notebook/notes/algorithms/bfs.md

title	TARGET DECK	FILE TAGS	tags
Breadth-First Search	Obsidian::STEM	algorithm data_structure::graph	bfs graph

Overview

Bread-first search operates on a graph G = \langle V, E \rangle and a source vertex s.

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%%ANKI Basic What is BFS an acronym for? Back: Breadth-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 Breadth-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 Cloze The {1:source} of breadth-first {2:search} is the {2:root} of the breadth-first {1:tree}. 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 BFS 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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%%ANKI Basic With respect to breadth-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 With respect to breadth-first trees, what does the parent 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 With respect to breadth-first trees, the predecessor of a node is also known as what? Back: The parent of the node. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic With respect to breadth-first trees, the parent of a node is also known as what? Back: The predecessor of the node. 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 BFS vertices? Back: A queue. 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 BFS? 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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%%ANKI Basic What basic graph algorithm is the following a demonstration of? ! Back: Breadth-first search. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic In BFS, what happens to the nodes found within the internal queue? Back: Undiscovered nodes adjacent to those in the queue are enqueued. 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 BFS or DFS is used to find shortest paths? Back: BFS. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic When can BFS not be used to find shortest paths? Back: When the graph in question has differently weighted edges. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic Which weighted graphs can BFS be used on to find shortest paths? Back: Graphs with equally weighted edges. Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic Which standard graph representation has worst-case BFS 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 BFS? 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).

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%%ANKI Basic Which standard graph representation has worst-case BFS 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).

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%%ANKI Basic Given graph \langle V, E \rangle with adjacency-matrix representation, what is the worst-case run time of BFS? Back: O(\lvert V \rvert^2) Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).

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%%ANKI Basic Why is BFS 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).

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%%ANKI Basic Why is BFS 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).