64 lines
3.5 KiB
Markdown
64 lines
3.5 KiB
Markdown
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# Day 7: The Treachery of Whales
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[https://adventofcode.com/2021/day/7](https://adventofcode.com/2021/day/7)
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## Description
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### Part One
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A giant [whale](https://en.wikipedia.org/wiki/Sperm_whale) has decided your submarine is its next meal, and it's much faster than you are. There's nowhere to run!
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Suddenly, a swarm of crabs (each in its own tiny submarine - it's too deep for them otherwise) zooms in to rescue you! They seem to be preparing to blast a hole in the ocean floor; sensors indicate a _massive underground cave system_ 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 blast a large enough hole for your submarine to get through. However, it doesn't look like they'll be aligned before the whale catches you! Maybe you 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 input). Crab submarines have limited fuel, so you need to find a way to make all of their horizontal positions match while requiring them to spend as little fuel as possible.
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For example, consider the following horizontal positions:
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16,1,2,0,4,2,7,1,2,14
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This means there's a crab with horizontal position `16`, a crab with 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. You could choose any horizontal position to align them all on, but the one 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 expensive outcomes include aligning at position `1` (`41` fuel), position `3` (`39` fuel), or position `10` (`71` fuel).
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Determine the horizontal position that the crabs can align to using the least 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 misunderstand crab engineering?
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As it turns out, crab submarine engines <span title="This appears to be due to the modial interaction of magneto-reluctance and capacitive duractance.">don't burn fuel at a constant rate</span>. Instead, each change of 1 step in horizontal position costs 1 more unit of fuel than the last: the first step costs `1`, the second step costs `2`, the third step costs `3`, and so on.
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As each crab moves, moving further becomes more expensive. This changes the best horizontal position to align them all on; in the example above, this 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; 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 fuel possible so they can make you an escape route! _How much fuel must they spend to align to that position?_
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