## In a DAG, finding the path with the highest score

Given a directed, acyclic graph in which each node has an assigned integer score, what is a fast way of finding the path from a start and end vertex with the highest cumulative score? I thought of a DFS approach in which we start at the end and run the graph in the reverse way, saving at each node the best cumulative score attainable. To print the results, we start at the first node and greedily pick the next node with the highest cumulative score. However, I don’t think this is the best way as we might be traversing the same paths a lot of times if we are given an unfriendly graph. Is there a better way of doing this?

## What is the highest average roll you can get with artisan’s tools?

Using any magic items, classes, feats, et cetera, what is the highest average roll that you can roll using a set of artisan’s tools?

## What is the highest possible AC?

Assuming you are level 20, and have access to any magic item, how high can you get AC (permanently or for a set duration)?

Constraints:

Magic items are those on the tables in the D&D 5th Edition DMG.
Spells, skills, feats and abilities available to a player character are eligible for use/consideration.

No buffing, no other help from an ally. This AC is achieved by a single player character.

Extra clarification: Time and magic items are limited to practical use. Think of it as a game plan for a campaign with a very generous DM.

## D&D 5E: Can the Glamour Bard and Swords Bard deal as much DPR as the highest DPR classes over the course of an adventuring day? [duplicate]

This question is an exact duplicate of:

• D&D 5E: Are the new Bard Class Options more effective than all other classes with their options? [closed]

I’m looking for a detailed analysis of the new bard colleges (and bard base class features) compared to the capabilities of all other classes and class options.

## New Class Options

The class options I am looking at are:

• College of Glamour bard
• College of Swords bard

## Criteria

I’m looking for mechanical analysis of features. Mainly the result of features. Such as healing word having nearly identical results as the fighters second wind. It takes a limited resource. (something the fighter and bard can only do a few times a day)

## Perspective

All mechanical obstacles can be broken down into the following situations:

• Overcoming enemies in combat
• Overcoming enemies in interaction (socialization)
• Overcoming environmental obstacles or traps in exploration

If you compare class abilities and powers in how effective they are at overcoming those obstacles then it becomes much easier to compare them. Keep in mind player roleplaying and DM fiat can overcome those obstacles also, but that is outside the scope of this question as each DM and player will have different abilites to bypass those obstacles using roleplaying and DM fiat. Through my own research I’ve found that the Players Handbook Bard Colleges combined with the base Bard class can be built in such a way that they can overcome the above obstacles at least as well as any other class. To narrow the scope of this question you can compare the new class options against the college of Lore and the college or valor. If they are more effective then I’ll accept that they can do what other classes do, and better.

Some metrics that can be used are:

• All questions assume comparison of each class/subclass is reasonably optimized.
• Multi-classing shouldn’t be used because this is a question between classes
• Magic items can’t be assumed and should be left off.
• Feats are features of all classes, so they can be used.
• Assume the average adventuring day listed in the Dungeon Masters Guide.
• Starting stats for characters should be point buy.
• If possible an analysis of levels 3-20 should be included with notes on where changes occur.

Can the Glamour Bard and Swords Bard deal as much DPR as the highest DPR classes over the course of an adventuring day?

## What are the highest damage outputs for a Warlock of the Fiend? (Pact of the Chain)

My now 3rd level tiefling Warlock of the Fiend just took the pact of the chain (Her familiar is a Quasit). So far I’ve found this to be effective:

Armor of Agathys (Now always cast at 2nd level: +10 temp. hp & 10 cold damage to anything that attacks her) +

Hellish Rebuke (Dexterity save, 2d10 fire damage on a failed save, or half as much damage on a successful one to a creature that hits her; 1/per long rest but still nice for a reaction)

+ Dark One’s Blessing after the Armor of Agathys disappears (Free temp. Hp for when she kills something = Charisma modifier + warlock level [7])

Her turn: Typically in combat, this means smoking everything in sight with Eldritch Blast; 1d10 force [+4 from Agonizing Blast] and if in a pinch, uses Cloud of daggers to catch several enemies at once.

Not too bad, I would say she’s able to pull her weight in combat with this, but I want to make her a heavier hitter. What are some of the best damage combos, invocations, etc for a Warlock?

Note: Can be answered for any level warlock, Knowing possible builds for the future would be nice, not just for 3rd level.

## What’s the highest damage output for a Level 8 Grave Domain Cleric? [closed]

Assuming I can cast spells like spiritual weapon and spirit guardians in a single turn as well as spells like healing world and guiding bolt, what is the highest damage output in a single turn for me as a Kalishtar 8th level Grave Domain cleric?

All magic items available in Eberron are on the table as options.

Ability score modifiers:

• STR: 2
• Dex: 0
• CON: 3
• INT: 3
• WIS: 5
• CHA: 2

## Highest safe rung problem?

Highest Safe rung problem : There are many rungs on a ladder in increasing order of height. A bottle is thrown from a rung, and depending on the height of the rung, the bottle may break or may not (bottle breaks for higher height rungs, and doesn’t for lower rungs). We need to find the maximum height safe rung for which the bottle doesn’t break given that:

(1) We have only 1 bottle with us.

(2) We have infinite bottles with us.

(3) We have exactly 2 bottles with us.

(4) We have k bottles with us. ($$1 \leq k$$).

Design algorithms for solving (1) – (4) in best possible time complexity. (Also note that (3) and (4) should be an asymptotic improvement over (1).]

My method: (1) is just a linear search and (2) is a divide and conquer approach to solving the problem. I cannot find an asymptotically improved algorithm for (3) – the only methods which I kept thinking of provide some constant factor improvements in time complexity over (1), I am absolutely clueless on how to solve for (3) and (4).

P.S: This is a problem from Chapter 1 of Kleinberg and Tardos. I couldn’t find it’s solution online.

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## What is the highest total result one can get for a skill check?

I was bored, so I decided to try to calculate what could be the highest total result one could obtain for a skill check.

Answers can include officially published material, including magic items – but no Unearthed Arcana. Wish is also not to be included.