1.7: List of Data Structures
- Page ID
- 8434
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Tables \(\PageIndex{1}\) and \(\PageIndex{2}\) summarize the performance of data structures in this book that implement each of the interfaces, List, USet, and SSet, described in Section 1.2. Figure \(\PageIndex{1}\) shows the dependencies between various chapters in this book. A dashed arrow indicates only a weak dependency, in which only a small part of the chapter depends on a previous chapter or only the main results of the previous chapter.
Table \(\PageIndex{1}\): Summary of List and USet implementations.
\(\texttt{List}\) implementations
| \(\mathtt{get(i)}/\mathtt{set(i,x)}\) | \(\mathtt{add(i,x)}/\mathtt{remove(i)}\) | ||
|---|---|---|---|
| \(\texttt{ArrayStack}\) | \(O(1)\) | \(O(1+\mathtt{n}-\mathtt{i})\)A | § 2.1 |
| \(\texttt{ArrayDeque}\) | \(O(1)\) | \(O(1+\min\{\mathtt{i},\mathtt{n}-\mathtt{i}\})\)A | § 2.4 |
| \(\texttt{DualArrayDeque}\) | \(O(1)\) | \(O(1+\min\{\mathtt{i},\mathtt{n}-\mathtt{i}\})\)A | § 2.5 |
| \(\texttt{RootishArrayStack}\) | \(O(1)\) | \(O(1+\mathtt{n}-\mathtt{i})\)A | § 2.6 |
| \(\texttt{DLList}\) | \(O(1+\min\{\mathtt{i},\mathtt{n}-\mathtt{i}\})\) | \(O(1+\min\{\mathtt{i},\mathtt{n}-\mathtt{i}\})\) | § 3.2 |
| \(\texttt{SEList}\) | \(O(1+\min\{\mathtt{i},\mathtt{n}-\mathtt{i}\}/\mathtt{b})\) | \(O(\mathtt{b}+\min\{\mathtt{i},\mathtt{n}-\mathtt{i}\}/\mathtt{b})\)A | § 3.3 |
| \(\texttt{SkiplistList}\) | \(O(\log \mathtt{n})\)E | \(O(\log \mathtt{n})\)E | § 4.3 |
\(\texttt{USet}\) implementations
| \(\mathtt{find(x)}\) | \(\mathtt{add(x)}/\mathtt{remove(x)}\) | ||
|---|---|---|---|
| A Denotes an amortized running time. E Denotes an expected running time. |
|||
| \(\texttt{ChainedHashTable}\) | \(O(1)\)E | \(O(1)\)A,E | § 5.1 |
| \(\texttt{LinearHashTable}\) | \(O(1)\)E | \(O(1)\)A,E | § 5.2 |
Table \(\PageIndex{2}\): Summary of SSet and priority Queue implementations.
\(\texttt{SSet}\) implementations
| \(\mathtt{find(x)}\) | \(\mathtt{add(x)}/\mathtt{remove(x)}\) | ||
|---|---|---|---|
| \(\texttt{SkiplistSSet}\) | \(O(\log \mathtt{n})\)E | \(O(\log \mathtt{n})\)E | § 4.2 |
| \(\texttt{Treap}\) | \(O(\log \mathtt{n})\)E | \(O(\log \mathtt{n})\)E | § 7.2 |
| \(\texttt{ScapegoatTree}\) | \(O(\log \mathtt{n})\) | \(O(\log \mathtt{n})\)A | § 8.1 |
| \(\texttt{RedBlackTree}\) | \(O(\log \mathtt{n})\) | \(O(\log \mathtt{n})\) | § 9.2 |
| \(\texttt{BinaryTrie}\)I | \(O(\mathtt{w})\) | \(O(\mathtt{w})\) | § 13.1 |
| \(\texttt{XFastTrie}\)I | \(O(\log \mathtt{w})\)A,E | \(O(\mathtt{w})\)A,E | § 13.2 |
| \(\texttt{YFastTrie}\)I | \(O(\log \mathtt{w})\)A,E | \(O(\log \mathtt{w})\)A,E | § 13.3 |
| \(\texttt{BTree}\) | \(O(\log \mathtt{n})\) | \(O(B+\log \mathtt{n})\)A | § 14.2 |
| \(\texttt{BTree}\)X | \(O(\log_B \mathtt{n})\) | \(O(\log_B \mathtt{n})\) | § 14.2 |
(Priority) \(\texttt{Queue}\) implementations
| \(\mathtt{findMin()}\) | \(\mathtt{add(x)}/\mathtt{remove()}\) | ||
|---|---|---|---|
| I This structure can only store \(\texttt{w}\)-bit integer data. X This denotes the running time in the external-memory model; see Chapter 14. |
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| \(\texttt{BinaryHeap}\) | \(O(1)\) | \(O(\log \mathtt{n})\)A | § 10.1 |
| \(\texttt{MeldableHeap}\) | \(O(1)\) | \(O(\log \mathtt{n})\)E | § 10.2 |
