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Asked: 2026-05-28T13:38:08+00:00

I’m having trouble understanding space complexity. My general question is: how can the space

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I’m having trouble understanding space complexity. My general question is: how can the space complexity of an algorithm on a tree be smaller than the number of nodes in the tree? Here’s a specific example:

If b is the branching factor
d is Depth of shallowest goal node and,
m is Maximum length of any path in the state space

For DFS, the space complexity is supposed to be O(bm). I thought it would just always be the size of the tree? Where’s the rest of the tree and how do we use the entire tree with only O(bm) space complexity?

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1 Answer

  1. Editorial Team

    Because space complexity represents the extra space it takes besides the input.

    Complexity, in general, is defined related to turing machines. The space an algorithm takes is the extra number of cells needed for it to run. The input cells are not taken into account, and can be reused by the algorithm to reduce extra storage.

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