Categorygithub.com/sebnyberg/aocaoc2021day24
package
0.0.0-20240925134824-13afb22f4087
Repository: https://github.com/sebnyberg/aoc.git
Documentation: pkg.go.dev
Overview
Dependencies
8
Dependents
0

# README

Day 24

This day took a really long time to figure out, so I thought it would be best to include a README.

The first order of business is to read the input and try to parse instructions into some kind of simplified set of rules.

A good thing to note is that only three lines are possibly different between instruction sets:

  • Line 4: divisor (henceforth d)
  • Line 5: constant added to x (henceforth a)
  • Line 15: constant added to y (henceforth b)
if z % 26 + a == w {
  x := 0
  z := z / div
  z *= (25*x + 1)
  z += x*(w+b)
} else {
  x := 1
  z := z / div
  z *= (25*x + 1)
  z += x*(w+b)
}

This can be simplified as:

cond := z%26 + a == w
z /= div
if !cond {
  z = z*26 + w + b
}

When the divisor is 1, the constant a happens to be positive and greater than 10 (see input). This means that the condition will always fail, resulting in the z*26 operation.

There are 7 such div z 1 operations in the input. This means that z*26 will happen at least 7 times. Since the goal is to have z be zero (0), the other 7 operations must undo these actions somehow.

This tells us that whenever there is div z 26, the condition must be true, i.e. z%26+a == w must be true.

This is how the input w is formed: each digit must be such that it is possible to match relevent criteria.

For my input this gives:

  1. [d1+7]
  2. [d1+7,d2+8]
  3. [d1+7,d2+8,d3+10]
  4. [d1+7,d2+8], [d3+10-2==d4]
  5. [d1+7], [d3+10-2==d4,d2+8-10==d5]
  6. [d1+7,d6+6], [d3+10-2==d4,d2+8-10==d5]
  7. [d1+7], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7]
  8. [], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7,d1+7-5==d8]
  9. [d9+1], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7,d1+7-5==d8]
  10. [d9+1,d10+8], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7,d1+7-5==d8]
  11. [d9+1], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7,d1+7-5==d8,d10+8-14=d11]
  12. [d9+1,d12+13], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7,d1+7-5==d8,d10+8-14=d11]
  13. [d9+1], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7,d1+7-5==d8,d10+8-14=d11,d12+13-14=d13]
  14. [], [d3+10-2==d4,d2+8-10==d5,d6+6-14==d7,d1+7-5==d8,d10+8-14=d11,d12+4-14=d13,d9+1-5=d14]

Constraints:

  • d1 + 2 = d8
  • d2 - 2 = d5
  • d3 + 8 = d4
  • d6 - 8 = d7
  • d9 - 4 = d14
  • d10 - 6 = d11
  • d12 - 1 = d13

Maximizing constraints yield the max answer:

7......9......