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.
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.
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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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 .
The -th level has leaves each with cost , so the total cost of the -th level is .
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