Graphs/Breadth First Traversal: Difference between revisions
From charlesreid1
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The fact that the BFS tree yields shortest paths is a natural consequence of how the BFS process works. | The fact that the BFS tree yields shortest paths is a natural consequence of how the BFS process works. | ||
==Pseudocode== | |||
<pre> | |||
def bfs(g, s, discovered): | |||
discovered = empty map | |||
create new queue | |||
queue.add(s) | |||
while queue is not empty: | |||
u = queue.pop() | |||
for e in incident_edges(u): | |||
v = opposite_edge(u, e) | |||
if v not in discovered: | |||
// add (v,e) to discovered | |||
discovered[v] = e | |||
queue.add(v) | |||
</pre> | |||
=Related= | =Related= | ||
Revision as of 11:23, 9 September 2017
Also see BFS
Notes
What BFS Gets Us
Breadth-first search is important because it gets us the shortest path (the path with the fewest number of edges) from a vertex u to a vertex v. To state this more rigorously, a path in a breadth-first search tree rooted at vertex u to any other vertex v is guaranteed to be the shortest path from u to v (where shortest path denotes number of edges).
The fact that the BFS tree yields shortest paths is a natural consequence of how the BFS process works.
Pseudocode
def bfs(g, s, discovered): discovered = empty map create new queue queue.add(s) while queue is not empty: u = queue.pop() for e in incident_edges(u): v = opposite_edge(u, e) if v not in discovered: // add (v,e) to discovered discovered[v] = e queue.add(v)
Related
Graphs:
- Graphs#Graph Traversals
- Graphs/Depth First Traversal
- Graphs/Breadth First Traversal
- Graphs/Euler Tour
- Graphs/Euler Circuit
Traversals on trees:
Breadth-first search and traversal on trees:
Depth-first search and traversal on trees:
OOP design patterns:
Flags
