BFS和DFS

Depth-first search:

访问顺序： A, B, D, F, E, C, G.

Pseudocode

Input: A graph G and a vertex v of G

Output: A labeling of the edges in the connected component of v as discovery edges and back edges

1  procedure DFS(G,v):
2      label v as explored
3      for all edges e in G.adjacentEdges(v) do
4          if edge e is unexplored then
5              w ← G.adjacentVertex(v,e)
6              if vertex w is unexplored then
7                  label e as a discovery edge
8                  recursively call DFS(G,w)
9              else
10                 label e as a back edge

Breadth-first search

Algorithm

The algorithm uses a queue data structure to store intermediate results as it traverses the graph, as follows:

1. Enqueue the root node
2. Dequeue a node and examine it
   • If the element sought is found in this node, quit the search and return a result.
   • Otherwise enqueue any successors (the direct child nodes) that have not yet been discovered.
3. If the queue is empty, every node on the graph has been examined – quit the search and return "not found".
4. If the queue is not empty, repeat from Step 2.

Note: Using a stack instead of a queue would turn this algorithm into a depth-first search.

Pseudocode

Input: A graph G and a root v of G

1  procedure BFS(G,v):
2      create a queue Q
3      enqueue v onto Q
4      mark v
5      while Q is not empty:
6          t ← Q.dequeue()
7          if t is what we are looking for:
8              return t
9          for all edges e in G.adjacentEdges(t) do
12             u ← G.adjacentVertex(t,e)
13             if u is not marked:
14                  mark u
15                  enqueue u onto Q
16     return none