In each of the problems below compute the average case time complexity (or expected time) of the given code. State your answer using asymptotic notation. Show your work for this problem by stating what the different cases are, the probability of each case, and how long each case takes. Also show the calculation of the expected time. a) def foo (n): #randomly choose a number between 0 and n-1 in constant time k np.random.randint (n) if k np. sqrt (n): for i in range(n): print (i) print('Never mind...') else: b) def bogosearch (numbers, target): """search by randomly guessing. numbers is an array of n numbers""" n len (numbers) while True: #randomly choose a number between 0 and n-1 in constant time guess = np.random.randint (n) if numbers [guess] == target: return guess In this part, you may assume that the numbers are distinct and that the target is in the array. Hint: if 0 < b < 1, then Σ1p.bp-1 = (1-b)².

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
icon
Related questions
Question
100%
In each of the problems below compute the average case time complexity (or expected time) of the given
code. State your answer using asymptotic notation. Show your work for this problem by stating what the
different cases are, the probability of each case, and how long each case takes. Also show the calculation of
the expected time.
a) def foo (n):
#randomly choose a number between 0 and n-1 in constant time
k np.random.randint (n)
if k np. sqrt (n):
for i in range(n):
print (i)
print('Never mind...')
else:
b) def bogosearch (numbers, target):
"""search by randomly guessing. numbers is an array of n numbers"""
n = len (numbers)
while True:
#randomly choose a number between 0 and n-1 in constant time
guess = np.random.randint (n)
if numbers [guess]
== target:
return guess
In this part, you may assume that the numbers are distinct and that the target is in the array.
Hint: if 0 < b < 1, then 1p.bp-1
(1-b)².
=
Transcribed Image Text:In each of the problems below compute the average case time complexity (or expected time) of the given code. State your answer using asymptotic notation. Show your work for this problem by stating what the different cases are, the probability of each case, and how long each case takes. Also show the calculation of the expected time. a) def foo (n): #randomly choose a number between 0 and n-1 in constant time k np.random.randint (n) if k np. sqrt (n): for i in range(n): print (i) print('Never mind...') else: b) def bogosearch (numbers, target): """search by randomly guessing. numbers is an array of n numbers""" n = len (numbers) while True: #randomly choose a number between 0 and n-1 in constant time guess = np.random.randint (n) if numbers [guess] == target: return guess In this part, you may assume that the numbers are distinct and that the target is in the array. Hint: if 0 < b < 1, then 1p.bp-1 (1-b)². =
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Concept of Randomized Approximation Algorithm
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Database System Concepts
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education