Graphs/Breadth First Traversal
From charlesreid1
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
