What are key differences between BFS and DFS?

Key differences between BFS and DFS are:

• BFS is vertex-based algorithm while DFS is an edge-based algorithm.
• Queue data structure is used in BFS. On the other hand, DFS uses stack or recursion.
• Memory space is efficiently utilised in DFS (O(log n)) while space utilisation in BFS (O(n)) is not effective.
• A depth-first search uses a stack, which contains nodes from root to the node being searched. So at most the radius of the graph (or depth of the tree).
• A breadth-first search uses a queue, which contains nodes at the front of the search. So at most all nodes at distance d.
• If you have a balanced (or mostly so) k-ary tree, it’s depth, i.e. radius, will be only O(log n), while the lowest layer will contain O(n) nodes (n/2 for binary tree and even more for higher degrees).
• BFS is optimal algorithm while DFS is not optimal. DFS may produce a much longer path than BFS.
• DFS constructs narrow and long trees. As against, BFS constructs wide and short tree.
• DFS is a genuinely recursive algorithm that uses stack for backtracking purposes, not for storing the vertex discovery “front” (as is the case in BFS).