[algorithm] When is it practical to use Depth-First Search (DFS) vs Breadth-First Search (BFS)?

I understand the differences between DFS and BFS, but I'm interested to know when it's more practical to use one over the other?

Could anyone give any examples of how DFS would trump BFS and vice versa?

Depth-first Search

Depth-first searches are often used in simulations of games (and game-like situations in the real world). In a typical game you can choose one of several possible actions. Each choice leads to further choices, each of which leads to further choices, and so on into an ever-expanding tree-shaped graph of possibilities.

For example in games like Chess, tic-tac-toe when you are deciding what move to make, you can mentally imagine a move, then your opponent’s possible responses, then your responses, and so on. You can decide what to do by seeing which move leads to the best outcome.

Only some paths in a game tree lead to your win. Some lead to a win by your opponent, when you reach such an ending, you must back up, or backtrack, to a previous node and try a different path. In this way you explore the tree until you find a path with a successful conclusion. Then you make the first move along this path.

Breadth-first search

The breadth-first search has an interesting property: It first finds all the vertices that are one edge away from the starting point, then all the vertices that are two edges away, and so on. This is useful if you’re trying to find the shortest path from the starting vertex to a given vertex. You start a BFS, and when you find the specified vertex, you know the path you’ve traced so far is the shortest path to the node. If there were a shorter path, the BFS would have found it already.

Breadth-first search can be used for finding the neighbour nodes in peer to peer networks like BitTorrent, GPS systems to find nearby locations, social networking sites to find people in the specified distance and things like that.

Nice Explanation from http://www.programmerinterview.com/index.php/data-structures/dfs-vs-bfs/

An example of BFS

Here’s an example of what a BFS would look like. This is something like Level Order Tree Traversal where we will use QUEUE with ITERATIVE approach (Mostly RECURSION will end up with DFS). The numbers represent the order in which the nodes are accessed in a BFS:

In a depth first search, you start at the root, and follow one of the branches of the tree as far as possible until either the node you are looking for is found or you hit a leaf node ( a node with no children). If you hit a leaf node, then you continue the search at the nearest ancestor with unexplored children.

An example of DFS

Here’s an example of what a DFS would look like. I think post order traversal in binary tree will start work from the Leaf level first. The numbers represent the order in which the nodes are accessed in a DFS:

Differences between DFS and BFS

Comparing BFS and DFS, the big advantage of DFS is that it has much lower memory requirements than BFS, because it’s not necessary to store all of the child pointers at each level. Depending on the data and what you are looking for, either DFS or BFS could be advantageous.

For example, given a family tree if one were looking for someone on the tree who’s still alive, then it would be safe to assume that person would be on the bottom of the tree. This means that a BFS would take a very long time to reach that last level. A DFS, however, would find the goal faster. But, if one were looking for a family member who died a very long time ago, then that person would be closer to the top of the tree. Then, a BFS would usually be faster than a DFS. So, the advantages of either vary depending on the data and what you’re looking for.

One more example is Facebook; Suggestion on Friends of Friends. We need immediate friends for suggestion where we can use BFS. May be finding the shortest path or detecting the cycle (using recursion) we can use DFS.

The following is a comprehensive answer to what you are asking.

In simple terms:

Breadth First Search (BFS) algorithm, from its name "Breadth", discovers all the neighbours of a node through the out edges of the node then it discovers the unvisited neighbours of the previously mentioned neighbours through their out edges and so forth, till all the nodes reachable from the origional source are visited (we can continue and take another origional source if there are remaining unvisited nodes and so forth). That's why it can be used to find the shortest path (if there is any) from a node (origional source) to another node if the weights of the edges are uniform.

Depth First Search (DFS) algorithm, from its name "Depth", discovers the unvisited neighbours of the most recently discovered node x through its out edges. If there is no unvisited neighbour from the node x, the algorithm backtracks to discover the unvisited neighbours of the node (through its out edges) from which node x was discovered, and so forth, till all the nodes reachable from the origional source are visited (we can continue and take another origional source if there are remaining unvisited nodes and so forth).

Both BFS and DFS can be incomplete. For example if the branching factor of a node is infinite, or very big for the resources (memory) to support (e.g. when storing the nodes to be discovered next), then BFS is not complete even though the searched key can be at a distance of few edges from the origional source. This infinite branching factor can be because of infinite choices (neighbouring nodes) from a given node to discover. If the depth is infinite, or very big for the resources (memory) to support (e.g. when storing the nodes to be discovered next), then DFS is not complete even though the searched key can be the third neighbor of the origional source. This infinite depth can be because of a situation where there is, for every node the algorithm discovers, at least a new choice (neighbouring node) that is unvisited before.

Therefore, we can conclude when to use the BFS and DFS. Suppose we are dealing with a manageable limited branching factor and a manageable limited depth. If the searched node is shallow i.e. reachable after some edges from the origional source, then it is better to use BFS. On the other hand, if the searched node is deep i.e. reachable after a lot of edges from the origional source, then it is better to use DFS.

For example, in a social network if we want to search for people who have similar interests of a specific person, we can apply BFS from this person as an origional source, because mostly these people will be his direct friends or friends of friends i.e. one or two edges far. On the other hand, if we want to search for people who have completely different interests of a specific person, we can apply DFS from this person as an origional source, because mostly these people will be very far from him i.e. friend of friend of friend.... i.e. too many edges far.

Applications of BFS and DFS can vary also because of the mechanism of searching in each one. For example, we can use either BFS (assuming the branching factor is manageable) or DFS (assuming the depth is manageable) when we just want to check the reachability from one node to another having no information where that node can be. Also both of them can solve same tasks like topological sorting of a graph (if it has). BFS can be used to find the shortest path, with unit weight edges, from a node (origional source) to another. Whereas, DFS can be used to exhaust all the choices because of its nature of going in depth, like discovering the longest path between two nodes in an acyclic graph. Also DFS, can be used for cycle detection in a graph.

In the end if we have infinite depth and infinite branching factor, we can use Iterative Deepening Search (IDS).

Breadth First Search is generally the best approach when the depth of the tree can vary, and you only need to search part of the tree for a solution. For example, finding the shortest path from a starting value to a final value is a good place to use BFS.

Depth First Search is commonly used when you need to search the entire tree. It's easier to implement (using recursion) than BFS, and requires less state: While BFS requires you store the entire 'frontier', DFS only requires you store the list of parent nodes of the current element.

This is a good example to demonstrate that BFS is better than DFS in certain case. https://leetcode.com/problems/01-matrix/

When correctly implemented, both solutions should visit cells that have farther distance than the current cell +1. But DFS is inefficient and repeatedly visited the same cell resulting O(n*n) complexity.

For example,

1,1,1,1,1,1,1,1, 
1,1,1,1,1,1,1,1, 
1,1,1,1,1,1,1,1, 
0,0,0,0,0,0,0,0,

Because Depth-First Searches use a stack as the nodes are processed, backtracking is provided with DFS. Because Breadth-First Searches use a queue, not a stack, to keep track of what nodes are processed, backtracking is not provided with BFS.

Some algorithms depend on particular properties of DFS (or BFS) to work. For example the Hopcroft and Tarjan algorithm for finding 2-connected components takes advantage of the fact that each already visited node encountered by DFS is on the path from root to the currently explored node.

According to the properties of DFS and BFS. For example,when we want to find the shortest path. we usually use bfs,it can guarantee the 'shortest'. but dfs only can guarantee that we can come from this point can achieve that point ,can not guarantee the 'shortest'.

When tree width is very large and depth is low use DFS as recursion stack will not overflow.Use BFS when width is low and depth is very large to traverse the tree.

When you approach this question as a programmer, one factor stands out: if you're using recursion, then depth-first search is simpler to implement, because you don't need to maintain an additional data structure containing the nodes yet to explore.

Here's depth-first search for a non-oriented graph if you're storing “already visited” information in the nodes:

def dfs(origin):                               # DFS from origin:
    origin.visited = True                      # Mark the origin as visited
    for neighbor in origin.neighbors:          # Loop over the neighbors
        if not neighbor.visited: dfs(neighbor) # Visit each neighbor if not already visited

If storing “already visited” information in a separate data structure:

def dfs(node, visited):                        # DFS from origin, with already-visited set:
    visited.add(node)                          # Mark the origin as visited
    for neighbor in node.neighbors:            # Loop over the neighbors
        if not neighbor in visited:            # If the neighbor hasn't been visited yet,
            dfs(neighbor, visited)             # then visit the neighbor
dfs(origin, set())

Contrast this with breadth-first search where you need to maintain a separate data structure for the list of nodes yet to visit, no matter what.

DFS is more space-efficient than BFS, but may go to unnecessary depths.

Their names are revealing: if there's a big breadth (i.e. big branching factor), but very limited depth (e.g. limited number of "moves"), then DFS can be more preferrable to BFS.

On IDDFS

It should be mentioned that there's a less-known variant that combines the space efficiency of DFS, but (cummulatively) the level-order visitation of BFS, is the iterative deepening depth-first search. This algorithm revisits some nodes, but it only contributes a constant factor of asymptotic difference.

For BFS, we can consider Facebook example. We receive suggestion to add friends from the FB profile from other other friends profile. Suppose A->B, while B->E and B->F, so A will get suggestion for E And F. They must be using BFS to read till second level. DFS is more based on scenarios where we want to forecast something based on data we have from source to destination. As mentioned already about chess or sudoku. Once thing I have different here is, I believe DFS should be used for shortest path because DFS will cover the whole path first then we can decide the best. But as BFS will use greedy's approach so might be it looks like its the shortest path, but the final result might differ. Let me know whether my understanding is wrong.

One important advantage of BFS would be that it can be used to find the shortest path between any two nodes in an unweighted graph. Whereas, we cannot use DFS for the same.

I think it depends on what problems you are facing.

1. shortest path on simple graph -> bfs
2. all possible results -> dfs
3. search on graph(treat tree, martix as a graph too) -> dfs ....