Difference between revisions of "TADM2E 5.12"
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(Solution of 5.12) |
(Undo revision 1145 by FuckyouMatt (talk)) |
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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) | ||
Latest revision as of 12:09, 2 August 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
