Using BFS for topological sort

Question

Can Breadth first Search be used for finding topological sorting of vertices and strongly connected components in a graph?

If yes how to do that? and If not why not?

we generally use Depth first search in these problems but What will be the problem if I try to implement using BFS?

Will code like this work?

def top_bfs(start_node):
    queue = [start_node]
    stack = []
    while not queue.empty():
        node = queue.dequeue()
        if not node.visited:
            node.visited = True
            stack.push(node)
            for c in node.children:
                queue.enqueue(c) 
    stack.reverse()
    return stack

Answer 1

Yes, you can do topological sorting using BFS. Actually I remembered once my teacher told me that if the problem can be solved by BFS, never choose to solve it by DFS. Because the logic for BFS is simpler than DFS, most of the time you will always want a straightforward solution to a problem.

You need to start with nodes of which the indegree is 0, meaning no other nodes direct to them. Be sure to add these nodes to your result first.You can use a HashMap to map every node with its indegree, and a queue which is very commonly seen in BFS to assist your traversal. When you poll a node from the queue, the indegree of its neighbors need to be decreased by 1, this is like delete the node from the graph and delete the edge between the node and its neighbors. Every time you come across nodes with 0 indegree, offer them to the queue for checking their neighbors later and add them to the result.

public ArrayList<DirectedGraphNode> topSort(ArrayList<DirectedGraphNode> graph) {

  ArrayList<DirectedGraphNode> result = new ArrayList<>();
    if (graph == null || graph.size() == 0) {
      return result;
    }
  Map<DirectedGraphNode, Integer> indegree = new HashMap<DirectedGraphNode, Integer>();
  Queue<DirectedGraphNode> queue = new LinkedList<DirectedGraphNode>();

//mapping node to its indegree to the HashMap, however these nodes
//have to be directed to by one other node, nodes whose indegree == 0
//would not be mapped.
  for (DirectedGraphNode DAGNode : graph){
      for (DirectedGraphNode nei : DAGNode.neighbors){
          if(indegree.containsKey(nei)){
              indegree.put(nei, indegree.get(nei) + 1);
          } else {
              indegree.put(nei, 1);
          }
      }
  }


//find all nodes with indegree == 0. They should be at starting positon in the result
  for (DirectedGraphNode GraphNode : graph) {
      if (!indegree.containsKey(GraphNode)){
          queue.offer(GraphNode);
          result.add(GraphNode);
      }
  }


//everytime we poll out a node from the queue, it means we delete it from the 
//graph, we will minus its neighbors indegree by one, this is the same meaning 
//as we delete the edge from the node to its neighbors.
  while (!queue.isEmpty()) {
      DirectedGraphNode temp = queue.poll();
      for (DirectedGraphNode neighbor : temp.neighbors){
          indegree.put(neighbor, indegree.get(neighbor) - 1);
          if (indegree.get(neighbor) == 0){
              result.add(neighbor);
              queue.offer(neighbor);
          }
      }
  }
  return result;
}

Answer 2

The fact that they have similar names doesn't make them similar methods.

DFS is typically implemented with LIFO (a stack if you will) - last in first out.

BFS typically implemented with FIFO (a queue if you will) - first in first out.

You can walk a graph in any way you want, and eventually come out with a topological order of its nodes. But if you want to do it efficiently, then DFS is the best option, as the topological order of the nodes essentially reflects their depth in the graph (well, "dependency-depth" to be more accurate).