Depth First Search

• A companion to Breadth first search.

• DFS(G = (V,E))
  
   for each vertex $u \in V$
      u.color = unexplored
      u.parent = null
   time = 0
   for each vertex $u \in V$
      if u.color = unexplored
        DFS-VISIT(G,u)
  
  DFS-VISIT(G,u)
  
   time = time + 1
   u.start = time
   u.color = active
   for each $v \in u.Adj$ do
      if v.color = unexplored
          v.parent = u
          DFS-VISIT(G,v)
      u.color = done
      time = time + 1
      u.finish = time; 
  
      

• 
• Does the start and finish time about a node tell us anything?
  • Assume N1: $[s_1, f_1]$, N2: $[s_2, f_2]$
  • What if $s_1 \lt s_2 \lt f_2 \lt f_1$?
  • What if $s_1 \lt f_1 \lt s_2 \lt f_2$?