BFS的一个重要优势是，它可以用于寻找未加权图中任意两个节点之间的最短路径。 然而，我们不能用DFS来做同样的事情。

DFS比BFS更节省空间，但可能会深入到不必要的深度。

它们的名字揭示了:如果有很大的广度(即大的分支因子)，但深度非常有限(例如有限的“移动”数量)，那么DFS可能比BFS更受欢迎。

关于国际发展基金

应该提到的是，有一个不太为人所知的变体，它结合了DFS的空间效率，但(累积)BFS的水平顺序访问，是迭代深化深度优先搜索。该算法对一些节点进行了重访，但只贡献了一个常数因子的渐近差分。

以下是对你的问题的全面回答。

简单来说:

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.

因此，我们可以得出什么时候使用BFS和DFS。假设我们正在处理一个可管理的有限分支因子和一个可管理的有限深度。如果搜索的节点很浅，即在原始源的一些边之后可以到达，那么最好使用BFS。另一方面，如果搜索的节点较深，即从原始源处经过大量边后可以到达，那么最好使用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.

最后，如果我们有无限的深度和无限的分支因子，我们可以使用迭代深化搜索(IDS)。

这是一个很好的例子，说明BFS在某些情况下优于DFS。https://leetcode.com/problems/01-matrix/

当正确实现时，两个解决方案都应该访问比当前单元格+1距离更远的单元格。 但DFS效率低，重复访问同一单元，导致复杂度为O(n*n)。

例如,

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,

这在很大程度上取决于搜索树的结构以及解的数量和位置(也就是搜索项)。

If you know a solution is not far from the root of the tree, a breadth first search (BFS) might be better. If the tree is very deep and solutions are rare, depth first search (DFS) might take an extremely long time, but BFS could be faster. If the tree is very wide, a BFS might need too much memory, so it might be completely impractical. If solutions are frequent but located deep in the tree, BFS could be impractical. If the search tree is very deep you will need to restrict the search depth for depth first search (DFS), anyway (for example with iterative deepening).

但这些只是经验法则;你可能需要尝试一下。

我认为在实践中，你通常不会以纯粹的形式使用这些算法。可能会有一些启发式方法，有助于首先探索搜索空间中有希望的部分，或者您可能希望修改搜索算法，以便能够有效地并行化它。

根据DFS和BFS的性质。 例如，当我们要求最短路径时。 我们通常使用bfs，它可以保证“最短”。 但是DFS只能保证我们可以从这一点可以到达那一点，不能保证‘最短’。