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90 lines
3.4 KiB
Markdown
90 lines
3.4 KiB
Markdown
3 years ago
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https://adventofcode.com/2021/day/7
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## \--- Day 7: The Treachery of Whales ---
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A giant [whale](https://en.wikipedia.org/wiki/Sperm_whale) has decided your
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submarine is its next meal, and it's much faster than you are. There's nowhere
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to run!
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Suddenly, a swarm of crabs (each in its own tiny submarine - it's too deep for
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them otherwise) zooms in to rescue you! They seem to be preparing to blast a
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hole in the ocean floor; sensors indicate a _massive underground cave system_
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just beyond where they're aiming!
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The crab submarines all need to be aligned before they'll have enough power to
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blast a large enough hole for your submarine to get through. However, it
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doesn't look like they'll be aligned before the whale catches you! Maybe you
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can help?
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There's one major catch - crab submarines can only move horizontally.
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You quickly make a list of _the horizontal position of each crab_ (your puzzle
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input). Crab submarines have limited fuel, so you need to find a way to make
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all of their horizontal positions match while requiring them to spend as
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little fuel as possible.
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For example, consider the following horizontal positions:
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[code]
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16,1,2,0,4,2,7,1,2,14
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[/code]
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This means there's a crab with horizontal position `16`, a crab with
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horizontal position `1`, and so on.
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Each change of 1 step in horizontal position of a single crab costs 1 fuel.
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You could choose any horizontal position to align them all on, but the one
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that costs the least fuel is horizontal position `2`:
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* Move from `16` to `2`: `14` fuel
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* Move from `1` to `2`: `1` fuel
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* Move from `2` to `2`: `0` fuel
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* Move from `0` to `2`: `2` fuel
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* Move from `4` to `2`: `2` fuel
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* Move from `2` to `2`: `0` fuel
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* Move from `7` to `2`: `5` fuel
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* Move from `1` to `2`: `1` fuel
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* Move from `2` to `2`: `0` fuel
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* Move from `14` to `2`: `12` fuel
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This costs a total of `_37_` fuel. This is the cheapest possible outcome; more
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expensive outcomes include aligning at position `1` (`41` fuel), position `3`
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(`39` fuel), or position `10` (`71` fuel).
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Determine the horizontal position that the crabs can align to using the least
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fuel possible. _How much fuel must they spend to align to that position?_
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## \--- Part Two ---
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The crabs don't seem interested in your proposed solution. Perhaps you
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misunderstand crab engineering?
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As it turns out, crab submarine engines don't burn fuel at a constant rate.
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Instead, each change of 1 step in horizontal position costs 1 more unit of
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fuel than the last: the first step costs `1`, the second step costs `2`, the
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third step costs `3`, and so on.
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As each crab moves, moving further becomes more expensive. This changes the
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best horizontal position to align them all on; in the example above, this
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becomes `5`:
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* Move from `16` to `5`: `66` fuel
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* Move from `1` to `5`: `10` fuel
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* Move from `2` to `5`: `6` fuel
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* Move from `0` to `5`: `15` fuel
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* Move from `4` to `5`: `1` fuel
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* Move from `2` to `5`: `6` fuel
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* Move from `7` to `5`: `3` fuel
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* Move from `1` to `5`: `10` fuel
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* Move from `2` to `5`: `6` fuel
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* Move from `14` to `5`: `45` fuel
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This costs a total of `_168_` fuel. This is the new cheapest possible outcome;
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the old alignment position (`2`) now costs `206` fuel instead.
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Determine the horizontal position that the crabs can align to using the least
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fuel possible so they can make you an escape route! _How much fuel must they
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spend to align to that position?_
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