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.

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

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Concept explainers

Concept of Randomized Approximation Algorithms

Randomized algorithms are algorithms that use random numbers to determine what to do next at any point in their logic. This means that it uses randomization for operation in the logic. Due to this randomness, the time and space complexity of the standard algorithm is reduced.

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.
=

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