Data Structures and Algorithms in Java
6th Edition
ISBN: 9781118771334
Author: Michael T. Goodrich
Publisher: WILEY
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Chapter 4, Problem 4R
Program Plan Intro
Log-log scale:
This plot is a two-dimensional graph which contains the numerical data on horizontal and vertical axes. The equation
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The question describes a function S(k) which is defined as the sum of the positive divisors of a positive integer k, minus k itself. The function S(1) is defined as 1, and for any positive integer k greater than 1, S(k) is calculated as S(k) = σ(k) - k, where σ(k) is the sum of all positive divisors of k.
Some examples of S(k) are given:
S(1) = 1
S(2) = 1
S(3) = 1
S(4) = 3
S(5) = 1
S(6) = 6
S(7) = 1
S(8) = 7
S(9) = 4
The question then introduces a recursive sequence a_n with the following rules:
a_1 = 12
For n ≥ 2, a_n = S(a_(n-1))
Part (a) of the question asks to calculate the values of a_2, a_3, a_4, a_5, a_6, a_7, and a_8 for the sequence.
Part (b) modifies the sequence to start with a_1 = k, where k is any positive integer, and the same recursion formula applies: for n ≥ 2, a_n = S(a_(n-1)). The question notes that for many choices of k, the sequence a_n will eventually reach and remain at 1, but this is not always the case. It asks to find, with an explanation, two specific…
Given g = {(1,c),(2,a),(3,d)}, a function from X = {1,2,3} to Y = {a,b,c,d}, and f = {(a,r),(b,p),(c,δ),(d,r)}, a function from Y to Z = {p, β, r, δ}, write f o g as a set of ordered pairs.
For the given tabulating problem, solve for the needed:
Note: This problem was quoted from:
An Introduction to Matlab
David F. Gri_ths
formerly of Department of
Mathematics, The University of
Dundee, Dundee DD1 4HN
Scotland, UK
Exercise 14.1 Tabulate the functions
y = (x² + 3) sin πx²
and
z =sin? wæ/(x^2+3)
for x = 0,0.2,..., 10. Hence, tabulate the func-
tion
(x² + 3) sin 7x² sin² π.χ
(x−²+3)
Plot a graph of w over the range 0 ≤ x ≤ 10.
W=
- Write a computer algorithm (with python) for tabulating the resulting numbers.
- Write a computer algorithm (with matlab) for tabulating the resulting numbers.
- Verify the code results with hand calculations and show it as real table.
Chapter 4 Solutions
Data Structures and Algorithms in Java
Ch. 4 - Prob. 1RCh. 4 - The number of operations executed by algorithms A...Ch. 4 - The number of operations executed by algorithms A...Ch. 4 - Prob. 4RCh. 4 - Prob. 5RCh. 4 - Prob. 6RCh. 4 - Prob. 7RCh. 4 - Prob. 8RCh. 4 - Prob. 9RCh. 4 - Prob. 10R
Ch. 4 - Prob. 11RCh. 4 - Prob. 12RCh. 4 - Prob. 13RCh. 4 - Prob. 14RCh. 4 - Prob. 15RCh. 4 - Prob. 16RCh. 4 - Prob. 17RCh. 4 - Prob. 18RCh. 4 - Prob. 19RCh. 4 - Prob. 20RCh. 4 - Prob. 21RCh. 4 - Prob. 22RCh. 4 - Show that 2n+1 is O(2n).Ch. 4 - Prob. 24RCh. 4 - Prob. 25RCh. 4 - Prob. 26RCh. 4 - Prob. 27RCh. 4 - Prob. 28RCh. 4 - Prob. 29RCh. 4 - Prob. 30RCh. 4 - Prob. 31RCh. 4 - Prob. 32RCh. 4 - Prob. 33RCh. 4 - Prob. 34RCh. 4 - Prob. 35CCh. 4 - Prob. 36CCh. 4 - Prob. 37CCh. 4 - Prob. 38CCh. 4 - Prob. 39CCh. 4 - Prob. 40CCh. 4 - Prob. 41CCh. 4 - Prob. 42CCh. 4 - Prob. 43CCh. 4 - Draw a visual justification of Proposition 4.3...Ch. 4 - Prob. 45CCh. 4 - Prob. 46CCh. 4 - Communication security is extremely important in...Ch. 4 - Al says he can prove that all sheep in a flock are...Ch. 4 - Consider the following justification that the...Ch. 4 - Consider the Fibonacci function, F(n) (see...Ch. 4 - Prob. 51CCh. 4 - Prob. 52CCh. 4 - Prob. 53CCh. 4 - Prob. 54CCh. 4 - An evil king has n bottles of wine, and a spy has...Ch. 4 - Prob. 56CCh. 4 - Prob. 57CCh. 4 - Prob. 58CCh. 4 - Prob. 59CCh. 4 - Prob. 60PCh. 4 - Prob. 61PCh. 4 - Perform an experimental analysis to test the...Ch. 4 - Prob. 63P
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