# Depth-first search in Python

I wrote this DFS in Python and I was wondering if it correct. Somehow it seems too simple to me.

Each node is a class with attributes:

• visited: Boolean

• sons: list of nodes linked to the current node.

This code should work both for directed and undirected graphs.

def DFS(node):

node.visited = True

if node == None:
return

// perform some operation on the node
do_something(node)

to_visit = [son in node.sons if not son.visited]
for son in to_visit:
DFS(node)

• Is this pseudo-code? This bit won't compile in Python: [son in node.sons if !son.visited] Jan 26, 2015 at 6:49

DFS should keep track of all the nodes visited. Not the node.

The node only properties is it self, and it's children.

graph = {'A': set(['B', 'C']),
'B': set(['A', 'D', 'E']),
'C': set(['A', 'F']),
'D': set(['B']),
'E': set(['B', 'F']),
'F': set(['C', 'E'])}

def dfs(graph, start):
visited, stack = set(), [start]
while stack:
vertex = stack.pop()
if vertex not in visited:
stack.extend(graph[vertex] - visited)
return visited

dfs(graph, 'A') # {'E', 'D', 'F', 'A', 'C', 'B'}


As you can see DFS is called just once and it keeps track of visted nodes all the way, it will use pop(-1) so it will Depth-search, you could either change to pop(0), so it would Breadth-First Search. It's the same concept, the only difference is which node is visited in which order.

Your implementation will have some problems if the graph is too deep, because it could raise a Maximum recursion depth exceeded.

• Unless I'm missing something, if you only ever add unvisited nodes to the stack, you shouldn't need the if vertex not in visited check (presuming a node cannot have two links to the same child). Which you want would depend on whether set subtraction or contains is faster (I would guess the latter).
– sapi
Jan 26, 2015 at 9:47
• Makes sense. Seems redundant. The code ain't mine tho, the link provide may have some info on that. Jan 26, 2015 at 10:02
• @sapi A node would be pushed multiple times to stack if it can be reached from multiple nodes that happen to be visited before it. Jan 26, 2015 at 11:05
• @JanneKarila Good point; I was picturing a top-down tree (where that won't occur for a DFS), but of course that's a very specific case.
– sapi
Jan 26, 2015 at 12:57
• You are using set to keep track of visit order but set() is not guaranteed to give correct order. visited should be a list. Sep 1, 2017 at 8:53

Having visited as a property of a node feels a bit like a leaky abstraction because it embeds the needs of a particular tree operation into the more general abstraction of graphs and nodes.

To me, a node is a data structure that has some pointers to zero or more children and perhaps stores a value - depending on the semantics of a particular graph. Consider an acyclic graph with all values at stored at leaves versus various cyclic graphs with values stored at each node.

In the cyclic graph case depth first search is not directly applicable until an appropriate starting node has been selected and though the concept of visited may make sense for some cyclic graph algorithms, it wouldn't in the case of other algorithms such as Dijkstra’s shortest path.

To separate concerns, a depth first search algorithm might create it's own object consisting of a generalized node object and a visited field...or use any of many other data structure approaches.

Without isolation algorithms operating on the graph must walk it a second time to clear the visited field. If there is concurrency, then graph algorithms must lock the entire data structure and the depth first search should have transaction semantics.

• Depth first search is actually applicable for cyclic graphs. Jan 26, 2015 at 0:28
• @ILoveCoding Not productively before some meaningful selection of starting node. For utility some sort of appropriate acyclic element must be found or created via transformation. Jan 26, 2015 at 1:02

Checking if node == None makes no sense, immediately after having set node.visited = True. It will either crash or never match.

In any case, if mode is None is the standard way to check for None, and storing the visited flag in the graph modes themselves ruins the graph for future traversals.

Nope, it is not correct. The problem is that the to_visit list can change after visiting a child of the currect node(for example, on a full graph with 3 vertices your implementation will visit the third node twice(if you run the depth-first search from the first vertex)). However, it is easy to fix it. You can just iterate over all children of the current node and run a depth-first from a child if it has not been visited yet(using an if statement inside the for loop).