4.9: Exercises
- Page ID
- 21112
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The code for this chapter is in the ch13
directory of ThinkJavaCode
. See [Section 0.4] for instructions on how to download the repository. Before you start the exercises, we recommend that you compile and run the examples.
Exercise \(\PageIndex{1}\)
You can learn more about the sorting algorithms in this chapter, and others, at www.sorting-algorithms.com/. This site includes explanations of the algorithms, animations that show how they work, and analysis of their efficiency.
Exercise \(\PageIndex{2}\)
The goal of this exercise is to implement the shuffling algorithm from this chapter.
- In the repository for this book, you should find a file called Deck.java that contains the code in this chapter. Check that you can compile it in your environment.
- Add a
Deck
method calledrandomInt
that takes two integers,low
andhigh
, and returns a random integer betweenlow
andhigh
, including both. You can use thenextInt
provided byjava.util.Random
, which we saw in Section 8.7. But you should avoid creating aRandom
object every timerandomInt
is invoked. - Write a method called
swapCards
that takes two indexes and swaps the cards at the given locations. - Write a method called
shuffle
that uses the algorithm in Section 13.2.
Exercise \(\PageIndex{3}\)
The goal of this exercise is to implement the sorting algorithms from this chapter. Use the Deck.java file from the previous exercise (or create a new one from scratch).
- Write a method called
indexLowest
that uses thecompareCard
method to find the lowest card in a given range of the deck (fromlowIndex
tohighIndex
, including both). - Write a method called
selectionSort
that implements the selection sort algorithm in Section 13.3. - Using the pseudocode in Section 13.4, write the method called
merge
. The best way to test it is to build and shuffle a deck. Then usesubdeck
to form two small subdecks, and use selection sort to sort them. Then you can pass the two halves tomerge
to see if it works. - Write the simple version of
mergeSort
, the one that divides the deck in half, usesselectionSort
to sort the two halves, and usesmerge
to create a new, sorted deck. - Write a recursive version of
mergeSort
. Remember thatselectionSort
is a modifier andmergeSort
is a pure method, which means that they get invoked differently:deck.selectionSort(); // modifies an existing deck deck = deck.mergeSort(); // replaces old deck with new
Exercise \(\PageIndex{4}\)
The goal of this exercise is to practice top-down programming by implementing “insertion sort”. Read about insertion sort at www.sorting-algorithms.com/insertion-sort. Write a method named insertionSort
that implements this algorithm.
Exercise \(\PageIndex{5}\)
Write a toString
method for the Deck
class. It should return a single string that represents the cards in the deck. When it’s printed, this string should display the same results as the print
method in Section 13.1.
- Hint
-
You can use the
+
operator to concatenate strings, but it is not very efficient. Consider usingjava.lang.StringBuilder
; you can find the documentation by doing a web search for “Java StringBuilder”.