## What is the optimal way to maneuver into and out of the Healing Spirit spell to maximize healing?

The healing spirit spell states:

You call forth a nature spirit to soothe the wounded. The intangible spirit appears in a space that is a 5-foot cube you can see within range. The spirit looks like a transparent beast or fey (your choice).

Until the spell ends, whenever you or a creature you can see moves into the spirit’s space for the first time on a turn or starts its turn there, you can cause the spirit to restore 1d6 hit points to that creature (no action required). The spirit can’t heal constructs or undead.

As a bonus action on your turn, you can move the spirit up to 30 feet to a space you can see.

I’m wondering what the optimal way to maneuver into and out of the spell for maximized healing is. Note that the following questions already exists:

• How does the spell Healing Spirit work?

Established there are some facts of how this sort of spell works:

1. Creating the spell on top of a creature does not restore any hit points to them
2. Moving the spell onto a creature with your bonus action does not restore any hit points to them
3. You don’t need to end your turn in the healing spirit’s space, you only have to move through it.

For the purposes of this question I am not interested in class features that modify healing like the Life Domain Cleric’s Discipline of Life and Supreme Healing features or the Warlock’s Gift of the Ever-Living Ones Eldritch Invocation. I am only interested in ways to maneuver into and out of the space most effectively.

Another way to think of this is the following: What is the maximum number of times a creature can be healed by this spell per round?

## Rules/Constraints:

1. From the section on “Moving Around Other Creatures”:

You can move through a nonhostile creature’s space. […] Remember that another creature’s space is difficult terrain for you.

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

2. This is a party of four, and they do not have any mounts available unless they summon them.

3. You only “move into the spirit’s space” when you use your own movement to enter said space; being grappled and dragged into the space, being hurled into it by thunderwave, and being carried into it on a mount do not count.

## How to maximize f while minimizing g at the same time?

Lately, I have been dealing with a problem that I didn’t know how to name it to solve it properly.

The problem is as follow: lets a assume that we have a set of element A. And, we have two function f and g, where for any sub-set B \in A, where |B|< k, k is a constraint:

1. f(B) : estiamtes the gain obtainted by the set B.
2. g(B) : estiamtes the lost obtainted by the set B.

In our problem we have two strategies S1, S2 which depends on the circumstances of the environment

1. S1: selelects a set B that maximize the gain
2. S2: selelects a set B that minimize the lost

my strategy is a hybride strategy, which is selecting a sets B1 and B2 where |B1|+|B2|

NT: given that there are several circumstances some times S1 works more effecientlly , and some cases S2 works better

is ther anyone who knows what type of problem? any documentation about it ? since it is a NP-hard problem, is there way to find an approximation with in the optimal solution?

## At what point is Empower Spell better than Maximize Spell?

When I’m trying to increase the output of my spells such as Fireball, Cure Critical Wounds or Magic Missile, I can’t decide whether Empower Spell or Maximize Spell is better.

I’d like to compare only the effects of the feats, without involving the difference in spell level adjustment for each one since I’m prioritizing the output of the spell without regards to the cost involved in to cast it.

## Assigning values to nodes and edges a tree to maximize node whose value is larger than all adjacent edges

A node is valid if its value is greater than all of its adjacent edges.

Task is to maximize the number of valid nodes.

Given $$n$$ values for nodes and $$n-1$$ values for edges, how do I assign these values (to nodes and edges) to a given input tree so the number of valid nodes is maximized?

## How to maximize the number of filled grid squares in a partially filled grid with Tetris shapes

So here’s the problem:

-You are given a partially filled grid of size mxn (represented by a matrix of 1s and 0s where a 1 signifies that grid square is occupied by a block and a 0 signifies that grid square is empty)

-You must minimize the number of empty grid squares by filling this grid with Tetris shapes which are each composed of exactly 4 blocks (a block is 1×1)

What is an algorithm that can consistently do this given any mxn partially-filled grid?

## How do I maximize my turns for damage with this Battle Smith melee character?

What would be the correct sequence of actions on 1st turn, and following turns for an Battle Smith Artificer to Maximize damage?

They are a 3rd level variant human (Dual Wielder feat) with a Strength and Intelligence modifier of +3. We are using the 2019-2 version of the Artificer.

They are armed with

• 2 Yklwa 1d8 (with throwing property) using TWF

• One being infused with Enchant Weapon +1,
• and the second with Returning Weapon +1 (no action on return).

They could cast either

• Arcane weapon 1d6 (variable) or
• Searing Smite 1d6 (fire)

And they have the ability to command their Iron Defender as a Bonus Action to attack with a 1d8 + 2 damage attack, or take the help action.

## What would be the best classes/races/feats/backgrounds to maximize range for an melee weapon

Currently im using one of my characters which is a bugbear and they get 5ft extra range, and a weapon with the range, heavy, and 2 handed. (Is there any more ways to increase this, so next time I create A character I will know. )

## What Feats do I want to take to maximize my effectiveness with a crossbow?

I’m building a high-ish level Alchemist to jump into a campaign, and I’m thinking it’ll be fun to build around being a master of infusing crossbow shots for high damage with Explosive Missile, using Improved Snap Shot (and occasional Grenadier infusions) to keep incoming attackers at bay.

The problem is, I’ve always been terrible with keeping track of ranged combat feats and understanding the ‘tree’ such as it were. I already have the following feats:

• Point Blank Shot
• Rapid Shot
• Precise Shot
• Weapon Focus
• Imp. Critical
• Snap Shot/Imp. Snap Shot

What am I missing? I’ve already ruled out Focused Shot for reasons of action economy.

Additionally, are there any classes or archetypes (other than a few levels of fighters for more feats, obviously), that would provide a lot of bang for the buck in a small dip to help this build out?

## Maximize violate constraint of non approximated function

here is my code

Maximize[{-(10/17) - x + (20 (1 + x))/(17 (2 + x)), 0 <= x <= 1.5}, x] 

The result I got: {6.66134*10^-16, {x -> -9.79755*10^-16}}

As you can see, the function is pretty simple, yet Maximize failed to find the maximum of it ( I suspect it is at x= 0) Why is it the case, and what can I do to fix it? Thank you so much!

## Is resampling random variables to maximize value NP-hard?

Setup Let $$S = {X_1, …, X_n}$$ be a set of binary random variable, i.e. $$X_i \in \{0, 1\}$$. Let $$A = \{a_0, a_1, …, a_n\}$$ represent different values of outcomes of $$S$$, more specifically if for a given outcome of $$S$$, say $$\{X_1 = x_1, …, X_n = x_n\}$$, let $$j = \sum_{i=1}^nx_i$$, then we get value $$a_j$$.

Objective Given an outcome $$\{X_1 = x_1, …, X_n = x_n\}$$, with associated value $$a_j$$, suppose you can select up to $$\alpha \leq n$$ number of $$X_i$$‘s to have their outcomes re-rolled. Select the set of $$X_i$$‘s that, in expectation, yields the greatest value of $$A$$. (For clarity, the nodes are selected all at once, then all re-rolls happen simultaneously, no node may be re-rolled more than once.)

Question Is this problem and NP optimization problem, or does their exist a polynomial time algorithm to solve it.

Work so Far So far iv worked out that if $$A$$ defines a monotone sequence, then the optimal set of variables to resample can be computed in polynomial time. To see this, suppose that $$A$$ is monotone increasing, then a greedy selection scheme is optimal. Namely, from all nodes that have outcome $$X_i = 0$$ that have not yet been selected to be resampled, pick the $$X_i$$ with the greatest $$P(X_i=1)$$. Do this until you select $$\alpha$$ variables, or no such variables with outcome 0 exist. A similar scheme works when $$A$$ is decreasing.

I also tried a dynamic programming approach which has not yet been fruitful.

But it is not clear to me if in the general case, there exists a polynomial time algorithm to compute the optimal solution or if the problem is NP-hard. To me, although I dont have much to back this up yet, it seems like it should be commutable in polynomial time.

Any help is greatly appreciated.