4. ALGORITHM FindSomething(A[0..n-1]) // Input: An array A[0..n-1] of real numbers > 0 if n = 1 return A[0] else val1 FindSomething(A[0.. n-2]) if val1 <= A[n-1] return val1 else return A[n-1] a) What does the algorithm do? b) Assume that the basic operations are the comparisons. Construct a recurrence relation C(n) that gives the number of times the basic operation is executed for an input of size n. Clearly state the initial condition. c) Solve the recurrence relation C(n) using the Master Theorem (if applicable) or back substitution. Show all of the steps. d) What is the basic time efficiency of this algorithm? Use Θ notation
4. ALGORITHM FindSomething(A[0..n-1]) // Input: An array A[0..n-1] of real numbers > 0 if n = 1 return A[0] else val1 FindSomething(A[0.. n-2]) if val1 <= A[n-1] return val1 else return A[n-1] a) What does the algorithm do? b) Assume that the basic operations are the comparisons. Construct a recurrence relation C(n) that gives the number of times the basic operation is executed for an input of size n. Clearly state the initial condition. c) Solve the recurrence relation C(n) using the Master Theorem (if applicable) or back substitution. Show all of the steps. d) What is the basic time efficiency of this algorithm? Use Θ notation
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
4.
// Input: An array A[0..n-1] of real numbers > 0
if n = 1
return A[0]
else
val1 FindSomething(A[0.. n-2])
if val1 <= A[n-1]
return val1
else
return A[n-1]
a) What does the algorithm do?
b) Assume that the basic operations are the comparisons. Construct a
recurrence relation C(n) that gives the number of times the basic operation is
executed for an input of size n. Clearly state the initial condition.
c) Solve the recurrence relation C(n) using the Master Theorem (if applicable) or
back substitution. Show all of the steps.
d) What is the basic time efficiency of this algorithm? Use Θ notation.
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