Approximate algorithms for class P problems

As a part of my Algorithm course we studied Approximate Algorithms for NP-complete or NP-hard problems, e.g. “set cover”, “vertex cover”, “load balancing”, etc. My professor asked us as an extra activity to learn an approximate algorithm for a P problem. I searched a lot on google but all I found were NP problems.

I was wondering if anybody can help and tell me a approximate algorithm for a problem with already a exact polynomial algorithm? It will be very much better if the algorithm be short and easy.

Is there a way to ask in game (i.e. in a non-meta way) what a character’s class is?

Is there a way to ask in game (i.e. in a non-meta way) what a character’s class is? There have been a few times when my character is meeting an NPC (allied combatant) or another PC and it’s bugging me that I can’t think of a non-meta way to ask what their class is.

My goal is to figure out what a character can do. I don’t care (in this context) if, for example, a sorcerer is a bandit (that’s background) — the point is learning that their fighting style is that of a sorcerer.

I’ve had my DM or fellow player tell me to RP finding out.

Anyone have any ideas?

Do Spellcaster Class DCs not increase?

This feels like a stupid question, but I can’t find any actual answers.

While building a higher level character to play with the system a little, I noticed what appears to be an omission. At some point in each classes progression the Class DC will increase incrementally.

For example:

Mighty Rage Barbarian lvl 11th

Your rage intensifies and lets you burst into action. Your proficiency rank for your barbarian class DC increases to expert. You gain the Mighty Rage free action.

But in the spellcasting classes the Class DC is not explicity mentioned in what appears to be the appropriate feats.

Example

Expert Spellcaster Wizard lvl 7th

Extended practice of the arcane has improved your capabilities. Your proficiency ranks for arcane spell attack rolls and spell DCs increase to expert.

Is this a weird omission in the actual writing or am I completely misunderstanding the way Class DCs work and the spellcasting classes just use their Spell DC instead of the Class DC?

Randomized version of the class $APX$?

Is there a class which is to APX what BPP is to P?

I’m looking for a definition that is like the following:

“For $ r > 0$ , an $ r$ -RPCA (randomized polynomial-time constant-factor approximation) algorithm for a function problem $ T : \Sigma^* \to \mathbb{N}$ is a probabilistic Turing machine $ A$ with the following property: $ A$ runs in time $ poly(|x|)$ and has $ \mathbb{P}( r^{-1} T(x) \leq A(x) \leq r T(x)) \geq 2/3$ .”

I think that either a class like this exists and has a standard name, or there is something wrong with it. I’m looking for a similar definition with which to cleanly state a result.

How does the UA Revised Ranger’s “Greater Favored Enemy” interact with “Favored Foe” from the UA Class Feature Variants?

If a Revised Ranger chooses to use the Favored Foe variant from the most recent Unearthed Arcana, they replace their original Favored Enemy feature. How does this interact with their existing Greater Favored Enemy feature?

Even when the Ranger doesn’t have access to Favored Enemy, do the benefits it provides still apply to the Greater Favored Enemy?

Favored Enemy (original)

Beginning at 1st level, you have significant experience studying, tracking, hunting, and even talking to a certain type of enemy commonly encountered in the wilds. Choose a type of favored enemy: beasts, fey, humanoids, monstrosities, or undead. You gain a +2 bonus to damage rolls with weapon attacks against creatures of the chosen type. Additionally, you have advantage on Wisdom (Survival) checks to track your favored enemies, as well as on Intelligence checks to recall information about them. When you gain this feature, you also learn one language of your choice, typically one spoken by your favored enemy or creatures associated with it. However, you are free to pick any language you wish to learn.

Favored Foe (variant)

You can call on your bond with nature to mark a creature as your favored enemy for a time: you know the hunter’s mark spell, and Wisdom is your spellcasting ability for it. You can use it a certain number of times without expending a spell slot and without requiring concentration a number of times equal to your Wisdom modifier (a minimum of once). You regain allexpended uses when you finish a long rest. When you gain the Spellcasting feature at 2ndlevel, hunter’s mark doesn’t count against the number of ranger spells you know.

Greater Favored Enemy (original)

At 6th level, you are ready to hunt even deadlier game. Choose a type of greater favored enemy: aberrations, celestials, constructs, dragons, elementals, fiends, or giants. You gain all the benefits against this chosen enemy that you normally gain against your favored enemy, including an additional language. Your bonus to damage rolls against all your favored enemies increases to +4. Additionally, you have advantage on saving throws against the spells and abilities used by a greater favored enemy.

(emphasis is mine)

Would multiclassing in the same class (different non-stacking archetypes) break the game too much?

I know that as per RAW you can stack multiple archetype as long they dont conflict when changing the same class feature.

But would it be too game breaking to treat 2 non-stacking archetypes as different classes?

I mean, the game allows a 10 barbarian (titan mauler) 10 fighter (Two-Handed Fighter) to exist, but not a 10 fighter (titan fighter) 10 fighter (Two-Handed Fighter).

As far I understand, the idea of no stacking is to prevent receiving x features at the cost of x/2.

So treating to non-stacking archetypes as differents this problem would be resolved no?


And just to point it out, I know that some archetypes are fundamentally opposed, for example a 2-handed fighter and a tower shield specialist.

But ignoring this cases, would it be possible?

What happens if you apply Practiced Spellcaster to a prestige class?

Say you’re a 14th-level Sorcerer with 1 level in Archmage who then goes Fighter. You take Practiced Spellcaster (CA p.82) to boost your Sorcerer CL, and then later take it again to boost your Archmage CL.

Since Archmage inherits its spellcasting from Sorcerer, does this mean that at character level 20th, your caster level for everything is 14+4+1+4=20, so even though you don’t know 8th/9th-level spells, your Delayed Blast Fireball deals its full 20d6 (for example)?

Homebrew monk class and subclass with magic armor

I’m making my own Monk class and subclasses for fun with the following mechanical modifications:

  1. Unarmored Defense (10 + Dex + Wis) will be replaced with Armored Defense with a magically bonded light armor (12 + Dex + 1/2 Wis) only while wearing it. Also, Unarmored Movement would only be usable while wearing the armor, not the other way around (and still thinking about reducing it a bit).

  2. No shield or armor outside his own magic bonded armor, and no weapons proficiency. Just unarmed martial arts attacks. While wearing the armor, the monk would be able to add his proficiency bonus to the unarmed martial arts attacks damage.

  3. The monk gains a number of extra Ki points equal to his proficiency bonus.

Would it be over-powered or gamebreaking to make half-flavour half-gameplay changes like these? (I’m not looking for feedback about flavor or personal tastes, just the balance question.)