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0 pointsscott_s2y ago0 comments

This function is O(1): https://github.com/scotts/streamflow/blob/master/streamflow..... All other tree operations are also constant, because the fact that it is a 3-level tree is hardcoded.

Asymptotic bounds are useful when your input can grow arbitrarily large. When your input is fixed, the bounds become less useful and you should focus on the particulars of your case. In the case I'm presenting, the work done traversing the tree will be the same every time; it is O(1). That doesn't necessarily mean it's fast enough! It still may do too much work for the use case. For instance, I can imagine someone saying that the function above does too much pointer chasing for their use case.

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ot2y ago

> This function is O(1)

I think I addressed that in my comment, but to be more explicit, this function is O(1) too:

  size_t find_sorted(void* object, void** list, size_t size) {
    for (size_t i = 0; i < SIZE_MAX; ++i) {
      if (i < size && list[i] > object) return i;
    }
    return SIZE_MAX;
  }

If O(1) cannot distinguish your function from this function, what is its informational value?

> Asymptotic bounds are useful when your input can grow arbitrarily large

But your inputs can't grow arbitrarily large, that's why you can hardcode 3 levels. O(1) is an asymptotic bound, and my point is that it is not very informative here.

scott_sOP2y ago

I'm really not sure what you're overall point here is. Yes, I agree with you. Your function is O(2^64) which is technically O(1). Your point, which I agree with, is that's completely useless information. It does not help our understanding of performance at all. Calling such a function O(1) is technically true, but both misleading and not informative. What I'm not clear on is how that relates to the discussion we're having here.

The original poster said they wanted a O(1) solution to a problem. I presented one. That solution happens to be based on a data structure whose algorithms are, in the general case, O(log n). But we're not dealing with a general case, we're dealing with a specific case. And because of that specific case, we can write algorithms that are O(1). Unlike your example, these algorithms have a very small n; 3, to be exact. That is meaningful to describe as O(1) in this case because we can reduce the work down to a small constant.

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fragmede2y ago

This is O(n) because you're still doing the i < size comparison, even though you've moved it out of the for loop.

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ot2y ago

> This function is O(1)

I think I addressed that in my comment, but to be more explicit, this function is O(1) too:

  size_t find_sorted(void* object, void** list, size_t size) {
    for (size_t i = 0; i < SIZE_MAX; ++i) {
      if (i < size && list[i] > object) return i;
    }
    return SIZE_MAX;
  }

If O(1) cannot distinguish your function from this function, what is its informational value?

> Asymptotic bounds are useful when your input can grow arbitrarily large

But your inputs can't grow arbitrarily large, that's why you can hardcode 3 levels. O(1) is an asymptotic bound, and my point is that it is not very informative here.

scott_sOP2y ago

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fragmede2y ago

This is O(n) because you're still doing the i < size comparison, even though you've moved it out of the for loop.

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