# Difference between revisions of "TADM2E 5.12"

From Algorithm Wiki

m (Adding signature to solution) |
m (Translation fixes) |
||

Line 5: | Line 5: | ||

Extensions: | Extensions: | ||

BFS stops at a depth of 2 | BFS stops at a depth of 2 | ||

− | - Depth 1-adjacent v in the original | + | - Depth 1-adjacent v in the original graph |

− | - Depth 2-adjacent v in the | + | - Depth 2-adjacent v in the graph square |

BFS uses the vertex statuses unopened, open, and processed | BFS uses the vertex statuses unopened, open, and processed | ||

- Open and processed vertexes are not added to the queue again | - Open and processed vertexes are not added to the queue again | ||

Line 14: | Line 14: | ||

- In a graph of 1 vertex, when adding 1 vertex, 1+ edge is added | - In a graph of 1 vertex, when adding 1 vertex, 1+ edge is added | ||

- In a complete graph of n vertices, the number of edges is determined by the Handshaking lemma | - In a complete graph of n vertices, the number of edges is determined by the Handshaking lemma | ||

− | - - For a complete | + | - - For a complete directed graph |E| = n * (n - 1) edges |

− | - - For a complete | + | - - For a complete not directed graph |E| = n * (n - 1) / 2 edges</pre> |

--[[User:Bkarpov96|Bkarpov96]] ([[User talk:Bkarpov96|talk]]) 07:48, 30 June 2020 (UTC) | --[[User:Bkarpov96|Bkarpov96]] ([[User talk:Bkarpov96|talk]]) 07:48, 30 June 2020 (UTC) |

## Revision as of 07:55, 30 June 2020

Algorithm: BFS of each vertex v ∈ V, O(|V| * (|V| + |E|)) Saving adjacent vertexes to an adjacency matrix or adjacency list O(1) Extensions: BFS stops at a depth of 2 - Depth 1-adjacent v in the original graph - Depth 2-adjacent v in the graph square BFS uses the vertex statuses unopened, open, and processed - Open and processed vertexes are not added to the queue again Time complexity of the algorithm O (|V| * (|V| + |E|)) = O((|V|)^2 + |V * E|)) = O(|V * E|) - The number of edges does not grow slower than the number of vertexes - In a graph of 1 vertex, when adding 1 vertex, 1+ edge is added - In a complete graph of n vertices, the number of edges is determined by the Handshaking lemma - - For a complete directed graph |E| = n * (n - 1) edges - - For a complete not directed graph |E| = n * (n - 1) / 2 edges