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Graph traversal algorithms: Depth First Search

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• Caveat in graph traversal
  • Unlike trees, a graph can have cycles:

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  • We must maintain some visitation information, otherwise we will loop forever

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• Visitation information
  • visited[]:

    boolean visited[]; // denote whether a node has been visited

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• Depth First Search:    go deep (before going wide)
  • Depth first search:

    Visit an arbitrary node x Mark node x as visited Visit each unvisited node that is incident to x

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  • Java code:

    public void dfs(int i) { int j; visited[i] = true; // Mark node as "visited" printNode(i); for ( j = 0; j < NNodes; j++ ) { if ( adjMatrix[i][j] > 0 && !visited[j] ) { dfs(j); // Visit node } } }

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  • Example: dfs(0)

    dfs(0): dfs(0) → dfs(1) dfs(1) → dfs(0) (because node 0 is "visited");   dfs(1) → dfs(7) dfs(7) → dfs(1);   dfs(7) → dfs(2) dfs(2) → dfs(3) dfs(3) → dfs(0);   dfs(3) → dfs(2);   dfs(3) → dfs(4) dfs(4) → dfs(3);   dfs(4) → dfs(8) dfs(8) → dfs(0);   dfs(8) → dfs(4);   return to dfs(4) return to dfs(3) return to dfs(2) dfs(2) → dfs(3);   dfs(2) → dfs(5) dfs(5) → dfs(2);   dfs(5) → dfs(6) dfs(6) → dfs(5);   return to dfs(5) return to dfs(2) return to dfs(7) return to dfs(1) return to dfs(0) DONE

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  • Example Program: (Demo above code)                                                
    • The DFS Prog file: click here
    • Test program file: click here

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• Alternative implementation: use a stack
  • We can avoid using recursion by pushing active nodes onto a stack

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  • Active node

    Active node = a node where we still have to visit all its neighbor nodes

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  • Psuedo code:

    /* =================================================== Dept First Traversal of a graph without recursion =================================================== */ dfs() { pick a node x.... push(x); visited[x] = true; while ( stack != empty ) { n = node at stack top (peek only); nextNode = an unvisited node adjacent to n; if ( nextNode exists ) { visited[nextNode] = true; push(nextNode); // Process this node first } else { /* ----------------------------------------------------- Node at top of stack has no unvisited neighbor nodes ----------------------------------------------------- */ pop(); // Move on to the next node on the stack } } }

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  • Example Program: (Demo above code)                                                
    • The DFS without using recursion Prog file: click here
    • Test program file: click here