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Problem 8: Divide and Conquer Recurrences Consider the recurrence that naturally arises in some divide-and-conquer algorithms:   T(1) = 1,   T(n) = 4T(n/2) + n for n > 1    [a] Explain what the initial condition and the various parts of this recurrence mean in the context of the analysis of algorithms. [b] Use the Master Theorem to determine the order of magnitude of T(n). [c] Using the methods of our course, derive a closed-form formula for T(n). [d] For the case n = 2, test your formula for T(n) against the original recurrence.

Problem 8: Divide and Conquer Recurrences Consider the recurrence that naturally arises in some divide-and-conquer algorithms:   T(1) = 1,   T(n) = 4T(n/2) + n for n > 1    [a] Explain what the initial condition and the various parts of this recurrence mean in the context of the analysis of algorithms. [b] Use the Master Theorem to determine the order of magnitude of T(n). [c] Using the methods of our course, derive a closed-form formula for T(n). [d] For the case n = 2, test your formula for T(n) against the original recurrence.

Database System Concepts
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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Problem 8: Divide and Conquer Recurrences

Consider the recurrence that naturally arises in some divide-and-conquer algorithms:

 

T(1) = 1,   T(n) = 4T(n/2) + n for n > 1

  

[a] Explain what the initial condition and the various parts of this recurrence mean in the context of the analysis of algorithms.

[b] Use the Master Theorem to determine the order of magnitude of T(n).

[c] Using the methods of our course, derive a closed-form formula for T(n).

[d] For the case n = 2, test your formula for T(n) against the original recurrence.

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