(a) Write a linear time ( 6(n) ) divide and conquer algorithm to calculate x", that is x is raised to the power n. Assume x and n are both >=0. (b) Analyze the time complexity of your algorithm in the worst-case by first writing its recurrence relation. (c) Can you improve your algorithm in Part a to accomplish the result in O(log n) time complexity (we still look for a divide and conquer algorithm). If yes, write the corresponding algorithm, write the recurrence relation for its time complexity and analyze it. If no, justify your answer.

(a) Write a linear time ( 6(n) ) divide and conquer algorithm to calculate x", that is x is raised to the power n. Assume x and n are both >=0. (b) Analyze the time complexity of your algorithm in the worst-case by first writing its recurrence relation. (c) Can you improve your algorithm in Part a to accomplish the result in O(log n) time complexity (we still look for a divide and conquer algorithm). If yes, write the corresponding algorithm, write the recurrence relation for its time complexity and analyze it. If no, justify your answer.

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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Question

100%

(a) Write a linear time ( 0(n) ) divide and conquer algorithm to calculate x", that is x is
raised to the power n. Assume x and n are both >=0.
(b) Analyze the time complexity of your algorithm in the worst-case by first writing its
recurrence relation.
(c) Can you improve your algorithm in Part a to accomplish the result in O(log n) time
complexity (we still look for a divide and conquer algorithm). If yes, write the corresponding
algorithm, write the recurrence relation for its time complexity and analyze it. If no, justify
your answer.

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