深度优先图遍历

Question

I'm trying to print a depth-first traversal. I have the following code which continues to give me a seg fault. It seems to be occurring when I try to print the last vertex in the graph. The first traversal I do starting at vertex 'A', works as it should. But when I try to do a depth-first print starting from D, I get the seg fault. Here is my source code:

Here is my original source code:

void wdigraph::depth_first(int u) const {

  bool found = false;

  vector<bool> visited;             // create a boolean vector
  for(int i =0; i < size; i++)      // the size of the graph
    visited.push_back(false);       // to mark when a node has been visited

  stack<int> depth_first;           // used to hold vertices that have been visited
  visited[u] = true;                // mark as visited
  cout << label[u];                 // print first vertex
  depth_first.push(u);              // put first vertex on stack

  while(!all_visited(visited)) {    // continue until all vertices have been visited
    found = false;

    for(unsigned i = 0; i < visited.size() && !found; i++) {
      if(adj_matrix[u][i] != 0 && !visited[i]) {  // found next vertex
        cout << "->" << label[i];   // print vertex
        visited[i] = true;          // mark vertex as visited
        depth_first.push(i);        // push vertx onto stack
        found = true;               // set found = true to end for loop
        u = i;
      }//endif
    }//endfor  

    if(found == false) {            // no available neighbors
      u = depth_first.top();        // get top of stack
      depth_first.pop();            // pop from stack
    }//endif
  }//endwhile 

  cout << '\n';
}

void wdigraph::print_graph() const {
  cout << '\n';
  cout << "No of Nodes = " << size << endl;

  cout << "\nAdjacency Matrix\n" << endl;

  cout << "  |";
  for(int i = 0; i < size; i++)
    cout << "  " << label[i];

  cout << '\n';

  cout << "--|";
  for(int i = 0; i < size; i++)
    cout << "---";
  cout << '\n';

  for(int i = 0; i < size; i++) {
    cout << label[i] << " |";

    for(int j = 0; j < size; j++) {
      if(adj_matrix[i][j] != 0)
        cout << " " << setw(2) << right << adj_matrix[i][j];
      else
        cout << "  -";
    }//endjfor

      cout << '\n';

      if(i != size-1)
        cout << "  |" << endl;
  }//endifor

  cout << '\n';
}
bool all_visited(vector<bool> &v) {
  for(unsigned i = 0; i < v.size(); i++)
    if(v[i] == false)
      return false;

  return true;
}

This is the header file and the constructor:

// definition of weighted digraph

#define NO_NODES   1    // default size for no of nodes in digraph
#define LINK_PROB  0.25 // prob of having direct link between nodes
#define MAX_WEIGHT 10   // max weight factor for links
class wdigraph {
public:
    wdigraph ( int = NO_NODES );            // default constructor
    ~wdigraph ( ) { };                      // destructor
    int get_size ( ) const { return size; } // returns size of digraph

    void depth_first ( int ) const;// traverses graph using depth-first search
    void print_graph ( ) const;    // prints adjacency matrix of digraph

private:
    int size;                               // size of digraph
    vector < char > label;                  // node labels
    vector < vector < int > > adj_matrix;   // adjacency matrix
};

// default class constructor

wdigraph :: wdigraph ( int n ) : size ( n )
{
    // allocate dynamic memory

    label = vector < char > ( size );
    adj_matrix = vector < vector < int > > ( size );
    for ( int i = 0; i < size; i++ )
        adj_matrix [ i ] = vector < int > ( size );

    // assign labels to each node

    label [ 0 ] = 'A';
    for ( int i = 1; i < size; i++ )
        label [ i ] = label [ i - 1 ] + 1;

    // determine weights for links between nodes randomly
    // and build adjacency matrix

    srand ( 1 );
    for ( int i = 0; i < size; i++ ) {
        adj_matrix [ i ] [ i ] = 0;
        bool flag = false;
        for ( int j = 0; j < size; j++ ) {
            if ( j == i ) continue;
            double r = ( double ) rand ( ) / RAND_MAX;
            adj_matrix [ i ] [ j ] =
                ( r <= LINK_PROB ) ? rand ( ) % MAX_WEIGHT + 1 : 0;
            if ( adj_matrix [ i ] [ j ] > 0 ) flag = true;
        }

        // if node is not connected to any other node, then
        // connect this node to random node

        if ( size > 1 && !flag ) {
            int k; while ( ( k = rand ( ) % size ) == i ) ;
            adj_matrix [ i ] [ k ] = rand ( ) % MAX_WEIGHT + 1;
        }
    }
}

Here is the main routine:

#define M  3   // print every M-th node's path when traversing
#define N2 5   // number of nodes in second graph
#define N3 20  // number of nodes in third graph


void proc_graph(wdigraph&);       // function declaration

int main() {
  // create three weighted digraphs
  wdigraph graph1(NO_NODES);
  wdigraph graph2(N2);
  wdigraph graph3(N3);

  //proc_graph(graph1);   // print first graph
  proc_graph(graph2);   // print first graph
  //proc_graph(graph3);   // print first graph

  return 0;
}

void proc_graph(wdigraph &g) {
  cout << '\n';
  cout << "A Weighted Digraph" << endl;    // print header
  cout << "__________________" << endl;    // print header underline

  g.print_graph();                         // print graph

  cout << "Paths by Depth-First Search" << endl;
  for(int i = 0; i < g.get_size(); i += M)
    g.depth_first(i);
}

This is the output that I am getting. The graph shows the weight of each edge. A '-' means there is no edge.

A Weighted Digraph
__________________

No of Nodes = 5

Adjacency Matrix

  |  A  B  C  D  E
--|---------------
A |  -  -  -  6  -
  |
B |  -  -  8  -  -
  |
C |  7  -  -  -  -
  |
D |  7  9 10  -  1
  |
E |  4  - 10  -  -

Paths by Depth-First Search
A->D->B->C->E
Segmentation fault (core dumped)

If I remove the u = i code from the for loop, then my program works fine. Here is my output when I try to print the third graph. Notice, my traversal is not traveling correctly.

Answer 1

So I figured out my problem using the following algorithm. Hope this will help anyone having the same problem.

push current onto stack
mark as visited
print current
while (stack is not empty) {
  current = stack top
  of N neighbors of current, find first that hasnt been visited
    if such neighbor exists
      add to stack
      mark as visited
      print
    if no neighbor exists
      pop from stack
}