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- Depth first search(DFS) is a generalization of preorder traversal.
- Preorder traversal Depth First Search Algorithm Assignment Help ie, visit root, visit left subtree, visit right subtree
| DFS(G) // take a graph of the Depth First Search algo is 1: each vertex (u E V[G]) //initialize all vertices as follows 2: do colour[u] <- grey 3: pi[u] <- NIL// initialize all vertices to having no parent vertex 4: tm <- 0 // Zero out time 5: for each vertex (u E V[ G ] //initialize all vertices as follows 6: do if colour[ u ] = 'grey'' 7: then, depth_first_serch_visit( u ) depth_first_serch_visit( u ) 1: colour[ u ] <- white 2: tm <- (tm + 1) //tm = time 3: P[ u ] tm 4: for each v E Adj[ u ]=> Explore edge(u, v) 5: do if colour[ v ] = gray 6: then pi[ v ] <- u 7: DFS_VISIT( v ) 8: colour[ u ] BLACK => blacken u; it is finished 9: f[ u ]: tm <- (tm + 1) |
Example: Find the shortest sequence of dfs on the given graph, The vertices of the depth first search sequence is Q, R, S, T, U, V, W, X, Y, Z. where the initial state is ‘Q’ and the desired goal state is ‘W’, show the successive values of open and closed and the traversed path.
| Iteration # | x | Open | Closed |
| 0 | - | [ Q ] | [ ] |
| 1 | Q | [ R S T] | [A] |
| 2 | R | [U V S T] | [R Q] |
| 3 | U | [X Y V ST] | [U R Q] |
| 4 | X | [Y V S T] | [X U R Q] |
| 5 | Y | [V S T] | [Y X U R Q] |
| 6 | V | [Z S T] | [V Y X U R Q] |
| 7 | Z | [S T] | [Z V Y X U R Q] |
| 8 | S | [W T] | [S Z V Y X U R Q] |
| 9 | W | W IS THE GOAL | |
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