# 1.7: List of Data Structures

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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.
$$\texttt{BinaryHeap}$$ $$O(1)$$ $$O(\log \mathtt{n})$$A § 10.1
$$\texttt{MeldableHeap}$$ $$O(1)$$ $$O(\log \mathtt{n})$$E § 10.2 Figure $$\PageIndex{1}$$: The dependencies between chapters in this book.

This page titled 1.7: List of Data Structures is shared under a CC BY license and was authored, remixed, and/or curated by Pat Morin (Athabasca University Press) .