Dijkstra same weight but different edges [closed]

I read about Djikstra’s algorithm and I want to be sure about two fundamental things, would appreciate if you could answer me mathematically so I can understand how words are translated to math so I can use it in other uses as well.

so here are my questions:

  1. if we mark the shortest path Djikstra’s algorithm found in some network with $ n$ stations in some topological construction: does it necessarily find the shortest path between each pair of vertices?
  2. assume there’s at least an additional path, somewhere from $ s$ to $ t$ , with same weight but with different edges (meaning both paths don’t have a common edge), how can we find this edge?

I don’t understand it well and I will really appreciate explanation so I can understand it better.

Watched videos, read materials online, and tried to concise what I am not sure about so I can request it here to deepen my understanding.

thank you for your time and assistance

0-1 knapsack problem with minimum and maximum weight capacity

In classical 0-1 knapsack problem we have maximum allowed value for the weight – weight capacity.

Let’s restrict total knapsack weight by min and max values

$ $ M \leq \sum_{i=1}^{n}{w_i x_i} \leq W $ $

Is there any known algorithm for this problem? Is there anything known which is better than brute force?

I failed to find anything about the given knapsack problem variation.

Homunculus: worth its own weight?

I started a new campaign and the DM started me with an egg, which I just discovered contains a homunculus. (egg, whatever). I looked up its stats and it seems…awful. The create homunculus spell from XGtE is 6th-level, while the find familiar spell is 1st-level. Is there something I’m missing here? What makes the homunculus 5 spell levels better than other familiars?

Finding Minimum Weight Subgraph with k Vertices

Assume a complete graph G={V,E} that has n vertices and $ C_{n}^{2}$ edges, and the weights of E are all positive. I am trying to find a complete subgraph containing k vertices, and it has the maximum sum of edge weights among all the complete subgraph with k vertices. My question is, other than the brutal force method that needs to traverse all posible subgraph with k vertices ($ C_{n}^{k}$ ), is there an algorithm that is faster than the brutal force, or has polynomial complexity?

By what factor does weight of a melee weapon change if created for a creature with a size class other than medium

So it’s safe to assume that a small creature will have a lighter weapon than a medium creature and a large creature will have a heavier weapon than a medium creature since the amount of material used in the weapon will differ. How much of a factor would the weapons weight change by? My best guess would be two since each size class is effectively twice as large as the previous size class.

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Should weight of PC itself counts at weight capacity calculation?

Imagine dwarf Alice (200 pounds) and gnome Bob (40 pounds). Both characters have 10 Strength.

So, as PHB says, both of them are able to carry 10 × 15 = 150 pounds.

Does it mean that Bob’s effective capacity is 150 – 40 = 110 pounds and Alice’s effective capacity is 150 – 200 = -50, which means she has problems with carying her own body?

Or maybe character weight does not count for capacity calculation purposes?

Has there been clarification of the Random Weight Table in the Player’s Handbook?

I was reading through the Player’s Handbook today to make a character when I saw the Random Height and Weight tables. Looking at that, I saw that the weight, for a Tiefling, was 110 lbs * (2d4). Surely, I thought, a 220-880 lb tiefling is a little bit much compared to their 4’11” – 6’1″ height, so I looked at the others, and they are all similar.

Amusingly, the Mountain Dwarf has a weight of 130 lbs * (2D6), which can result in a character of the range of 260-1560 lbs, or close to a full ton of dwarf.

Has there ever been any clarification on this?