tree must include at least three topmost levels including the root and two bottom-most levels including the leaf.

Added by Sherri N.

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