# What is the space complexity of iterative deepening search?

When using iterative deepening, is the space complexity, $$O(d)$$, where $$b$$ is the branching factor and $$d$$ the length of the optimal path (assuming that there is indeed one)?

Iterative deepening search (IDS) is a search algorithm that iteratively uses depth-first search (DFS), which has a space complexity of $$O(bm)$$, where $$m$$ is the maximum depth, with progressively bigger depths, and it turns out that its space complexity is $$O(bd)$$.