Can’t Understand the formula for processing speed of each job

I am trying to understand the formula for processing speed of each job. I got the formula from the following link:

Fair Online Scheduling for Selfish Jobs on Heterogeneous Machines

The other details are provided below:

Description1

I can’t understand what is the basis (i.e. the fundamental logic) of the following formula. Speed (i.e. Velocity) is given by : S= V * t

Why we have this fraction term in the formula? What does the denominator represent? I think it is representing the processing time of each job.

Somebody please guide me

Description 2

How (if at all) do Wild Magic Surges stack with each other?

First off there are a lot of rules on combining/overlapping effects:

The effects of the same spell cast multiple times don’t combine, however. Instead, the most potent effect–such as the highest bonus–from those castings applies while their durations overlap, or the most recent effect applies if the castings are equally potent and their durations overlap.

Player’s Handbook: Chapter 10, Spellcasting; Combining Magical Effects

[…] When two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap […] Game features include spells, class features, feats, racial traits, monster abilities, and magic items […]

Dungeon Master’s Guide: Chapter 8, Running The Game; Combining Game Effects (errata)

When two or more effects have the same proper name, only one of them applies while the durations of the effects overlap (a duration is a time span of 1 round or more). The most potent effect–such as the highest bonus–is the one that applies, or the most recent effect applies if the effects are equally potent.

The Essentials Kit: Chapter 0, Welcome to Dungeons & Dragons; Effects with the Same Name Don’t Stack


That all said we also know that things with the same name don’t stack regardless of how different the actual effects might be, for example:

  • If you cast a spell with different effect options twice on the same creature, do multiple castings of the spell stack?
  • If you cast Blindness/Deafness as a 3rd level spell, can you target one creature with both effects?
  • Do the Stone Golem's Slow feature and the Slow spell combine?

In all these cases, despite the actual effects being quite different, the name of the effect is the same and so they cannot stack.


How do these rules apply to Wild Magic Surges? In particular there are effects such as:

15-16: For the next minute, you regain 5 hit points at the start of each of your turns.
23-24: Your skin turns a vibrant shade of blue. A remove curse spell can end this effect.
61-62: For the next minute, you must shout when you speak.
71-72: You gain resistance to all damage for the next minute.

Can multiple different surges exist, simultaneously affecting the same creature? Are they considered to be the same class feature or to have the same proper name and thus do not stack?

Can multiple of the same surge (such as 15-16 above) exist, simultaneously affecting the same creature? Would you regain 10 hit points at the start of each of your turns or just 5?

How do Wild Magic Surges stack with each other (if at all)?

Is it possible to keep weights of left and right subtree at each node of BST that has duplicate values?


Is it possible to keep weights of left and right subtree at each node of BST that has duplicate values?

I must be able to delete a node completely(irrespective of how many times it is present)

Currently, in my code, I am keeping count variable in each node that records the number of times it is present in tree.

During insertion, I can increase the size of left and right subtree weight at each node according to if my value is less or more. but how do I adjust the weights when I delete a node(because I may delete a node with count >1)

How do Plant Growth and Slow interact with each other?

How do Plant Growth and Slow interact with each other?

If on spell-caster casts Plant Growth in an area and the other targets a creature with the Slow spell, what happens?

Supposing that the creature fails its saving throw against Slow would this mean that, while it is within the area affected by Plant Growth, its movement is two times, four times, or eight times slower?

I have got an inkling that the creature would only move 1 foot for every 8 feet of movement, but not sure is those two effects stack.

Thanks for your help with this.

Find and prove a linear algorithm that identifies all cycles and the length in a graph where each vertex has exactly one outgoing edge


Consider a directed graph on n vertices, where each vertex has exactly one outgoing edge. This graph consists of a collection of cycles as well as additional vertices that have paths to the cycles, which we call the branches. Describe a linear time algorithm that identifies all of the cycles and computes the length of each cycle. You can assume that the input is given as an array A, where A[i] is the neighbor of i, so that the graph has the edge (i, A[i]).

I kind of have an idea of how to approach the algorithm but have no idea what to do with the proof of my algorithm. So far I’m thinking of marking the vertices I have traversed, and every time a vertex points back to the ones that I’ve traversed I count one cycle and move on to the next unvisited vertex.

However, I am also very confused by the wording. Maybe I’m missing something and not understanding what the branches are supposed to do: am I right to assume that if the graph is connected (this graph can also be disconnected) and each edge only has one outgoing edge, there will only be one cycle? Since having just two cycles would require a vertex to point to two vertices and contradict the premise.

How to Tokenize a String and Save Each Substring Separately (Independent Names for Each Substring)

I am given two files one with the name of person and the location that they are from (Evan Lloyd|Brownsville) and one with the name and salary (Evan Lloyd|58697) (the line number that you find the employee on in the first file is not necessarily the line number that find the employee on in the second). The user inputs a location (whole or part). For example if they input “ville” or “Ville” it should include all of the employees in Brownsville, Clarksville, Greenville, etc. I am supposed to join the the name and salary and return them if they are in the city searched for i.e. “ville” or “Ville.” I am attempting to use a vector for both of the files vector(name, address) and vector(name, salary) and later return a vector of a string and tuple (address, (name, salary)) as my output. I don’t know how to tokenize the string for example “Evan Lloyd|Brownsville” into the substrings “Evan Lloyd” and “Brownsville” separately (without the |) and save them separately so that I can push both strings into my vector(name, address). How would I tokenize the strings that way or should I try something else entirely?

Find the max partition of unique elements where each element corresponds to the set pool containing that element

Given a list of sets:

a b c -> _ c d   -> d b d   -> b a c   -> a a c   -> c 

The objective is to find the max partition of unique elements with each element corresponding to the set containing that element.

I was thinking about ordering the elements in n * log(n) based on occurrence in other groups and then iteratively start with the lowest, and reorder the list each time based on subtracting the occurrences of other elements within the lists containing the removed element. We are able to do so, as each unique element contains a set of pointers to the lists where the element is contained in.

I can store the unique elements with its occurrences in a Min-Heap, where each unique element has handler to the node within the Min-Heap, thus we can remove the min and also decrease the key one for others within the same list as the contained element in log(n) giving that we have it’s handler.

Is the approach feasible at all, if not, what approach I can make use of?

Custom image dimensions for each category

Hi everyone and happy new year 2020,

I need to set up different image dimensions for each category of a website.

For example,

To set these dimensions for Category 1:

Catalog Images = 240 x 320px
Single Product Image = 470 x 627px
Product thumbnails = 75 x 100px

And these dimensions for category 2:

Catalog Images = 245 x 245px
Single Product Image = 470 x 470px
Product thumbnails = 75 x 75px

I use woocommerce.
How to do this? Is there any code or filter to affect to that a named…

Custom image dimensions for each category

What is the FPTAS alogorithm to find flow at each link for multi commodity flow problem?

I have a graph, and K commodities to route from source to destination. I want to find, what is the maximum beneficial flow for each of the commodity and the relevant paths. I understand the problem in general falls under NPC, hence I am looking for FPTAS algorithms.

I am struggling with the problem, so any intuitive idea to tackle the problem is also most welcome.