Combining TWO Monte Carlo algorithms to get a Las Vegas algorithm that solves the same problem

I came across a problem that I have no clue how to solve.

Consider two Monte Carlo algorithms, called A and B that both solve the same problem. A is true-biased and t-correct, while B is false-biased and z-correct. Show that you can combine both A and B to obtain a Las Vegas algorithm to solve the same problem.

Also, how would I find the best value of R, which is the probability of the las vegas algorithm to find the right answer? For this second part, how would I find this fictional value of R with no concrete example or data set, this question seems completely out of left field.

Thank you kindly for your time 🙂

Combining User Context in Machine-2-Machine OAuth2 Client Credential Flow

I have a REST API that is used by 2 separate application and is authenticating them by M2M OAuth2 Client Credential Flow.

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One of the two application is an automation service without user context. The second one is a REST API where users authenticate with OAuth2 Implicit Flow.

Now I need to include the user context in my common REST API too, since some information should only be shared to certain users.

What is a secure strategy to implement that scenario with OAuth2? I thought I could just include the user (or a fixed string in case of the automation service) into the Access Token of the Client Credential Flow but that doesn’t seem possible.

Combining Southern Magician and Arcane Disciple feats – Casting Attribute

I have trouble understanding the details of the full scope of the Southern Magician feat in conjuction with the Arcane Disciple feat:

Southern Magician [General]

(…) Benefit: Once per day per two spellcaster levels, you can cast a divine spell as an arcane spell, or vice versa. This enables you to bypass arcane spell failure due to armor, or gain additional benefit from spell that functions differently for a divine caster instead of an arcane caster, such as true seeing or magic weapon. (…)

The actual source of the spell’s power doesn’t change, nor does its means of preparation. You are merely weaving the strands of magic together in an unconventional way that makes the spell behave somewhat differently. [[Emphasis mine]]

and

Arcane Disciple [General]

(…)Benefit: Add the chosen domain’s spells to your class list of arcane spells. If you have arcane spellcasting ability from more than one class, you must pick which arcane spellcasting ability this feat applies to. Once chosen, this decision cannot be changed for that feat.

You may learn these spells as normal for your class; however, you use Wisdom (rather than the normal ability for your spellcasting) when determining the save DC for the spell. In addition, you must have a Wisdom score equal to 10 + the spell’s level in order to prepare or cast a spell gained from this feat. Each day, you may prepare (or cast, if you cast spells without preparation) a maximum of one of these domains spells of each level. (…) [[Emphasis mine]]

My questions would be:

  1. Does the emphasised “cast as arcane” have an impact on casting attribute from the Arcane Disciple feat. Eg: would a divine magic missile be controlled by the divine or arcane casting attribute? And an arcane sanctuary?

Obviously I’m looking at the angle, that if the casting attribute is based on the spell being divine or arcane, would mean that – with Southern Magician & Arcane Disciple combined – you would in the end of the day just gain add additional arcane spells to your spell book thus being freed from your divine casting attribute. Granted, just for a number of times / day.

Combining merge sort with insertion sort – Time complexity

I am learning algorithms from the CLRS book on my own, without any help. It has an exercise which combines merge sort {O(n log n)} with insertion sort {O($ n^{2} $ )}. It says that when the sub-arrays in the merge-sorting reach a certain size “k”, then it is better to use insertion sort for those sub-arrays instead of merge sort. The reason given is that the constant factors in insertion sort make it fast for small n. Can someone please explain this ?

It asks us to show that (n/k) sublists, each of length k, can be sorted by insertion sort in O(nk) worst-case time. I found from somewhere that the solution for this is O($ nk^{2}/n $ ) = O(nk). How do we get this part O($ nk^{2}/n $ ) ?

Thanks !

Is there a general consensus about not combining Unearthed Arcana (UA) materials with multi-classing?

Is there a general consensus about not combining Unearthed Arcana (UA) materials with multi-classing?

I have come across posts where contributors (in the comments) state that you cannot use a particular feature from Unearthed Arcana (UA) because the player had already chosen to multi-class.

Where does this notion come from?

I realise the DM has the final say on this, but is there an official statement in the published materials or a tweet to support this, or is it merely based on opinion?

The main argument I’ve seen is this: It is UA material and not part of the main set of rules yet; it has not been adjusted for multi-classing. Therefore players who multi-class are not be allowed to use materials from UA.

combining 2 or more password lists with crunch

how can i combine 2 or more password lists together like for example i have a passlist with names and a passlist with numbers so i wanna combine them like putting all the numbers in front or after the names

passlist1 contains too many names for example david-larry-kevin … passlist2 contains numbers 123-347-897672 and … then combine these 2 password lists together for something like dadvid123 david347 david897672 larry123 larry347 and … this is clear i want to combine two or more password lists together in crunch ,also no need to scripting tnx in advance

Combining Game Effects and Combining Magical Effects, and how does this relate to damage types?

Combining Game Effects and Combining Magical Effects, and how does this relate to damage types?

Fire Bolts and Fireballs!

I have a question about how to interpret the sections on Combining Game Effects and Combining Magical Effects. I have used fire damage and piercing damage as examples.

Combining Game Effects:

Different game features can affect a target at the same time. But 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. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items. (DMG p. 252)

Combining Magical Effects:

The effects of different spells add together while the durations of those spells overlap. 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. For example, if two clerics cast bless on the same target, that character gains the spell’s benefit only once; he or she doesn’t get to roll two bonus dice. (PHB p. 204)

To set the scene: Two Wizards, Pyro and Scorchee, enter a tavern, and they bump ito their arch-enemies, Rangers Legolad and Sir Pokealot – a fight ensues! They roll for initiative. L5 characters.

I’ve had to split it into two scenarios because each presents a nuance as to how to interpret “Combining Game Effects” and “Combining Magical Effects”.

Scenario 1: Both Wizards end up with the same initiative. When it comes to choose their actions: both of them cast Fire Bolt at Legolad and are successful in their ranged spell attacks. Does this mean that Legolad takes: two separate sets of damage of 2d10, or only one, because it is the same spell name?

Scenario 2: Both Wizards end up with the same initiative. One casts Fire Bolt at Sir Pokealot and hits; and the other casts Fireball (to the tavern keeper’s discontent), and he fails his saving throw. Does this mean that Sir Pokealot takes: 2d10 from the Fire Bolt and 8d6 from the Fireball; or only the damage from the spell that caused more damage, because it is the same damage type?

Combining Game Effects and Combining Magical Effects – how does this relate to spells with multiple effects?

Combining Game Effects and Combining Magical Effects – how does this relate to spells with multiple effects?

Here is the information from the Dungeon Master’s Guide and the Player’s Handbook that relates to my question.

Combining Game Effects:

Different game features can affect a target at the same time. But 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. For example, if a target is ignited by a fire elemental’s Fire Form trait, the ongoing fire damage doesn’t increase if the burning target is subjected to that trait again. Game features include spells, class features, feats, racial traits, monster abilities, and magic items. (DMG p. 252)

Combining Magical Effects:

The effects of different spells add together while the durations of those spells overlap. 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. For example, if two clerics cast bless on the same target, that character gains the spell’s benefit only once; he or she doesn’t get to roll two bonus dice. (PHB p. 204)

How does the information above interact with spells that have multiple effects? I have used three spells as examples because each of them represents a nuance, but they could all combine to provide an answer: Blindness/Deafness (PHB p. 219), Bestow Curse (p. 218) and Contagion (p. 227).

For Blindness/Deafness (separate conditions): If this is cast twice, once to cause Blindness and once to cause Deafness, does this mean that the creature is both blind and deaf? Or, because it’s part of the same spell, only one of the effects is present – if so, which one?

For Bestow Curse (various curses): If two separate casters bestow separate curses on the same creature, do both curses remain in place? If so, how does we decide which one is active?

For Contagion (natural diseases): If you cast Contagion multiple times, to cause different natural diseases, would the creature have multiple diseases active, or only one of them?

I appreciate your thoughts on this.