What is BFS’s space complexity in the worst case?

In the context of Breadth-First Search (BFS), the space complexity is primarily determined by the storage needed for the queue that keeps track of the nodes to explore. In the worst-case scenario, this space complexity can be expressed as O(b^d), where 'b' is the branching factor (the average number of children each node has), and 'd' is the depth of the shallowest solution.

As the algorithm explores the graph, it expands level by level. When reaching depth 'd', the number of nodes at that level can potentially be as high as b^d. In the worst case, if the search tree is fully utilized, the entire level of depth 'd' may need to be stored in memory at once, leading to exponential growth in memory usage. This is especially significant in cases where the tree or graph is broad and deep.

This characterization of space complexity highlights how BFS can become less efficient in terms of memory for very large or wide trees, indicating a potential drawback of the approach in search scenarios that require a large resource footprint.