What is the space complexity of Depth-first search?OptionsO(b)O(m)Greedy Best-First SearchO(bm)O(bl)

The space complexity of Depth-first search (DFS) is O(bm), where 'b' is the branching factor and 'm' is the maximum depth of the search.

Here's a step-by-step explanation:

1. DFS is an algorithm for traversing or searching tree or graph data structures. It uses a stack data structure to remember to get the next vertex to start a search when a dead end occurs in any iteration.

2. The space complexity of an algorithm quantifies the amount of space or memory taken by an algorithm to run as a function of the length of the input.

3. In DFS, in the worst case, you have to insert all the vertices into the stack.

4. The maximum number of nodes that might need to be stored in the stack is proportional to the maximum depth 'm' that the search algorithm might need to explore to the leaf nodes, times the branching factor 'b' (the maximum number of successors of any node).

5. Therefore, the space complexity of DFS is O(bm).