The Efficiency of Algorithms

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Chapter 3

• The Efficiency of Algorithms

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Figure 3.3 A Choice of Algorithms
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Figure 3.3.1 The Shuffle-Left Algorithm
Original Configuration
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit- First Copy
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit Second Copy
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit The Third Copy
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Figure 3.3.1 The Shuffle-Left Algorithm- The
Value of Legit After Last Item is Copied, the
Result is This
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit Reset the Right Hand Finger to
Start Again
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit Left and Right Hand Finger Move
Forward
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Figure 3.3.1 The Shuffle Left Algorithm The
Value of Legit Moving along, we pass over the
16.
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit-Seven Copies squeeze out O
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit - The 36, 42, 23, and 21 Are
Passed Over This is the Result
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Figure 3.3.1 The Shuffle-Left Algorithm The
Value of Legit Squeezing out Final 0 Gives This
Result
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Figure 3.3.1 The Shuffle Left Algorithm The
Value of Legit The Left Hand Finger is Pointing
At a Nonzero Element, so Another Advance of Both
Fingers Gives Us This Configuration.
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Figure 3.3.2 The Copy-Over Algorithm
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Figure 3.3.3 The Converging-Pointers Algorithm
The Value of Legit
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Figure 3.3.3 The Converging-Pointers Algorithm
The Value of Legit Legit and Right Are Reduced
by 1.
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Figure 3.3.3 The Converging-Pointers Algorithm
The Value of Legit The Value of Left Increases
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Figure 3.3.3 The Converging-Pointers Algorithm
The Value of Legit Position Right is Copied
Into Position Left
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Figure 3.3.3 The Converging-Pointers Algorithm
The Value of Legit Item at Position Left is
Still 0, Another Copy Takes Place
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Practice Problems - In the Data Cleanup Problem,
Suppose the Original Data Is Like This
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Figure 3.6 Values of Magnitude Work 2n
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Figure 3.7 Order of Magnitude - Work cn for
Various Values of c
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Figure 3.8 Order of Magnitude Growth of Work
cn for Various Values of c
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Figure 3.9 Order of Magnitude -Table of Calling
Information
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Figure 3.10 Order of Magnitude Work cn2 for
Various Values c
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Figure 3.11 The 0rder of Magnitude A
Comparison of n and n2
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Figure 3.12 Order of Magnitude For Large
Enough n, 0.25n2 Has Larger Values than 10n
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Figure 3.13 Order of Magnitude A Comparison of
Two Extreme T (n2) and T (n) Algorithms
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Using the Information in Figure 3.5 Fill in the
Above Table for the Number of Comparisons
required in the Sequential Search Algorithm
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Figure 3.14 Analysis of Algorithms Analysis of
Three Data Cleanup Algorithms
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Figure 3.16 Selection Sort Algorithms
Comparisons Required by Selection Sort
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Figure 3.17 Selection Sort Algorithms - An
Attempt to Exchange the Values at X and Y
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Figure 3.18 Selection Sort Algorithms
Exchanging the Values of X and Y
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Figure 3.21 Binary Search Values of n and lg n
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Figure 3.22 Binary Search A comparison of n
and lg n
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Figure 3.23 Summary Order-of-Magnitude Time
Efficiency Summary
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Figure 3.24 When Things Get Out of Hand Four
Connected Cities
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Figure 3.25 When Things Get Out of Hand
Hamiltonian Circuits Among All Paths from A in
Figure 3.24 with Four Links
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Figure 3.26 (a) When Things Get Out of Hand
Comparisons of lg n, n, n2, and 2n
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Figure 3.26 (b) When Things Get Out of Hand
Comparisons of lg n,n, n2, and 2n
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Figure 3.28 Approximation Problems A First-Fit
Solution to a Bin-Packing Problem
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Practice Problems Tree Shows All Paths with Two
Links That Begin At Node A
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Exercises Write the Data List that Results from
running the Shuffle-Left Algorithm to clean up
this Data
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Exercises A Linked List
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Exercises Draw a Linked List when Data Cleanup
is Performed on This Linked List