# Difference between revisions of "TADM2E 5.12"

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(Solution of 5.12) |
m (Adding signature to solution) |
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- - For a complete orgaf |E| = n * (n - 1) edges | - - For a complete orgaf |E| = n * (n - 1) edges | ||

- - For a complete neorgaph |E| = n * (n - 1) / 2 edges</pre> | - - For a complete neorgaph |E| = n * (n - 1) / 2 edges</pre> | ||

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

## Revision as of 07:48, 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 orgaf - Depth 2-adjacent v in the orgaf 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 orgaf |E| = n * (n - 1) edges - - For a complete neorgaph |E| = n * (n - 1) / 2 edges