What’s the most effective way to maximize skills as a character of any class?

I feel like Pathfinder skills are very compact when compared to 3.5 skills, as a result that makes each individual skill point worth more than each individual point in 3.5, due to combining some skills to form others that perform multiple functions.

Since skill points are more valuable, what are the best ways to gain as many skill points as possible as a character of any class? What’s the best way to optimize a skills modifiers for each set of classes below without affecting combat stats?

I’d prefer if the answers were formatted in the following way, explaining how each group can more easily gain skill modifiers:

  • High skill point classes: Rogue, Bard
  • Medium skill point classes: Monk, Barbarian, Alchemist
  • Low skill point classes: Fighter, Magic-users, Paladins

Compile most likely text based on faulty snippets

Input: Recognized text from images of labels taken with a cell phone in varying conditions. One image may enclose the entire text, or just a part of it.

Expected output: The most likely version of the original text, ideally with an indication of the certainty. More images will of course provide better results.

Even though it seems to me that this should be a rather common problem, I could not find any research, algorithms or code directly related.

My best idea so far (after three or four attempts of an implementation now discarded for various reasons…) was to find the best matches for various inputs, potentially by finding the longest common substrings, and then generate some sort of tree indicating the most frequent connections between individual characters. Parsing the tree should then return the most likely original. Even though this might work in principle, it’s always in the details, and there may be much more efficient solutions out there.

Thanks

Finding maximum subgraph with vertices of degree at most k

Let $ G = (V, E)$ be an undirected graph and $ U \subseteq V$ some subset of its vertices. An induced graph $ G[U]$ is graph created from $ G$ by removing all vertices that are not part of the set $ U$ .

I want to find a polynomial time algorithm that has graph $ G = (V, E)$ and integer $ k$ as input and returns a maximum set $ U \subseteq V$ with largest size such that all vertices of $ G[U]$ have degree at most $ k$ .

My idea with greedy algorithm that removes vertices with largest degree or vertices connected with most vertices with degree greater than $ k$ doesn’t work.

Does anyone know how to solve this problem in polynomial time?

What would be the most optimal way for a Pact of the Chain warlock to make use of a Sprite familiar?

I am playing an Archfey Warlock with the "Pact of the Chain" Pact Boon. For thematic reasons, I have chosen for my familiar to take the form of a sprite with the "fey" creature type.

The restriction I place on this question is that the above facts must remain true, these are fixed aspects that I do not want to change; hence any answer that states that the familiar should take another form, like an imp, are not valid answers to this question, regardless of how much more optimal that might be. In other words, this is not "how to optimise a Pact of the Chain warlock", but "how to optimise the use of the sprite as a Pact of the Chain warlock’s familiar".

Further restrictions are that I do not plan on multiclassing, so answers that require multiclassing are also not valid answers, and that I am limiting the range of levels in play to between 3 and 7, so answers that require me to be a higher level warlock are also not valid (although if an answer includes a "here’s what you can do at high levels too" section as an added extra, I won’t complain).

Given these restrictions, I want to get the best use out of my sprite familiar. Because of it’s tiny HP pool, so far I’ve just had it remain invisible and hide out of sight so that it doesn’t get shot and killed, since I’m still currently only level 3 and don’t really want to waste the resources resummoning it (later in the game, I assume this won’t be as much of a problem, but let’s assume that the familiar’s survivability is a concern of mine nonetheless, but not actually a hard restriction).

What are the best tactics to employ to make the sprite familiar as useful in combat as possible during late tier 1/early tier 2 play? I’m happy for people to suggest spells and invocations that the warlock themselves should pick in order to support the tactics that would enhance the sprite’s usefulness, but I don’t want this to turn into a question about optimising the warlock themselves; the focus should be on the sprite (in other words, assume the warlock is already optimised well enough for the purposes of this question).


Related Q&A: What can a familiar actually do? (except this question is about familiars generally, and the answers do not take into consideration the traits specific–if not unique–to a sprite, such as invisibility or potentially being able to poison an enemy or make it fall unconscious with the sprite’s shortbow attack)

Related Meta Q&A: Would this question about when it's better for a Pact of the Chain warlock to have their familiar attack be an on-topic bounded list question? (although no-one seemed to have an opinion either way, so I’ve gone ahead and asked it anyway; however, this meta Q&A can still be used as a platform to discuss the on-topic-ness of the question, should that become necessary)

[ General – Australia ] Open Question : Who would you say is the most embarrassing Australian?

I would nominate Belle Delphine for the English: https://www.youtube.com/watch?v=TL470fJMi7w This is what we have become. My, how the mighty have fallen. She made an absolute killing selling her bathwater for US$ 30 to people around the world. Who the fvck is buying that sh1t? Loads of people apparently because she is a millionaire now. It’s so embarrassing that we produce people like her.

Picking the most cost efficient sets

I have two 2D arrays: $ P[n][s]$ and $ C[n][s]$ , $ s \leq n$ .

P contains sets of nodes and $ C$ the cost of a set in $ P$ , e.g. the cost of $ P[2][2]$ is $ C[2][2]$ and a set $ p \in P = \{ s_0, s_1, …, s_{n-1} \}^q, q \leq n$ , e.g. $ p=\{s_0, s_3\}$ .

For every row I can pick at most one set but in the end the union of the picked sets needs to contain all nodes $ \{s_0, s_1, …, s_{n-1} \}$ .

How do I find the least expensive picks in linear time?

Finding most efficient sorting algorithm

Arr is an array that contains $ n$ numbers.
Suggest the most efficient algorithm for each case and analyze the runtime.
Explain why the algorithm you chose is the best one.

  1. Arr contains exactly $ \frac{n}{5}$ distinct values.
  2. Arr contains integers in the range $ [0, … , 𝑛^7 − 1]$ .
  3. There are exactly (𝑛 − √𝑛) integers in Arr, which are between 1 to 100. The remaining √𝑛 elements are not integers.

I was trying to look at some of the sorting algorithms and try to figure one by one which one is the best, but I believe there’s a better way to do it. What would be the right approach?