Recursion Trees Use the recursion tree method to determine the asymptotic upper bound of T(n). T(n) satisfies the recurrence T(n) = 2T(n-1) + n, and T(0)=0.

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Recursion Trees

Use the recursion tree method to determine the asymptotic upper bound of T(n).

T(n) satisfies the recurrence T(n) = 2T(n-1) + n, and T(0)=0.

Expert Solution
Step 1

The subproblem size for a node at depth i is .

Thus, the tree has n levels () and  leaves.

The total cost over all nodes at depth , for , is 2i.

The -th level has leaves each with cost , so the total cost of the -th level is .

 

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