Alice and Bob are at it again, this time trying to think of ways to optimize the two-child remove case. They come up with the following strategy: "At each node, keep track of the depth of that node's predecessor and successor. Then, if a two-child remove case occurs, pick whichever has a smaller depth." After thinking about it some more independently, they meet to discuss their thoughts on the optimization.
Bob thinks that their strategy is not possible to implement without signficant changes to the algorithm and its performance. Alice thinks that the strategy is viable to implement (albeit with some more complex machinery), but she also feels that the optimization may have some unintended consequences.
Both Alice and Bob's thoughts on the optimization are reasonable. Flesh out their concerns by choosing all of the following that may apply to the optimization.
The optimization would increase the space overhead, but only by a constant factor.
The optimization would increase the space overhead, and moreover, enough to change the space complexity of the algorithm.
The time complexity of the algorithm would change if the optimization were implemented.
The time complexity of the algorithm would not change if the optimization were implemented, but it would increase the constant factor.
Supposing the maintenance could be performed very efficiently, each remove operation would become more efficiently.
If the optimization were made, the tree may end up degenerating in the long run.
