81 lines
4.0 KiB
Markdown
81 lines
4.0 KiB
Markdown
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# 2020 Day 3: Toboggan Trajectory
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Copyright (c) Eric Wastl
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#### [Direct Link](https://adventofcode.com/2020/day/3)
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## Part 1
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With the toboggan login problems resolved, you set off toward the airport. While travel by toboggan might be easy, it's certainly not safe: there's very minimal steering and the area is covered in trees. You'll need to see which angles will take you near the fewest trees.
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Due to the local geology, trees in this area only grow on exact integer coordinates in a grid. You make a map (your puzzle input) of the open squares (`.`) and trees (`#`) you can see. For example:
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```
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..##.......
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#...#...#..
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.#....#..#.
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..#.#...#.#
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.#...##..#.
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..#.##.....
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.#.#.#....#
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.#........#
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#.##...#...
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#...##....#
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.#..#...#.#
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```
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These aren't the only trees, though; due to something you read about once involving arboreal genetics and biome stability, the same pattern repeats to the right many times:
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```
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..##.........##.........##.........##.........##.........##....... --->
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#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
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.#....#..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
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..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
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.#...##..#..#...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
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..#.##.......#.##.......#.##.......#.##.......#.##.......#.##..... --->
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.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
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.#........#.#........#.#........#.#........#.#........#.#........#
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#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...
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#...##....##...##....##...##....##...##....##...##....##...##....#
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.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.# --->
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```
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You start on the open square (`.`) in the top-left corner and need to reach the bottom (below the bottom-most row on your map).
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The toboggan can only follow a few specific slopes (you opted for a cheaper model that prefers rational numbers); start by **counting all the trees** you would encounter for the slope **right 3, down 1**:
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From your starting position at the top-left, check the position that is right 3 and down 1. Then, check the position that is right 3 and down 1 from there, and so on until you go past the bottom of the map.
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The locations you'd check in the above example are marked here with `O` where there was an open square and `X` where there was a tree:
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```
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..##.........##.........##.........##.........##.........##....... --->
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#..O#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
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.#....X..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
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..#.#...#O#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
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.#...##..#..X...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
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..#.##.......#.X#.......#.##.......#.##.......#.##.......#.##..... --->
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.#.#.#....#.#.#.#.O..#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
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.#........#.#........X.#........#.#........#.#........#.#........#
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#.##...#...#.##...#...#.X#...#...#.##...#...#.##...#...#.##...#...
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#...##....##...##....##...#X....##...##....##...##....##...##....#
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.#..#...#.#.#..#...#.#.#..#...X.#.#..#...#.#.#..#...#.#.#..#...#.# --->
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```
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In this example, traversing the map using this slope would cause you to encounter **`7`** trees.
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Starting at the top-left corner of your map and following a slope of right 3 and down 1, **how many trees would you encounter?**
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## Part 2
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Time to check the rest of the slopes - you need to minimize the probability of a sudden arboreal stop, after all.
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Determine the number of trees you would encounter if, for each of the following slopes, you start at the top-left corner and traverse the map all the way to the bottom:
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- Right 1, down 1.
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- Right 3, down 1. (This is the slope you already checked.)
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- Right 5, down 1.
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- Right 7, down 1.
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- Right 1, down 2.
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In the above example, these slopes would find `2`, `7`, `3`, `4`, and `2` tree(s) respectively; multiplied together, these produce the answer **`336`**.
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**What do you get if you multiply together the number of trees encountered on each of the listed slopes?**
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