Suppose you have an algorithm that operates on a set of data with n elements. If therecurrence formula that computes the time requirement for the algorithm is given byT(n)=(2T(n − 1) + D(cif n > 1if n = 1where D and C are constants, which of the following gives the order of complexity of thealgorithm?a. nb. n²c. n³d. 2¹e. None of the answers.

Time Complexity:Time complexity is a measure of the computational efficiency of an algorithm, describing the amount of time an algorithm takes to complete as a function of the size of the input to the algorithm. It provides an estimation of the upper bound on the running time of an algorithm in terms of the input size.Solution:The given recurrence relation is:Let's analyze the recurrence relation to find the order of complexity.Since is a constant, let The term inside the parentheses is a geometric series with a common ratio of terms:Now, let's look at the dominant term in this expression as n approaches infinity.The dominant term is and it grows exponentially with n. Therefore, the order of complexity of the algorithm is So, the correct answer is: (d). Conclusion:The conclusion is that the order of complexity of the algorithm, as determined by the given recurrence relation, is exponential, specifically This means that the time requirement for the algorithm grows exponentially with the size of the input data. As n increases, the time complexity grows very rapidly, making the algorithm less efficient for larger input sizes.

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Suppose you have an algorithm that operates on a set of data with n elements. If the recurrence formula that computes the time requirement for the algorithm is given by (2T(n-1) + D T(n)= (c if n > 1 if n = 1 where D and C are constants, which of the following gives the order of complexity of the algorithm? a. n b. n² c. n³ d. 2¹ e. None of the answers.

Suppose you have an algorithm that operates on a set of data with n elements. If the recurrence formula that computes the time requirement for the algorithm is given by (2T(n-1) + D T(n)= (c if n > 1 if n = 1 where D and C are constants, which of the following gives the order of complexity of the algorithm? a. n b. n² c. n³ d. 2¹ e. None of the answers.

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

Suppose you have an algorithm that operates on a set of data with n elements. If the
recurrence formula that computes the time requirement for the algorithm is given by
T(n)
=
(2T(n − 1) + D
(c
if n > 1
if n = 1
where D and C are constants, which of the following gives the order of complexity of the
algorithm?
a. n
b. n²
c. n³
d. 2¹
e. None of the answers.

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