Why does a breadth first search use more memory than depth first?

Question

I can\'t find an answer to this online, and in other answers to questions similar to this it just seems to be a given that an advantage of DFS is that it uses less memory than D

Answer 1

BFS doesn't always use more memory. The tree you have, in particular, is an example where is doesn't.

Consider this tree: (source)

With BFS, at some stage, all nodes from 8-15 will be in memory.

With DFS, you'll never have more than 4 nodes in memory (equal to the height of the tree).

The difference gets a lot worse as the tree goes larger (as long as it stays fairly full).

More specifically, BFS uses O(branchingFactor^maxDepth) or O(maxWidth) memory, where-as DFS only uses O(maxDepth).

If maxWidth < maxDepth, BFS should use less memory (assuming you use similar representations for both), but this is rarely true.