AoC 2016/11 - New representation


On with Advent of Code puzzle 11 from 2016: adopting a new, more compact representation.

One of the things that are quite evident in the solution so far is that it’s a memory hog. I blame my representation for this and, to a lesser unscientific degree, the algorithm.

So, we will try to adopt a different approach that is much more compact. We will go back to a time when things were simpler, screens were blocky and a single bit would mean anything, if you put enough imagination.

Losing a lot of generality, we can pragmatically observe that:

  • in the most challenging puzzle version, there are seven different elements;
  • there are four floors.

Having less than (or equal to!) eight elements means that we can fit the whole floors state in two 32-bits unsigned integers:

  • one for microchips, one for generators;
  • each octet represents a floor;
  • each bit in a octet is 1 if the corresponding item is there, 0 otherwise

As a convention, we will assume that floor 4 is the least significant octet in the unsigned integer, and floor 1 is the most significant one. It might be the other way around, of course, but I thought it best to underline the fact that we’re aiming to bring everything to floor 4 eventually, and this representation heads us towards minimizing the integers in the representation.

On top of this, we only need to track the position of the elevator, which takes another unsigned char (as a minimum). Consistently with the representation for the floors, we will assume that 0 means elevator at the fourth floor and 3 means elevator at the first floor.

As a concession to more recent times, though, we will:

  • track the number of actual different elements, because it will come handy later, and
  • fit this all in a hash with explicative keys, like microchips, generators, elevator, and n_elements.

As an example, let’s consider the input for the first part of the puzzle:

my $start_puzzle_1 = {
   elevator   => 0,
   generators => 0b00000001_00011110_00000000_00000000,
   microchips => 0b00000001_00000000_00011110_00000000,
   n_elements => 5,

Our goal will be:

my $goal_puzzle_1 = {
   elevator   => 0,
   generators => 0b00000000_00000000_00000000_00011111,
   microchips => 0b00000000_00000000_00000000_00011111,
   n_elements => 5,

For part 2 we will have instead:

my $start_puzzle_2 = {
   elevator   => 0,
   generators => 0b01100001_00011110_00000000_00000000,
   microchips => 0b01100001_00000000_00011110_00000000,
   n_elements => 7,

my $goal_puzzle_2 = {
   elevator   => 0,
   generators => 0b00000000_00000000_00000000_01111111,
   microchips => 0b00000000_00000000_00000000_01111111,
   n_elements => 7,

This will hopefully help us keep memory at bay… let’s hope for the best!

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