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Traversal introduction
Many algorithms that involve graphs must involve some way to traverse the elements of a graph. The two simplest ways of traversal are depth-first search (DFS) and breadth-first search (BFS). The major difference here is the order in which nodes are traversed.
If we start from vertex 0 in the tree, in what order would you expect depth-first search to traverse the nodes? (There are multiple correct answers!)
0
/ \
1 2
/ \
3 4
Note that a single traversal step checks for already-visited nodes. So, if the path is 0 -> 1 -> 3, the path cannot become 0 -> 1 -> 3 -> 1.
What about starting from vertex 0 in this graph?
0 --- 1
| |
3 --- 2
What about this one?
0
/ \
1 5
/ \ \
2 3 6
\ / /
4 7
\ /
8
Formalizing the algorithm
Based on these examples, can we create a formal algorithm that takes a starting node, producing a valid traversal path for all three graphs?
An example for this graph:
0 --- 1
| |
3 --- 2
- Arguments: starting node
0 - Expected output: