Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

levels. BFS can also be thought of as a traversal using a string and paint, with BFS
unrolling the string in a more conservative manner.
BFS starts at vertex s, which is at level 0 and defines the "anchor" for our string. In
the first round, we let out the string the length of one edge and we visit all the
vertices we can reach without unrolling the string any farther. In this case, we visit,
and paint as "visited," the vertices adjacent to the start vertex s—these vertices are
placed into level 1. In the second round, we unroll the string the length of two edges
and we visit all the new vertices we can reach without unrolling our string any
farther. These new vertices, which are adjacent to level 1 vertices and not
previously assigned to a level, are placed into level 2, and so on. The BFS traversal
terminates when every vertex has been visited.
Pseudo-code for a BFS starting at a vertex s is shown in Code Fragment 13.10. We
use auxiliary space to label edges, mark visited vertices, and store collections
associated with levels. That is, the collections L 0 , L 1 , L 2 , and so on, store the
vertices that are in level 0, level 1, level 2, and so on. These collections could, for
example, be implemented as queues. They also allow BFS to be nonrecursive.
Code Fragment 13.10: The BFS algorithm.
We illustrate a BFS traversal in Figure 13.7.
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