Why is splitting a Rust's std::collections::LinkedList O(n)?

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The .split_off method on std::collections::LinkedList is described as having a O(n) time complexity. From the (docs):

pub fn split_off(&mut self, at: usize) -> LinkedList<T>

Splits the list into two at the given index. Returns everything after the given index, including the index.

This operation should compute in O(n) time.

Why not O(1)?

I know that linked lists are not trivial in Rust. There are several resources going into the how's and why's like this book and this article among several others, but I haven't got the chance to dive into those or the standard library's source code yet.

Is there a concise explanation about the extra work needed when splitting a linked list in (safe) Rust?

Is this the only way? And if not why was this implementation chosen?

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Maybe I'm misunderstanding your question, but in a linked list, the links of each node have to be followed to proceed to the next node. If you want to get to the third node, you start at the first, follow its link to the second, then finally arrive at the third.

This traversal's complexity is proportional to the target node index n because n nodes are processed/traversed, so it's a linear O(n) operation, not a constant time O(1) operation. The part where the list is "split off" is of course constant time, but the overall split operation's complexity is dominated by the dominant term O(n) incurred by getting to the split-off point node before the split can even be made.

One way in which it could be O(1) would be if a pointer existed to the node after which the list is split off, but that is different from specifying a target node index. Alternatively, an index could be kept mapping the node index to the corresponding node pointer, but it would be extra space and processing overhead in keeping the index updated in sync with list operations.

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  • Can someone explain the downvotes please (two downvotes at the time I wrote this comment)? This question seems absolutely fine to me.
  • but I haven't got the chance — so you haven't put any effort of your own into figuring out the answer on your own?
  • @LukasKalbertodt Not a downvoter, but I think there are two main reasons: first, the OP does not say why they believe it to be possible to implement split_off in O(1) time, so it's not possible to guess at the source of the confusion; and second, the question is worded as if it's blaming Rust's standard library for an inefficient implementation when in reality this is just how all linked lists work.
  • I think if the question had been phrased "I have heard that splitting a linked list is an O(1) operation; why is split_off O(n)?" it would probably not have been downvoted. (And it could have been tagged language-agnostic to boot)
  • The documentation for std::collections does have the more precise O(min(i, n-i)).