A certain recursive algorithm takes an input list of n elements. Divides the list into yn sub-lists, each with /n elements. Recursively solves each of these yn smaller sub- instances. Then spends an additional 0(n) time to combine the solutions of these sub- instances to obtain the solution of the main instance. As a base case, if the size of the input list is at most a specified positive constant, then the algorithm solves such a small instance directly in 0(1) time. a) Express the recurrence relation that governs T(n), the time complexity of this algorithm. b) Derive the solution to this recurrence relation: T(n) = 0(?). Mention which methods you used to derive your solution.

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
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A certain recursive algorithm takes an input list of n elements. Divides the list into Vn
sub-lists, each with yn elements. Recursively solves each of these yn smaller sub-
instances. Then spends an additional 0(n) time to combine the solutions of these sub-
instances to obtain the solution of the main instance.
As a base case, if the size of the input list is at most a specified positive constant, then
the algorithm solves such a small instance directly in 0(1) time.
a) Express the recurrence relation that governs T(n), the time complexity of this
algorithm.
b) Derive the solution to this recurrence relation: T(n) = 0(?).
Mention which methods you used to derive your solution.
Transcribed Image Text:A certain recursive algorithm takes an input list of n elements. Divides the list into Vn sub-lists, each with yn elements. Recursively solves each of these yn smaller sub- instances. Then spends an additional 0(n) time to combine the solutions of these sub- instances to obtain the solution of the main instance. As a base case, if the size of the input list is at most a specified positive constant, then the algorithm solves such a small instance directly in 0(1) time. a) Express the recurrence relation that governs T(n), the time complexity of this algorithm. b) Derive the solution to this recurrence relation: T(n) = 0(?). Mention which methods you used to derive your solution.
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