Is the DMG 3/4 cover diagram in 5e incorrect?

From page 250 and 251 of the DMG:

To determine whether a target has cover against an attack or other effect on a grid, choose a corner of the attacker’s space… trace imaginary lines from that corner to every corner of any one square the target occupies. If one or two of those lines are blocked by an obstacle (including another creature), the target has half cover…

grid diagrams taken from the DMG. The final diagram shows the construction lines provided in the DMG to determine cover (showing 3/4th cover) as well as the question askers own construction lines, superimposed showing it should be half cover.

It looks like they just chose the wrong corner. If the attacker was moved one square to the north it would be 3/4 cover. Or do you think they meant "choose the closest corner"?

Minimize shadows placing light sources on a diagram of a room

I’m a CS student and came upon this problem:

Given a diagram of a room with obstacles in it (like walls or furniture), find the 4 best places to put light sources in it so the room has the most light possible, or you can think of, minimizing the amount of shadow in the room.

In other words, if you have 4 sources of light, which are the best places to put them so your room has maximum light (or minimum shadow).

I’ll append an example of a diagram so the problem can be better understood: example of a diagram

The solution I thought was to find the spot with most light and from there find the second one and so on. But something makes me think that it may exist a configuration which is better that doesn’t need to be the best from the beginning, kinda feels like a special case of the knapsack problem, if so I’d think of implementing a greedy algorithm or using genetic algorithms to give an approximation of the best places.

I’m not sure if it’s a math or a CS problem. I’d be grateful if at least someone points me in the right direction so I can do a better research, thank you very much!

Butterfly diagram from cooley-tukey algorithm

I am trying to understand the logic of this algorithm so i can implement my own but i am not understanding this diagram i see appearing many times in a fair few articles on the topic, i am teaching myself so i don’t have a computer science degree to help. But i understand the general idea behind the algorithm.

But this butterfly diagram is confusing me.

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How do you interpret this diagram from left to right mathematically speaking? It’s so confusing.. what are the arrows telling me to do in terms of math operations on the functions?

Need help designing ER Diagram

I am not a database engineer, I am just getting started with designing data models.

A User registers to my application. My application has Funds that are predefined with an InvestmentStrategy. A user deposits cash into their account Bankroll. A user invests from their Bankroll into a Fund or multiple. A fund buys into Investments. A User selects Picks to guide the InvestmentStrategy. The InvestmentStrategy uses historical Pick evidence by User to determine which Investments to make. Investments have Results, which pay Users based on performance. A User can leave a Fund. A User can withdraw from their Bankroll. A InvestmentStrategy can also pay percentage of profit to User.

This leads to a wide array of circular relationships. I am having a hard time drawing an ER diagram describing the entities and relationships above. Does anyone have examples or suggestions for how to create their model? Thanks!

Why does this finite state machine state transition diagram solution has more states than my solution?

I can’t figure out what is wrong with my solution and why does it differ from book’s solution. I think the only thing that matters is the previous state of A so that there should be two states, one for previous A=0 and one for previous A=1. Where am I mistaken? I would really appreciate any explanation.

this is the question

this is book's solution here

this is my solution