Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
11th Edition
ISBN: 9780134670942
Author: Y. Daniel Liang
Publisher: PEARSON
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Chapter 29, Problem 29.10PE
(Create a file for a graph) Modify Listing 29.3, TestWeightedGraph.java, to create a file for representing graph1. The file format is described in
12
0, 1, 807 | 0, 3, 1331 | 0, 5, 2097
1, 2, 381 | 1, 3, 1267
2, 3, 1015 | 2, 4, 1663 | 2, 10, 1435
3, 4, 599 | 3, 5, 1003
4, 5, 533 | 4, 7, 1260 | 4, 8, 864 | 4, 10, 496
5, 6, 983 | 5, 7, 787
6, 7, 214
7, 8, 888
8, 9, 661 | 8, 10, 781 | 8, 11, 810
9, 11, 1187
10, 11, 239
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By dragging statements from the left column to the right column below, give a proof by induction of the following statement:
an
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The correct proof will use 8 of the statements below.
Statements to choose from:
Note that a₁ =
9a0 + 8.
Now assume that P(n) is true for all n ≥ 0.
Your Proof: Put chosen statements in order in this
column and press the Submit Answers button.
Let P(n) be the predicate, "a = 9″ – 1".
απ = 90 − 1 =
Note that
Let P(n) be the predicate, "an
9" - 1 is a
solution to the recurrence relation an = 9an-1 +8
with ao = 0."
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Now assume that P(k + 1) is true.
Thus P(k) is true for all k.
Thus P(k+1) is true.
Then ak+1
=
9ak +8, so P(k + 1) is true.
= 1 − 1 = 0, as required.
Then = 9k — 1.
ak
Now assume that P(k) is true for an arbitrary
integer k ≥ 1.
By the recurrence relation, we have
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Then 9k+1 − 1 = 9(9*…
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Is this true? The first recorded use of the phrase "when pigs fly" in print is in a 1616 play by Ben Jonson called "The Devil is an Ass," in which a character says, "When pigs fly, good-night!!"
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Chapter 29 Solutions
Introduction to Java Programming and Data Structures, Comprehensive Version (11th Edition)
Ch. 29.2 - Prob. 29.2.1CPCh. 29.2 - Prob. 29.2.2CPCh. 29.3 - Prob. 29.3.1CPCh. 29.3 - Prob. 29.3.2CPCh. 29.3 - Show the output of the following code: public...Ch. 29.4 - Prob. 29.4.1CPCh. 29.4 - Prob. 29.4.2CPCh. 29.4 - Prob. 29.4.3CPCh. 29.4 - Prob. 29.4.4CPCh. 29.4 - Show the output of the following code: public...
Ch. 29.5 - Prob. 29.5.2CPCh. 29.5 - Prob. 29.5.3CPCh. 29.5 - Prob. 29.5.4CPCh. 29.5 - Prob. 29.5.5CPCh. 29.5 - Prob. 29.5.6CPCh. 29.5 - Show the output of the following code: public...Ch. 29.6 - Prob. 29.6.1CPCh. 29.6 - Prob. 29.6.2CPCh. 29.6 - Prob. 29.6.3CPCh. 29 - (Modify weight in the nine tails problem) In the...Ch. 29 - (Find a minimum spanning tree) Write a program...Ch. 29 - (Create a file for a graph) Modify Listing 29.3,...Ch. 29 - Prob. 29.11PECh. 29 - Prob. 29.12PE
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