Depth first search

• In this search, we explore "deep" instead of wide
• Again, we are going to color nodes
  • White, not yet visited
  • Grey, visited but not yet done (discovered but not explored)
  • Black, finished
• We will add other fields as well
  • parent - a pointer to the parent or predicesor in the DFS graph
  • d - an integer representing when the node was discovered
  • f - an integer representing when the node was finished.
• Algorithm

  • DFS(G)
    (1)  foreach vertex u in V[G]
    (2)     u.color = WHITE
    (3)     u.parent = NIL
    (4)  time =  1
    (5)  foreach vertex u in V[G]
    (6)     if u.color = white
    (7)        DFS-VISIT(u,G)
          

  • DFS-VISIT(u,G)
    (1)  u.color = GREY
    (2)  u.depth = time++
    (3)  foreach v Adjacient to u 
    (4)     if v.color = WHITE
    (5)        v.parent = u
    (6)        DFS-VISIT(v,G)
    (7)  u.color = BLACK
    (8)  u.finish = time++
          

• Performance
  • We color each node grey exactaly once (black too )
  • We visit each edge twice, one time each edge is colored grey
  • O(|V| + |E|)
• Edges
  • All edges in a graph can be classified as follows
  • A Tree edge is an edge in the DFS tree
  • A Back edge is an edge connecting a descendent to an ancestor
  • A Forward edge connects an ancestor to a descendant
  • A Cross edge connects non related nodes in the DFS tree