Is the space inside a demiplane considered “outdoors” for the purposes of Control Weather?

The demiplane spell creates a door that leads to another plane of existence:

You create a shadowy door on a flat solid surface that you can see within range. The door is large enough to allow Medium creatures to pass through unhindered. When opened, the door leads to a demiplane that appears to be an empty room 30 feet in each dimension, made of wood or stone. […]

It seems that this room is the entirety of this plane. There is nothing beyond the ceiling, floor, or walls. In a sense, the ceiling is the limit of the “sky,” although if it has weather is questionable.

Given all this, is the space inside a demiplane considered “outdoors” for the purposes of the control weather spell? Control weather requires that:

[…] You must be outdoors to cast this spell. Moving to a place where you don’t have a clear path to the sky ends the spell early.

Why does MergeSort have O(n) space complexity if it splits the array log(n) times?

I know this is a common algorithm with plenty of analysis, but when I searched for an answer the only one I found was “Merge Sorting has O(n) auxiliary space because it copies the array into L and R”.

I don’t understand this because as it is called recursively, before performing any operations, the entire array is still split log(n) times. When following the binary tree diagram representing the recursion, we see (if n=16) it splits into 2×8, 4×4, 8×2, 16×1.

Since all of these splits occur prior to any merging, why is the auxiliary space O(n) and not O(nlog(n))?

For Ring of Shooting Stars, can Ball Lightning affect a creature when you move it into their space?

The Ring of Shooting Stars has the following feature (emphasis mine):

Ball Lightning.

You can expend 2 charges as an action to create one to four 3-foot-diameter spheres of lightning. The more spheres you create, the less powerful each sphere is individually.

Each sphere appears in an unoccupied space you can see within 120 feet of you. The spheres last as long as you concentrate (as if concentrating on a spell), up to 1 minute. Each sphere sheds dim light in a 30-foot radius.

As a bonus action, you can move each sphere up to 30 feet, but no farther than 120 feet away from you. When a creature other than you comes within 5 feet of a sphere, the sphere discharges lightning at that creature and disappears. That creature must make a DC 15 Dexterity saving throw. On a failed save, the creature takes lightning damage based on the number of spheres you created. (4 spheres = 2d4, 3 spheres = 2d6, 2 spheres = 5d4, 1 sphere = 4d12)

Does this mean that the sphere discharges lightning whether you move it within 5 feet of a creature or whether a creature moves within 5 feet of it?

What happens if you move it within 5 feet of multiple creatures at once (or multiple creatures move within 5 feet of it at once)?

A state space for river crossing puzzle

I am solving the river crossing puzzle with 6 participants. You must transfer all the people across the river in this flash game respecting the following rules:

The ferry can carry no more than 2 people. Only the Adults (mom, dad and policeman) can operate the ferry. Dad can not be in the presence of the girls w/out Mom Mom can not be in the presence of the boys w/out Dad The thief can not be alone with any of the family w/out the policeman.

We need to create the state space and as I am creating mine I am not sure if I am doing it properly.

In my case I represent the state as A/B where A are the people on the left side and B are the people on the right side. This is what I have so far. I feel like I will get a lot of states, so I am worried that I am doing something wrong. Is this correct?

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Find an infinite set of strings that are compressable better than in $O(\log n)$ space

The task is to find an infinite set of strings $ a_1,a_2\ldots$ , where $ |a_{i+1}|>|a_i|$ and to find a compression algorithm $ f$ for these strings, such that $ |f(a_i)|=o(\log_2 |a_i|)$ with $ i\to\infty$ .

I have considered a set of strings with minimal entropy: $ a_1=b, a_2=bb$ , etc. The optimal compression algorithm for these strings is $ f : a_i\mapsto |a_i|$ , but this compresses each string only to $ O(\log i)$ space.

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Thank you.

If a creature starts their turn in another’s space, are they forced to move out?

Inspired by this question: Can a Druid pull a target through other creatures with Thorn Whip?

That Q&A concludes that it is possible for two creatures to unwillingly share the same space; for example, one creature could be pulled by thorn whip into the space of another creature.

Once the thorn whip caster’s turn is over, when it is one of the other two creature’s turns (either the one who was pulled or the one’s whose space was invaded), they will of course start their turn in another creature’s space.

From the PHB, p. 191:

Whether a creature is a friend or an enemy, you can’t willingly end your move in its space.

Are they allowed to end their turn in the other creature’s space if they don’t use any movement, or must they move out of the space (if they can; i.e. they have movement)?


Related:

  • What happens when your movement is set to zero while attempting to move through a friendly space? (accepted answer seems to imply that they would have to move, but this is not supported and comments dispute that unsupported point; also, that question is about )
  • Does the rule that you cannot willingly end your move in another creature's space force or prevent certain actions? (not the same as my question as it talks about sharing space on the creature in question’s turn, whereas mine is about not moving on your turn to avoid this)

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Thank you.

Is it possible to move through a guardian of faith’s space?

Per p. 191 of the Player’s Handbook, you can’t move through a hostile creature’s space unless they’re two sizes larger or smaller than you. You can move through a nonhostile creature’s space but can’t willingly stop there. Either way, another creature’s space is considered difficult terrain.

The guardian of faith spell creates a “Large spectral guardian” in “an unoccupied space of your choice”. My question is, should the guardian be regarded as a creature for purposes of moving through its space, or is it an impassable barrier? Nowhere in the spell description is it described as a creature, nor is it given an AC and hit points that would allow it to be attacked as one. It doesn’t get opportunity attacks against creatures that move away from it. On the other hand, it’s explicitly described as Large, and I can think of no other reason why that information would be relevant. Is there an official answer to this, or is it up to the GM?