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Robert Mion

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# RPG Simulator 20XX

## Advent of Code 2015 Day 21

Why not attempt Day 22 first?

• Any time a puzzle references another - earlier - puzzle, I try to solve the referenced puzzle(s) first...assuming there's important knowledge or skills to be gained from them that will help me solve the later one(s)

## Part 1

1. A finance-related boss battle? Exciting!
2. A shortest-path combination puzzle
3. How to do battle
4. Studying the example scenario for the battle's math
5. Writing an algorithm I could replay manually
6. Playing out a few more battles

### A finance-related boss battle? Exciting!

• Defeat the boss!
• But don't spend any more money than you have to to win!
• Even though the instructions say you have plenty!

### A shortest-path and permutation puzzle

• I must find the combination of weapons-armor-rings that costs the least and still defeats the boss

The combinations:

• 1 weapon (5), 0 armor, 0 rings = 5 options
• 1 weapon (5), 0 armor, 1 ring (6) = 30 options
• 1 weapon (5), 0 armor, 2 rings (6 * 5 = 30) = 150 options
• 1 weapon (5), 1 armor (5), 0 rings = 25 options
• 1 weapon (5), 1 armor (5), 1 ring (6) = 150 options
• 1 weapon (5), 1 armor (5), 2 rings (30) = 750 options

Total possible combinations:
`1110`

Yikes!

### How to do battle

• The player goes first
• Each attack damages the defender by at least 1 hit point
• As soon as any player has 0 hit points, the battle ends
• Each attacker's damage remains constant

Damage is calculated using this equation:

``````Attacker's damage score - Defender's armor score
``````
• The boss's hit points and scores are provided in the input and do not change
• The player's hit points are 100 and scores are decided based on the item(s) purchased
• It seems the answer to this puzzle is identifying the cost of the items that cause the battle to a real nail-biter!

### Studying the example scenario for the battle's math

Stats:

``````Player
Hit Points: 8
Damage: 5
Armor: 5

Boss
Hit Points: 12
Damage: 7
Armor: 2
``````

Calculating scores:

``````Player:
5 - 2 = 3

Boss:
7 - 5 = 2
``````

Rounds of battle:

``````   Boss  Player
0  12    8
1  9     6
2  6     4
3  3     2
4  0     0
``````

Interesting:

• In the example, both player's hit points were evenly divisible by their respective damage score
``````12 % 3 == 0
8 % 2 == 0

12 / 3 == 4
8 / 2 == 4

If equal, Player wins
Else, whoever's is smaller loses
``````

By my logic:

• Check whether the reminder after dividing the starting hit points by the damage received is 0
• If it is, calculate the quotient of the hit points and damage received
• Else, calculate 1 + the quotient of the difference of hit points and the remainder, then the damage received

So, using the example:

``````12 % 3 == 0 ? 12 / 3 : 1 + ((12 - (12 % 3)) / 3)
// 4
8 % 2 == 0 ? 8 / 2 : 1 + ((8 - (8 % 2)) / 2)
// 4
``````

Then:

• If boss's amount is less than or equal to player's, player wins
• Else, boss wins

### Writing an algorithm I could replay manually

Extracting the boss's stats:

``````let [BossHP, BossDmg, BossDef] = input.matchAll(/\d+/g)].map(el => +el[0])
``````

Calculating the number of rounds survived:

``````function calculateRounds(hp, dmg) {
return hp % dmg == 0
? hp / dmg
: 1 + ((hp - (hp % dmg)) / dmg)
}
``````

Simulating the battle:

``````function battle(stats) {
let BossRounds = calculateRounds(
stats.BossHP,
stats.P1Dmg - stats.BossDef
)
let P1Rounds = calculateRounds(
stats.P1HP,
stats.BossDmg - stats.P1Def
)
return BossRounds <= P1Rounds ?
["P1 wins!", P1Rounds, BossRounds] :
["Boss wins!", BossRounds, P1Rounds]
}
``````

The parameter referenced above, `stats`, has this structure:

``````{
BossHP: BossHP,
BossDmg: BossDmg,
BossDef: BossDef,
P1HP: 100,
P1Dmg: 8,
P1Def: 4
}
``````

To replay, I just changed `P1Dmg` and `P1Def`:

``````P1Dmg: 4
P1Def: 0
Boss wins!

P1Dmg: 5
P1Def: 0
Boss wins!

P1Dmg: 6
P1Def: 0
Boss wins!

P1Dmg: 7
P1Def: 0
Boss wins!

P1Dmg: 8
P1Def: 0
Boss wins!
``````

Bummer. Looks like the player must carry more than just a weapon into battle to have a chance at winning!

### Playing out a few more battles

It's not enough to do 8 damage and have no armor.

What about 8 damage and all the armor: 8?

• As expected, player wins

Let's work backwards now until player loses:

``````P1Dmg: 8
P1Def: 8
P1 wins!

P1Dmg: 8
P1Def: 7
P1 wins!

P1Dmg: 8
P1Def: 6
P1 wins!

P1Dmg: 8
P1Def: 5
P1 wins!

P1Dmg: 8
P1Def: 4
P1 wins!

P1Dmg: 8
P1Def: 3
Boss wins!
``````

The lowest cost thus far:

``````P1Dmg: 8
P1Def: 4

Weapon: Longsword (40 gold)
Armor: Bandedmail (75 gold)
Ring: Damage +1 (25 gold)

Total cost: 140 gold
``````

What if player's damage is `9`?

``````P1Dmg: 9
P1Def: 4
P1 wins!

P1Dmg: 9
P1Def: 3
P1 wins!

P1Dmg: 9
P1Def: 2
P1 wins! Barely!

P1Dmg: 9
P1Def: 1
Boss wins!
``````

The lowest cost thus far:

``````P1Dmg: 9
P1Def: 2

Weapon: Longsword (40 gold)
Armor: Chainmail (31 gold)
Ring: Damage +2 (50 gold)

Total cost: 121 gold
``````

It's worth a try at the correct answer...

## Part 2

### I guess I'll keep playing!

This time, I must identify:

the most amount of gold I can spend and still lose the fight

• Seems smart to wear both the most expensive rings
• And I have to buy a weapon

``````P1Dmg: 7
P1Def: 4
Boss wins!

Weapon: Dagger (8 gold)
Armor: Bandedmail (75 gold)
Ring: Damage +3 (100 gold)

Total cost: 183 gold
``````

Oh, and with two rings:

``````P1Dmg: 8
P1Def: 3
Boss wins!

Weapon: Shortsword (10 gold)
Ring: Defense +3 (80 gold)
Ring: Damage +3 (100 gold)

Total cost: 190 gold
``````

• Nope. Too low.

Oh, another `(7, 4)` but with four items:

``````P1Dmg: 7
P1Def: 4
Boss wins!

Weapon: Dagger (8 gold)
Armor: Leather (13 gold)
Ring: Defense +3 (80 gold)
Ring: Damage +3 (100 gold)

Total cost: 201 gold
``````

• Yes, it is!

## I did it!!

• I solved both parts!
• By first building a round-calculating algorithm that performed simple arithmetic!
• Then, by building a battle-simulating algorithm!
• And playing it with different damage and defense values!
• And identifying the proper items that would tally to the winning - or losing - values!

If I hadn't stumbled on Part 1's correct answer so quickly, I was ready to write an algorithm using several nested `for` loops that simulated all `1110` of the options.

Thankfully, I didn't have to build such an algorithm!

Though, it may have been a fun - albeit frustrating and head-scratching - experience.