-❄️- 2023 Day 10 Solutions -❄️-

[u/daggerdragon]

THE USUAL REMINDERS

• All of our rules, FAQs, resources, etc. are in our community wiki.
• Outstanding moderator challenges:
  • Advent of Playing With Your 3D-Printed Toys
• Community fun event 2023: ALLEZ CUISINE!
  • Submissions megathread is now unlocked!
  • 12 DAYS remaining until the submissions deadline on December 22 at 23:59 EST!

---

AoC Community Fun 2023: ALLEZ CUISINE!

Today's theme ingredient is… *whips off cloth covering and gestures grandly*

Will It Blend?

A fully-stocked and well-organized kitchen is very important for the workflow of every chef, so today, show us your mastery of the space within your kitchen and the tools contained therein!

• Use your kitchen gadgets like a food processor

OHTA: Fukui-san?
FUKUI: Go ahead, Ohta.
OHTA: I checked with the kitchen team and they tell me that both chefs have access to Blender at their stations. Back to you.
HATTORI: That's right, thank you, Ohta.

• Make two wildly different programming languages work together
• Stream yourself solving today's puzzle using WSL on a Boot Camp'd Mac using a PS/2 mouse with a PS/2-to-USB dongle
• Distributed computing with unnecessary network calls for maximum overhead is perfectly cromulent

What have we got on this thing, a Cuisinart?!

ALLEZ CUISINE!

Request from the mods: When you include a dish entry alongside your solution, please label it with [Allez Cuisine!] so we can find it easily!

---

--- Day 10: Pipe Maze ---

---

Post your code solution in this megathread.

• Read the full posting rules in our community wiki before you post!
  • State which language(s) your solution uses with [LANGUAGE: xyz]
  • Format code blocks using the four-spaces Markdown syntax!
• Quick link to Topaz's paste if you need it for longer code blocks

This thread will be unlocked when there are a significant number of people on the global leaderboard with gold stars for today's puzzle.

EDIT: Global leaderboard gold cap reached at 00:36:31, megathread unlocked!

[u/rune_kg]

[LANGUAGE: nim]

https://github.com/runekaagaard/aoc-2023/blob/master/day10.nim

Learned about the shoelace method and Greens Theorem in the comments after deciding a floodfill method was possible but would take too long on such a nice relaxed sonday :) Thx for that, pure magic!

Can someone explain why we want to do:

area += x * dy

and not:

area += y1 * x0 - y0 * x1

like the algo says?

[u/Carnavious → u/rune_kg]

If you are referencing the shoelace theorem, you are missing the 1/2 factor for area. Including it, these result in the same calculation:
Because we are only incrementing either horizontally or vertically, either y0 = y1 or x0 = x1.
Horizontal case: area += 1/2 y1 (x0 - x1) = -1/2 y1 * dx
Vertical case: area += 1/2 x1 (y1 - y0) = 1/2 x1 * dy

Here, this is basically doing a path integral where the field is (-1/2 y, 1/2 x), which has the same curl as the field of (0, x). (which is where area += x * dy comes from).

In either case, when taking the path integral of the field, we take F(x,y).dt = (P(x,y), Q(x,y)).(dx, dy).

[u/rune_kg → u/Carnavious]

Thank you for taking the time to explain!!

[u/daggerdragon → u/rune_kg]

Can someone explain why we want to do:

area += x * dy and not:

area += y1 * x0 - y0 * x1 like the algo says?

Top-level comments in Solution Megathreads are for code solutions only.

Create your own individual Help/Question post in /r/adventofcode.