Depth First Search

• The idea of breadth first search is to explore the graph in "layers".
• The idea of deapth first search is more like exploring a maze.
  • Start at a given point
  • Explore along a path until
    • You reach a dead end.
    • You loop back upon yourself.
  • When this happens, backtrack and explore a new path.
• Do we know any tools that might help us with backtracking?
  • Answer
    A stack.
• Can you design this algorithm?
• They provide two versions
  • Algorithm 1
    • Show Algorithm

      DFS(G,s)
      
       For all v in V
          v.status = unexplored
       Endfor
       s.status = discovered
       s.parent = null
       DFSVisit(G,s)
      
      
      DFSVisit(G,v) 
      
       For each u adjacent to v
          If u.status = unexplored
             u.status = discovered
             u.parent = v
             DFSVisit(u)
          EndIF
       EndFor 
       v.status = finished 
       

    • In some versions, the last part of DFS is
    • Show Algorithm

      
       For each v in V
          If v.status = unexplored
             v.status = discovered
             v.parent = null
             DFSVisit(G,v)
          EndIf
       EndFor 
       

  • A second version
    • Show Algorithm

      DFS(G,s)
      // S is a stack
      
       For each v in V
          v.status = unexplored
       EndFor
       s.status = discovered
       s.parent = null
       S.push(s)
       While S is not empty
          v = S.Pop
          v.status = finished
          For each u adjacent to v
             if u.status = unexplored
                u.status = discovered
                u.parent = v
                S.push(u)
          EndFor
       EndWhile