[2022] [Day 12]: Hill Climbing Algorithm

[victoraugustofd]

Challenge description

You try contacting the Elves using your handheld device, but the river you're following must be too low to get a decent signal.

You ask the device for a heightmap of the surrounding area (your puzzle input). The heightmap shows the local area from above broken into a grid; the elevation of each square of the grid is given by a single lowercase letter, where a is the lowest elevation, b is the next-lowest, and so on up to the highest elevation, z.

Also included on the heightmap are marks for your current position (S) and the location that should get the best signal (E). Your current position (S) has elevation a, and the location that should get the best signal (E) has elevation z.

You'd like to reach E, but to save energy, you should do it in as few steps as possible. During each step, you can move exactly one square up, down, left, or right. To avoid needing to get out your climbing gear, the elevation of the destination square can be at most one higher than the elevation of your current square; that is, if your current elevation is m, you could step to elevation n, but not to elevation o. (This also means that the elevation of the destination square can be much lower than the elevation of your current square.)

For example:

Sabqponm
abcryxxl
accszExk
acctuvwj
abdefghi

Here, you start in the top-left corner; your goal is near the middle. You could start by moving down or right, but eventually you'll need to head toward the e at the bottom. From there, you can spiral around to the goal:

v..v<<<<
>v.vv<<^
.>vv>E^^
..v>>>^^
..>>>>>^

In the above diagram, the symbols indicate whether the path exits each square moving up (^), down (v), left (<), or right (>). The location that should get the best signal is still E, and . marks unvisited squares.

This path reaches the goal in 31 steps, the fewest possible.

What is the fewest steps required to move from your current position to the location that should get the best signal?

Challenge input

abccccccaaccaaccccaaaaacccccaaaaccccccccccccccccccccccccccccccccaaaaaaaaaaaaaaaaaaaccccccccccccccccaaaccccccccccccaacccccccccccccccccccccccccccccccccccccccccaaaa
abaaaaccaaaaaccccaaaaaccccccaaaaccccccccccccccccccccaaacccccccccccaaaaaaaaaaaaaaaaaaccccccccccccccccaaaaccccccaaacaaccccccccccccccccccccccccccccccccccccccccaaaaa
abaaacccaaaaaaaacaaaaaacccccaaaaccccccccccccccccccccaaaaacccccccccaaaaaaaaaaaaaaaaacccccccccaaccccaaaaaacccccccaaaaaccccaaccccccccccccccacccccccccccccccccccaaaaa
abaaacccccaaaaaccccaaaaccccccaaacccccccccccccccccccaaaaaccccccccccaaaaaacacaaaaaacccccccccccaaccccaaaaacccccccccaaaaaaccaaaaaaccccccccccaaaccccacccccccccccaaaaaa
abaacccccaaaaaccccaacccccccccccccccaaaaacccccccccccaaaaacccccccccaaaaaaaaccaaaaaaacccccccaaaaaaaaccaaaaacccccccaaaaaaaccaaaaacccccccccccaaacccaaaccccccccccccccaa
abaaacccaaacaacccccccccccccccccccccaaaaaccccccccccccaaaaacccccccaaaaaaaaaccaaccaaacccccccaaaaaaaaccaacccccccccaaaaaaccaaaaaaccccccccccccaaaacaaaaccccccccccccccaa
abaaacccccccaaccccccccccccccccccccaaaaaaccccccccccccaaccccccaacccaaaccaaaaccccccaacccccccccaaaacccccccccccccccaacaaaccaaaaaaaccccccccccccajjjjjjjcccccccccccccccc
abcaacccccccccccccccccccccccccccccaaaaaaccccccccccccccccccccaaaaccccccaaaaccccccccccccccaacaaaaaccccccccccccccccccaaccccaaaaaacccccccccccjjjjjjjjjcccccaaaccccccc
abccccccccccccccccccccccccccccccccaaaaaaccaaccccccccccccccaaaaaacccccccaaacccccccccccaacaaaaaaaaccccccccccccccccccccccccaaccaaccccccccaiijjjjojjjjcccccaaacaccccc
abcccccccccccccccccccccccaaacccccccaaacacaaacccccccccccccccaaaaccccaaccccccccccccccccaaaaaaacccaccccccccccccccccccccccccaacccccccccccaiiijjooooojjkccaaaaaaaacccc
abccccccccccccccccccccccaaaaccccccccccaaaaaccccccccccccccccaaaaacccaaaaaccccccccccccccaaaaaacccccccccccccccccccccccccccccccccccccciiiiiiiioooooookkkcaaaaaaaacccc
abccccccccccccccccccccccaaaaccccccccccaaaaaaaacccccccccccccaacaaccaaaaacccccccaaacccaaaaaaaaccccccccccccccccccccccccccccccccccchiiiiiiiiooooouoookkkccaaaaaaccccc
abcccccccccaaccccccccccccaaaccccccccccccaaaaacccccccccccccccccccccaaaaaccccccaaaacccaaaaacaacccccccccccccaacaacccccccccccccccchhhiiiinnnooouuuuoookkkccaaaaaccccc
abcccccccccaaacccccccccccccccccccccccccaaaaacccccccccccccccccccccccaaaaacccccaaaaccccccaaccccccccccccccccaaaaacccccccccccccccchhhnnnnnnnnouuuuuuppkkkkaaaaaaccccc
abccccccaaaaaaaacccaaccccccccccccccccccaacaaccaacaaccccccccccccccccaacccccccccaaaccccccaacccccccccccccccaaaaacccccccccccccccchhhnnnnnnnnntuuxuuupppkkkkkacccccccc
abccccccaaaaaaaacacaaaacccccccccccccccccccaaccaaaaacccccccccccccccccccccccccccccccccccccccccccccccccccccaaaaaacccccccaacccccchhhnnnnttttttuxxxuuppppkkkkkcccccccc
abcccccccaaaaaaccaaaaaaccccccccccaaccccccccccaaaaaccccccccccccccccccccccccaaacccccccccccccccccccccccccccccaaaaccaaccaaacccaaahhhnnntttttttuxxxxuupppppllllccccccc
abcccccccaaaaaacccaaaacccccccccaaaaaaccccccccaaaaaacccccccccccccccccccccccaaacccccccccccccccccccccccccccccacccccaaaaaaacaaaaahhhppntttxxxxxxxxuuuuvpppplllccccccc
abcccccccaaaaaacccaaaacccccccccaaaaaacccccaaaaaaaaaccccccccccccccccccccaaaaaaaacccccccccccccccccccccaaaccccccaacaaaaaaccaaaaahhhpppttxxxxxxxxyuuvvvvvppplllcccccc
abcccccccaaccaacccaacaccaaaaccccaaaaacccccaaaaaaaaaccccccccccccccccccccaaaaaaaacccccccccccccccccccccaaacaaaaaaaccaaaaaaaaaaaaahhppptttxxxxxxyyyyyyvvvppplllcccccc
SbccccccccccccccccccccccaaaacccaaaaacccccccaaaaaaaaacaaaccccccccaacccccccaaaaaccccccccaaaaacccccccccaaaaaaaaaaaaaaaaaaaaaaaaacgggpppttxxxxEzzyyyyyvvvqqqlllcccccc
abccccccccccccccccccccccaaaacccaaaaacccccccaaaaaaaaccaaaccccccccaaacaaccaaaaaaccccccccaaaaacccccccaaaaaaaaaaaaaaaaaaaaaaaaaaacgggpppsssxxxyyyyyyvvvvvqqlllccccccc
abcccaaaccccccccccccccccaaaccccccccccccccccaaaaaaaaaaaaaccccccccaaaaaaccaaaaaacccccccaaaaaacccaaaccaaaaaccaaaaaaaaaaaacccccccccgggppssswwyyyyyyvvvvqqqqlllccccccc
abcaaaaaccccccccccccccccccccccccccccccccccaaaaaaaaaaaaacccccccaaaaaaacccaccaaacccccccaaaaaacccaaacccaaaaaaaaaaaccccaaacccaaaaacgggppsswwwyyyyyyvvqqqqqlllcccccccc
abcaaaaaaccccccccccccccccccccccccccccccccccaaccaaaaaaaaaaaccccaaaaaaacccccccccccccccccaaaaacccaaacaaaacaaaaaaaaccccaaacccaaaaacggpppsswwwywwyyyvvqqqmmmlccccccccc
abcaaaaaacccccccaacaaccccccccccccccccccccccccccaaaaaaaaaaaccccccaaaaacccccccccccccccccaaaccaaaaaaaaaaacccccccaacccccccccaaaaaacggpppsswwwwwwwwyvvqqqmmmcccccccccc
abcaaaaaccccccccaaaaaccccccccccccccccccccccccccccaaaaaaaacccccccaacaaacccccccccccccccccccccaaaaaaaaaccccccccccccccccccccaaaaaagggoossswwwwrrwwwvvqqmmmccccccccccc
abcaaaaacccccccaaaaaccccccccccccccccccccccccccccaaaaaaacccccccccaaccccccccccccccccccccccccccaaaaaaacccccccccccaaaccccccccaaaaagggooosssssrrrrwwwvqqmmmcccaacccccc
abcccccccccccccaaaaaaccccccccccccccccccccaacccccccccaaaccccccccccccccccccccccccccccccccccccccaaaaaaccccccccccccaaaaccccccaaaccgggooosssssrrrrrwwrrqmmmcccaacccccc
abcccccccccccccccaaaacccccccccccccccccccaaaacccccccacaaacccccccccccccccccccccccccccccccccccccaaaaaaacccccccccaaaaaacccccccccccgffoooooosoonrrrrrrrrmmmccaaaaacccc
abcccccccccccccccaccccccccccccccccccccccaaaacccccccaaaaacccccccccccccccccccccccccccccccccccccaaacaaacccccccccaaaaacccccccccccccfffoooooooonnnrrrrrmmmddcaaaaacccc
abccccccccccccccccccccccccccccccccccccccaaaaccccccccaaaaacccccccccccccccccccccccccaaaccccccccaacccccccccccccccaaaaaccccccccccccffffoooooonnnnnnrnnmmmdddaaaaacccc
abcccccccccccccccccccccccccccccccccccccccccccccccccaaaaaacccccccccccccccccaaaaaccaaaacccccccccccccccccccccccccaacccccccccccccccfffffffffeeeennnnnnmmdddaaaacccccc
abcccccccaaaccccccccaccccccccccccccccccccccccccccccaaaaccccccccccccaaaccccaaaaaccaaaaccccccccccccccccccccccccccccccccccccccccccccfffffffeeeeennnnnmddddaaaaaccccc
abcccaaccaaacccccaaaacccccaacccccccccccccccccccccccccaaacccccccccccaaacccaaaaaacccaaaccccccccccccccccccccccccccccccccccccccccccccccffffeeeeeeeedddddddcccaacccccc
abcccaaaaaaacccccaaaaaaccaaacccccccccccccccccccccccccccacccccccccccaaaaccaaaaaaccccccccccccccccccccccccccaacccccccccaaaccccccccccccccaaaaaaeeeeedddddcccccccccccc
abcccaaaaaacccccccaaaacccaaacaaaccccaaaacccccccccaaacaaaccccccaacccaaaacaaaaaaacccccccccccccccccccccccccaaaccccccccaaaacccccccccccccccccccaaaaeeddddccccccccccccc
abccccaaaaaaaacccaaaaaaaaaaaaaaaccccaaaacccccccccaaaaaaacccccaaacccaaaaaaaaaacccccccccccccccccccccccaaacaaaccccccccaaaaccccccccccccccccccccaaaccccccccccccccaaaca
abcccaaaaaaaaacccaacaaaaaaaaaaacccccaaaaccccccccccaaaaaacaaacaaacaaaaaaaaaacccccccccccccccaaacccccccaaaaaaaaaaccccccaaaccccccccccccccccccccaacccccccccccccccaaaaa
abcccaaaaaaaacccccccccccaaaaaacccccccaacccccccccccaaaaaaaaaaaaaaaaaaaaaaaaccccccccccccccccaaaacccccccaaaaaaaaacccccccccccccccccccccccccccccaaacccccccccccccccaaaa
abccaaaaaaacccccccccccccaaaaaaacccccccccccccccccaaaaaaaaaaaaaaaaaaaaaaaaaaacccccccccccccccaaaacccccccaaaaaaaacccccccccccccccccccccccccccccccccccccccccccccccaaaaa

Challenge year

2022

[victoraugustofd]

Challenge link

https://adventofcode.com/2022/day/12