notebook/notes/algorithms/bfs.md

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

## Overview

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

![[bfs.gif]]

%%ANKI
Basic
What is BFS an acronym for?
Back: **B**readth-**f**irst **s**earch.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
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END%%

%%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).
<!--ID: 1727042295717-->
END%%

%%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).
<!--ID: 1727042295723-->
END%%

%%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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END%%

%%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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END%%

%%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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END%%

%%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).
<!--ID: 1727044035958-->
END%%

%%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).
<!--ID: 1727044035963-->
END%%

%%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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END%%

%%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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END%%

%%ANKI
Basic
What basic graph algorithm is the following a demonstration of?
![[bfs.gif]]
Back: Breadth-first search.
Reference: Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).
<!--ID: 1727044035969-->
END%%

%%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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END%%

%%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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END%%

%%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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END%%

%%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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END%%

%%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).
<!--ID: 1727044035989-->
END%%

%%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).
<!--ID: 1727044035983-->
END%%

%%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).
<!--ID: 1727357400678-->
END%%

%%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).
<!--ID: 1727044035986-->
END%%

%%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).
<!--ID: 1727044184060-->
END%%

%%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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END%%

## Bibliography

* Thomas H. Cormen et al., Introduction to Algorithms, Fourth edition (Cambridge, Massachusett: The MIT Press, 2022).