Calculus: Early Transcendentals (2nd Edition)
2nd Edition
ISBN: 9780321947345
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
Publisher: PEARSON
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Chapter D2.2, Problem 23E
To determine
To find: The general solution of the differential equation
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Objective
Implement Bottom-Up Iterative MergeSort and analyze its efficiency compared to
recursive MergeSort. Unlike the recursive approach, which involves multiple function
calls and stack overhead, the bottom-up version sorts iteratively by merging small
subarrays first, reducing recursion depth and improving performance.
Task
1. Implement Bottom-Up Iterative MergeSort
о Start with single-element subarrays and iteratively merge them into larger
sorted sections.
Use a loop-based merging process instead of recursion.
○ Implement an efficient in-place merging strategy if possible.
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Compare execution time with recursive MergeSort on random, nearly
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Explain why the iterative version reduces function call overhead and when
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Code implementation with comments.
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A short report (1-2 pages) comparing performance.
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Given a shared data set, we allow multiple readers to read at the same time, and only one single writer can access the shared data at the same time. In the lecture slides, a solution is given. However, the problem is that the write cannot write forever, if there are always at least one reader.
How to ensure that the writer can eventually write? Propose your solution by using semaphores and implemented in Python
from threading import Thread, Semaphore
from time import sleep
from sys import stdout
class Reader(Thread):
def__init__(self, name):
self.n=name; Thread.__init__(self)
defrun(self):
globalnr, nw, dr, dw
whileTrue:
# ⟨await nw == 0 then nr += 1⟩
e.acquire()
ifnw>0:
#if nw > 0 or dw > 0 :
dr+=1; e.release(); r.acquire()
nr+=1
ifdr>0: dr-=1; r.release()
else: e.release()
# read data
stdout.write(self.n+' reading\n')
sleep(1)
# ⟨nr -= 1⟩
e.acquire()
nr-=1
ifnr==0anddw>0:
dw-=1 ; w.release()
else: e.release()
class Writer(Thread):
def__init__(self, name):…
Chapter D2 Solutions
Calculus: Early Transcendentals (2nd Edition)
Ch. D2.1 - Describe how to find the order of a differential...Ch. D2.1 - Prob. 2ECh. D2.1 - Prob. 3ECh. D2.1 - Give a general form of a second-order linear...Ch. D2.1 - Prob. 5ECh. D2.1 - Prob. 6ECh. D2.1 - Prob. 7ECh. D2.1 - Prob. 8ECh. D2.1 - Prob. 9ECh. D2.1 - Prob. 10E
Ch. D2.1 - Prob. 11ECh. D2.1 - Prob. 12ECh. D2.1 - Prob. 13ECh. D2.1 - Verifying solutions Verify by substitution that...Ch. D2.1 - Prob. 15ECh. D2.1 - Prob. 16ECh. D2.1 - Prob. 17ECh. D2.1 - Prob. 18ECh. D2.1 - Prob. 19ECh. D2.1 - Prob. 20ECh. D2.1 - Prob. 21ECh. D2.1 - Prob. 22ECh. D2.1 - Prob. 23ECh. D2.1 - Prob. 24ECh. D2.1 - Prob. 25ECh. D2.1 - Prob. 26ECh. D2.1 - Prob. 27ECh. D2.1 - Prob. 28ECh. D2.1 - Prob. 29ECh. D2.1 - Prob. 30ECh. D2.1 - Prob. 31ECh. D2.1 - Prob. 32ECh. D2.1 - Prob. 33ECh. D2.1 - Prob. 34ECh. D2.1 - Prob. 35ECh. D2.1 - Prob. 36ECh. D2.1 - Prob. 37ECh. D2.1 - Prob. 38ECh. D2.1 - Prob. 39ECh. D2.1 - Prob. 40ECh. D2.1 - Prob. 41ECh. D2.1 - Prob. 42ECh. D2.1 - Prob. 43ECh. D2.1 - Initial value problems Solve the following initial...Ch. D2.1 - Prob. 45ECh. D2.1 - Prob. 46ECh. D2.1 - Explain why or why not Determine whether the...Ch. D2.1 - Prob. 48ECh. D2.1 - Solution verification Verify by substitution that...Ch. D2.1 - Prob. 50ECh. D2.1 - Prob. 51ECh. D2.1 - Prob. 52ECh. D2.1 - Prob. 53ECh. D2.1 - Prob. 54ECh. D2.1 - Prob. 55ECh. D2.1 - Prob. 56ECh. D2.1 - Prob. 57ECh. D2.1 - Prob. 58ECh. D2.1 - Prob. 59ECh. D2.1 - Prob. 60ECh. D2.1 - Prob. 61ECh. D2.1 - Prob. 62ECh. D2.1 - Prob. 63ECh. D2.1 - Prob. 64ECh. D2.1 - Prob. 65ECh. D2.1 - Prob. 66ECh. D2.1 - Prob. 67ECh. D2.1 - Prob. 68ECh. D2.1 - Prob. 69ECh. D2.1 - Reduction of order Suppose you are solving a...Ch. D2.2 - Prob. 1ECh. D2.2 - Prob. 2ECh. D2.2 - Prob. 3ECh. D2.2 - Prob. 4ECh. D2.2 - Prob. 5ECh. D2.2 - Prob. 6ECh. D2.2 - Prob. 7ECh. D2.2 - Give the trial solution used to solve a...Ch. D2.2 - Prob. 9ECh. D2.2 - Prob. 10ECh. D2.2 - General solutions with distinct real roots Find...Ch. D2.2 - Prob. 12ECh. D2.2 - Prob. 13ECh. D2.2 - Prob. 14ECh. D2.2 - Initial value problems with distinct real roots...Ch. D2.2 - Prob. 16ECh. D2.2 - Prob. 17ECh. D2.2 - Prob. 18ECh. D2.2 - Prob. 19ECh. D2.2 - Prob. 20ECh. D2.2 - Prob. 21ECh. D2.2 - Prob. 22ECh. D2.2 - Prob. 23ECh. D2.2 - Prob. 24ECh. D2.2 - Prob. 25ECh. D2.2 - Prob. 26ECh. D2.2 - Prob. 27ECh. D2.2 - Prob. 28ECh. D2.2 - Prob. 29ECh. D2.2 - Prob. 30ECh. D2.2 - Prob. 31ECh. D2.2 - Prob. 32ECh. D2.2 - Prob. 33ECh. D2.2 - Prob. 34ECh. D2.2 - Initial value problems with Cauchy-Euler equations...Ch. D2.2 - Prob. 36ECh. D2.2 - Prob. 37ECh. D2.2 - Initial value problems with Cauchy-Euler equations...Ch. D2.2 - Prob. 39ECh. D2.2 - Prob. 42ECh. D2.2 - Prob. 43ECh. D2.2 - Prob. 44ECh. D2.2 - Prob. 45ECh. D2.2 - Prob. 46ECh. D2.2 - Prob. 47ECh. D2.2 - Prob. 48ECh. D2.2 - Prob. 49ECh. D2.2 - Prob. 50ECh. D2.2 - Prob. 51ECh. D2.2 - Cauchy-Euler equation with repeated roots It can...Ch. D2.2 - Prob. 53ECh. D2.2 - Prob. 54ECh. D2.2 - Prob. 55ECh. D2.2 - Prob. 56ECh. D2.2 - Prob. 57ECh. D2.2 - Prob. 58ECh. D2.2 - Prob. 59ECh. D2.2 - Prob. 60ECh. D2.2 - Prob. 61ECh. D2.2 - Cauchy-Euler equation with repeated roots One of...Ch. D2.2 - Prob. 63ECh. D2.2 - Prob. 64ECh. D2.2 - Prob. 65ECh. D2.2 - Prob. 66ECh. D2.3 - Explain how to find the general solution of the...Ch. D2.3 - Prob. 2ECh. D2.3 - Prob. 3ECh. D2.3 - Prob. 4ECh. D2.3 - Prob. 5ECh. D2.3 - Prob. 6ECh. D2.3 - Prob. 7ECh. D2.3 - Prob. 8ECh. D2.3 - Prob. 9ECh. D2.3 - Prob. 10ECh. D2.3 - Prob. 11ECh. D2.3 - Prob. 12ECh. D2.3 - Prob. 13ECh. D2.3 - Undetermined coefficients with exponentials Find a...Ch. D2.3 - Prob. 15ECh. D2.3 - Prob. 16ECh. D2.3 - Prob. 17ECh. D2.3 - Prob. 18ECh. D2.3 - Prob. 19ECh. D2.3 - Prob. 20ECh. D2.3 - Prob. 21ECh. D2.3 - Prob. 22ECh. D2.3 - Prob. 23ECh. D2.3 - Prob. 24ECh. D2.3 - Prob. 25ECh. D2.3 - Prob. 26ECh. D2.3 - Prob. 27ECh. D2.3 - Prob. 28ECh. D2.3 - Prob. 29ECh. D2.3 - Prob. 30ECh. D2.3 - Prob. 31ECh. D2.3 - Prob. 32ECh. D2.3 - Prob. 33ECh. D2.3 - Prob. 34ECh. D2.3 - Prob. 35ECh. D2.3 - Prob. 36ECh. D2.3 - Prob. 37ECh. D2.3 - Initial value problems Find the general solution...Ch. D2.3 - Prob. 39ECh. D2.3 - Prob. 40ECh. D2.3 - Prob. 41ECh. D2.3 - Prob. 42ECh. D2.3 - Prob. 43ECh. D2.3 - Prob. 44ECh. D2.3 - Prob. 45ECh. D2.3 - Prob. 46ECh. D2.3 - Prob. 47ECh. D2.3 - Prob. 48ECh. D2.3 - Prob. 49ECh. D2.3 - Prob. 50ECh. D2.3 - Prob. 51ECh. D2.3 - Variation of parameters Finding a particular...Ch. D2.4 - Explain the meaning of the words damped, undamped,...Ch. D2.4 - In the models discussed in this section, under...Ch. D2.4 - Prob. 3ECh. D2.4 - Prob. 4ECh. D2.4 - Prob. 5ECh. D2.4 - Prob. 6ECh. D2.4 - Prob. 7ECh. D2.4 - Prob. 8ECh. D2.4 - Prob. 9ECh. D2.4 - Free undamped oscillations Solve the initial value...Ch. D2.4 - Prob. 11ECh. D2.4 - Prob. 12ECh. D2.4 - Prob. 13ECh. D2.4 - Prob. 14ECh. D2.4 - Prob. 15ECh. D2.4 - Prob. 16ECh. D2.4 - Free damped oscillations Solve the initial value...Ch. D2.4 - Free damped oscillations Solve the initial value...Ch. D2.4 - Designing a shock absorber A shock absorber must...Ch. D2.4 - Designing a suspension system A spring in a...Ch. D2.4 - Forced damped oscillations 21.A 1-kg block hangs...Ch. D2.4 - Forced damped oscillations 22.A 20-kg block hangs...Ch. D2.4 - Prob. 23ECh. D2.4 - Prob. 24ECh. D2.4 - Prob. 25ECh. D2.4 - Prob. 26ECh. D2.4 - Prob. 27ECh. D2.4 - LCR circuits 28.The circuit in Exercise 27 (10-ohm...Ch. D2.4 - Prob. 29ECh. D2.4 - Prob. 30ECh. D2.4 - Prob. 31ECh. D2.4 - LCR circuits 32.Find the charge on the capacitor...Ch. D2.4 - Explain why or why not Determine whether the...Ch. D2.4 - Prob. 34ECh. D2.4 - Prob. 35ECh. D2.4 - Prob. 36ECh. D2.4 - Prob. 37ECh. D2.4 - Prob. 38ECh. D2.4 - Prob. 39ECh. D2.4 - Prob. 41ECh. D2.4 - Prob. 42ECh. D2.4 - Prob. 43ECh. D2.4 - Prob. 44ECh. D2.4 - Applications 4346.Horizontal oscillators The...Ch. D2.4 - Prob. 46ECh. D2.4 - Prob. 47ECh. D2.4 - Prob. 48ECh. D2.4 - Prob. 49ECh. D2.4 - Prob. 51ECh. D2.4 - Prob. 52ECh. D2.5 - Prob. 1ECh. D2.5 - Prob. 2ECh. D2.5 - Prob. 3ECh. D2.5 - Prob. 4ECh. D2.5 - Prob. 5ECh. D2.5 - Prob. 6ECh. D2.5 - Prob. 7ECh. D2.5 - Prob. 8ECh. D2.5 - Gain and phase lag functions Consider the...Ch. D2.5 - Prob. 10ECh. D2.5 - Prob. 11ECh. D2.5 - Solutions to oscillator equations Consider the...Ch. D2.5 - Prob. 13ECh. D2.5 - Solutions to oscillator equations Consider the...Ch. D2.5 - Prob. 15ECh. D2.5 - Prob. 16ECh. D2.5 - Prob. 17ECh. D2.5 - Prob. 18ECh. D2.5 - Analyzing circuit equations Consider the circuit...Ch. D2.5 - Prob. 20ECh. D2.5 - Prob. 21ECh. D2.5 - Prob. 22ECh. D2.5 - Prob. 23ECh. D2.5 - A high-pass filter Consider the LCR circuit shown...Ch. D2.5 - High-pass filters Consider the high-pass filter...Ch. D2.5 - Prob. 26ECh. D2.5 - High-pass filters Consider the high-pass filter...Ch. D2.5 - Prob. 28ECh. D2 - Prob. 1RECh. D2 - Prob. 2RECh. D2 - Prob. 3RECh. D2 - Prob. 4RECh. D2 - Solving homogeneous equations Find the general...Ch. D2 - Prob. 6RECh. D2 - Prob. 7RECh. D2 - Prob. 8RECh. D2 - Prob. 9RECh. D2 - Prob. 10RECh. D2 - Prob. 11RECh. D2 - Prob. 12RECh. D2 - Prob. 13RECh. D2 - Prob. 14RECh. D2 - Prob. 15RECh. D2 - Prob. 16RECh. D2 - Prob. 17RECh. D2 - Prob. 18RECh. D2 - Prob. 19RECh. D2 - Prob. 20RECh. D2 - Prob. 21RECh. D2 - Forced undamped oscillations A 4-kg block hangs on...Ch. D2 - Free damped oscillations A 0.2-kg block hangs on a...
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