4.3 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Depth-First Search | Obsidian::STEM | algorithm data_structure::graph |
|
Overview
Depth-first search operates on a graph G = \langle V, E \rangle and a source vertex s.
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%%ANKI Basic What is DFS an acronym for? Back: Depth-first search. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Cloze Depth-first search is characterized by a graph and a {source vertex}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic Which of undirected and directed graphs is DFS applicable to? Back: Both. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Basic
With respect to depth-first trees, what does the predecessor of a node N refer to?
Back: The node from which N was discovered.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic What ADT is typically used to manage the set of most recently discovered DFS vertices? Back: A stack. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Cloze A {1:queue} is to {2:BFS} whereas a {2:stack} is to {1:DFS}. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI Basic Which vertices are not discovered during a graph DFS? Back: Those not reachable from the source vertex. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Basic
What basic graph algorithm is the following a demonstration of?
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Back: Depth-first search.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Basic
Which standard graph representation has worst-case DFS running time of O(\lvert V \rvert + \lvert E \rvert)?
Back: The adjacency-list representation.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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%%ANKI
Basic
Given graph \langle V, E \rangle with adjacency-list representation, what is the worst-case run time of DFS?
Back: O(\lvert V \rvert + \lvert E \rvert)
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
END%%
%%ANKI
Basic
Which standard graph representation has worst-case DFS running time of O(\lvert V \rvert^2)?
Back: The adjacency-matrix representation.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
END%%
%%ANKI
Basic
Given graph \langle V, E \rangle with adjacency-matrix representation, what is the worst-case run time of DFS?
Back: O(\lvert V \rvert^2)
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
END%%
%%ANKI
Basic
Why is DFS of an adjacency-list representation O(\lvert V \rvert + \lvert E \rvert)?
Back: For each vertex being analyzed, we examine all of its adjacent vertices.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
END%%
%%ANKI
Basic
Why is DFS of an adjacency-matrix representation O(\lvert V \rvert^2)?
Back: For each vertex being analyzed, we must examine \lvert V \rvert entries for adjacent vertices.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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Bibliography
- Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).