The Historians are quite pixelated again. This time, a massive, black building looms over you - you're right outside the CPU!
While The Historians get to work, a nearby program sees that you're idle and challenges you to a race. Apparently, you've arrived just in time for the frequently-held race condition festival!
The race takes place on a particularly long and twisting code path; programs compete to see who can finish in the fewest picoseconds. The winner even gets their very own mutex!
They hand you a map of the racetrack (your puzzle input). For example:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...#...#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
The map consists of track (.
) - including the start (S
) and end (E
) positions (both of which also count as track) - and walls (#
).
When a program runs through the racetrack, it starts at the start position. Then, it is allowed to move up, down, left, or right; each such move takes 1 picosecond. The goal is to reach the end position as quickly as possible. In this example racetrack, the fastest time is 84
picoseconds.
Because there is only a single path from the start to the end and the programs all go the same speed, the races used to be pretty boring. To make things more interesting, they introduced a new rule to the races: programs are allowed to cheat.
The rules for cheating are very strict. Exactly once during a race, a program may disable collision for up to 2 picoseconds. This allows the program to pass through walls as if they were regular track. At the end of the cheat, the program must be back on normal track again; otherwise, it will receive a segmentation fault and get disqualified.
So, a program could complete the course in 72
picoseconds (saving 12 picoseconds
) by cheating for the two moves marked 1
and 2
:
###############
#...#...12....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...#...#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
Or, a program could complete the course in 64
picoseconds (saving 20 picoseconds
) by cheating for the two moves marked 1
and 2
:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...12..#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
This cheat saves 38 picoseconds
:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..E#...#...#
###.####1##.###
#...###.2.#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
This cheat saves 64 picoseconds
and takes the program directly to the end:
###############
#...#...#.....#
#.#.#.#.#.###.#
#S#...#.#.#...#
#######.#.#.###
#######.#.#...#
#######.#.###.#
###..21...#...#
###.#######.###
#...###...#...#
#.#####.#.###.#
#.#...#.#.#...#
#.#.#.#.#.#.###
#...#...#...###
###############
Each cheat has a distinct start position (the position where the cheat is activated, just before the first move that is allowed to go through walls) and end position; cheats are uniquely identified by their start position and end position.
In this example, the total number of cheats (grouped by the amount of time they save) are as follows:
- There are
14
cheats that save2
picoseconds. - There are
14
cheats that save4
picoseconds. - There are
2
cheats that save6
picoseconds. - There are
4
cheats that save8
picoseconds. - There are
2
cheats that save10
picoseconds. - There are
3
cheats that save12
picoseconds. - There is
1
cheat that saves20
picoseconds. - There is
1
cheat that saves36
picoseconds. - There is
1
cheat that saves38
picoseconds. - There is
1
cheat that saves40
picoseconds. - There is
1
cheat that saves64
picoseconds.
You aren't sure what the conditions of the racetrack will be like, so to give yourself as many options as possible, you'll need a list of the best cheats.
How many cheats would save you at least 100 picoseconds?