CLRS 22.3-1, How Come Solutions Online State There Can’t Be Edges From WHITE to GRAY nodes “at any point… during search”?

The exercise (from the book Introduction To Algorithms) states

Make a 3-by-3 chart with row and column labels WHITE, GRAY,and BLACK. In each cell (i, j) indicate whether, at any point during a depth-first search of a di- rected graph, there can be an edge from a vertex of color i to a vertex of color j . For each possible edge, indicate what edge types it can be. Make a second such chart for depth-first search of an undirected graph.

The colors WHITE, GRAY, BLACK correspond to Undiscovered, discovered but not finished, and finished. The following solution is what multiple sites & universities have posted(such as: walkccc, Rutgers University):

 |       | WHITE         | GRAY                | BLACK                | |-------|---------------|---------------------|----------------------| | WHITE | All kinds     | Cross, Back         | Cross                | | GRAY  | Tree, Forward | Tree, Forward, Back | Tree, Forward, Cross | | BLACK | -             | Back                | All kinds            | 

I will draw a minimal counter example as it helps understand my conflict:

counter-example

  • Start at node 0: 0 is GRAY
  • PAUSE
  • At this point, 3 is still white and has an edge to 0
  • Resume and keep going, eventually the edge from 3 to 0 will be discovered as a tree edge

This contradicts the solutions saying you can only have Cross/Back edges going form WHITE->GRAY. This example can be easily modified to contradict many of the elements in the table. I think the solutions are doing one of the following:

  • Assuming that the graph is a tree and that we start at its root. (Wrong as DFS doesn’t need a tree graph and any node can be started from).
  • More likely (Just thought of this), interpreting the question of "can there be an edge" as "can there be an edge that we have discovered". In which case, the solutions work, as although the edge from 3->0 was a WHITE->GRAY edge at one point, we hadn’t discovered it yet.

Where do D&D Orcs come from?

I’ve always assumed that with all modern fantasy, D&D included, their racial archetypes for their inhabitants always had their roots from Tolkien’s Lord of the Rings. And in part, I do believe there is enough healthy evidence to indicate that many of D&D’s Orc characteristics are indeed inspired from Tolkien’s Orc, whether it’s their physical prowess, inherent brutality (although this is likely to change very soon), militaristic organisation, etc.

But where do they really come from? Tolkien’s Orc stems from enslaved and corrupted elves who had their humanity literally tortured out of them. Where do D&D orcs come from and what makes them what they are?

How come non creatable/destroyable Roblox instances have :Destroy() :Clone() etc?

Roblox has many types of instances. But services and other NonCreatable Instances (ReplicatedStorage, Workspace, etc.) still have methods for creating or destroying. Why? Why do they have :Destroy() and :Clone() methods if they cannot be destroyed or created? What’s the point of inheriting these from the Instance class?

Why does an explorer’s pack come with more things that can fit in it?

The Explorer’s pack comes with a backpack and a bunch of stuff that (I assume) goes inside.

A Backpack can fit 30lbs in it. But the stuff – a bedroll (7), a mess kit (1), a tinderbox (1), 10 torches (10), 10 days of rations (20), and a waterskin (5) – totals 44lbs.

My party holds the weight of stuff a bit loosely, rather than playing RAW. But if you did play RAW, you wouldn’t be able to carry all the stuff you’re given. Why would the game designers do that?

Where has my History proficiency come from?

I’m new to DnD. I was typing up my character sheet (I’ve decided to do this every now and then as my annotations become more messy), and in the process I didn’t spot any reason for me to have the History proficiency I have.

It’s likely that I just made a mistake when making the sheet, but maybe I didn’t…

I’m a Dragonborn Paladin with an Outlander background and my subclass (Oath) is Redemption. According to this wiki, the race or subclass doesn’t give me any skill proficiency, while the background gives me Athletics & Survival and the class gives me a choice of two from Athletics, Insight, Intimidation, Medicine, Persuasion & Religion; I chose Medicine & Persuasion. So the 4 skills I have from my background and class are Athletics, Survival, Medicine & Persuasion… none of those are History (which I have in addition).

I also noticed an “origin” feature for my background, from which there are 10 origins: Forester, Trapper, Homesteader, Guide, Exile or outcast, Bounty hunter, Pilgrim, Tribal nomad, Hunter-gatherer, and Tribal marauder. The wiki doesn’t give any information on those, and I haven’t got one written on my sheet.

I’m currently Level 4; I don’t believe a level feature has given me an extra skill proficiency so far.

Where might I be getting this proficiency from?
Does my “origin” have anything to do with it?
What are the possible ways of getting a History proficiency?
Have I/my DM simply make a mistake when creating my character?

Can you add your the same modifier to damage rolls multiple times if they come from different instances?

A friend of mine is wanting to do a specific build and as far as I am aware you can not apply a modifier multiple times in this way. Can someone confirm if this is a RAW legal tactic?

Scenario: lv 6 tiefling celestial warlock, assuming 16 charisma

Cast shillelagh to make staff 1d8+cha [source: pact of the tome]

Then cast searing smite for 1d6+cha [source: teifling and celestial warlock’s radiant soul feature to add charisma mod]

Then green-flame blade attack for another 1d8+cha [celestial warlock’s radiant soul feature to add charisma mod]

A single hit would be 2d8+1d6+9

Do all these instances of charisma modifier stack like this?

how come wall of force isn’t over powered?

it just seems like a get-out-of-almost-any-fight free card would be kind of overpowered. you could escape almost any fight by cast wall of force behind you and running away . The spell description says that nothing can pass through and that it was indestructible except for a disintegrate spell, so enemies(or players) will be stuck unless they happen to know disintegrate. am I missing something?

How come there are TLS 1.3 signature algorithms when the client version stated is TLS 1.2?

I’m analyzing traffic in order to understand TLS Client Hello structure so I can parse it.

I read that TLS 1.3 adds more signature algorithms. However, I saw a Client Hello message that states that the client version is 1.2, but has the new TLS 1.3 signature algorithms (e.g. Signature Algorithm: ed25519 (0x0807), see attached packet ahead).

Does that make sense?

Can I just assume that regardless of the version, I need to handle those new signature algorithms as well?

This is the packet in WireShark format.

Should the Router or Firewall Come First?

Network scenario…. I have a typical enterprise network meaning ISP>>>>Edge Router>>>>>Firewall|DMZ>>>>Switch>>>LAN.

I know there are several debates on the internet about what device comes first but based on a typical medium size office 500 people, what should come first in the network architecture, the firewall or the router. My thought was that the router should come first because the IOS firewall would be the first line of defense, then a Palo or Sonicwall for the firewall would come next to take whats left. Let mw know if you think im wrong.