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04/05/09
22:43:28
1
29
CS 61B:
Lecture 29
Monday, April 6, 2009
GRAPHS (continued)
======
Breadthfirst search (BFS) is a little more complicated than depthfirst
search, because it’s not naturally recursive.
We use a queue so that vertices
are visited in order according to their distance from the starting vertex.
public void bfs(Vertex u) {
u.visit(null);
// Do some unspecified thing to u
u.visited = true;
// Mark the vertex u visited
q = new Queue();
// New queue.
..
q.enqueue(u);
// .
..initially containing u
while (q is not empty) {
v = q.dequeue();
for (each vertex w such that (v, w) is an edge in E) {
if (!w.visited) {
w.visit(v);
// Do some unspecified thing to w
w.visited = true;
// Mark the vertex w visited
q.enqueue(w);
}
}
}
}
Notice that when we visit a vertex,
public class Vertex {
we pass the edge’s origin vertex
protected Vertex parent;
as a parameter.
This allows us to
protected int depth;
do a computation such as finding
the distance of the vertex from
public void visit(Vertex origin) {
the starting vertex, or finding
this.parent = origin;
the shortest path between them.
if (origin == null) {
The visit() method at right
this.depth = 0;
accomplishes both these tasks.
} else {
this.depth = origin.depth + 1;
}
}
}
When an edge (v, w) is traversed to visit a Vertex w, the depth of w is set to
the depth of v plus one, and v is set to be the _parent_ of w.
The sequence of figures below shows BFS running on the city adjacency graph
(Albany, Kensington, Emeryville, Berkeley, Oakland, Piedmont) from last
lecture, starting from Albany.
A "V" is currently visited; a digit shows the
depth of a vertex that is marked visited; a "*" is a vertex which we try to
visit but discover has already been visited.
Underneath each figure of the
graph, I depict the queue and the current value of the variable "v" in bfs().
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