Toboggan Trajectory


Description

You need to get to the airport and can only travel by a toboggan through a tree covered area. The 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:

..##.......
#...#...#..
.#....#..#.
..#.#...#.#
.#...##..#.
..#.##.....
.#.#.#....#
.#........#
#.##...#...
#...##....#
.#..#...#.#

These aren’t the only trees, though; the same pattern repeats to the right many times:

..##.........##.........##.........##.........##.........##.......  --->
#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
.#....#..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
.#...##..#..#...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
..#.##.......#.##.......#.##.......#.##.......#.##.......#.##.....  --->
.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
.#........#.#........#.#........#.#........#.#........#.#........#
#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...#.##...#...
#...##....##...##....##...##....##...##....##...##....##...##....#
.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#.#..#...#.#  --->

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. 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:

..##.........##.........##.........##.........##.........##.......  --->
#..O#...#..#...#...#..#...#...#..#...#...#..#...#...#..#...#...#..
.#....X..#..#....#..#..#....#..#..#....#..#..#....#..#..#....#..#.
..#.#...#O#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#..#.#...#.#
.#...##..#..X...##..#..#...##..#..#...##..#..#...##..#..#...##..#.
..#.##.......#.X#.......#.##.......#.##.......#.##.......#.##.....  --->
.#.#.#....#.#.#.#.O..#.#.#.#....#.#.#.#....#.#.#.#....#.#.#.#....#
.#........#.#........X.#........#.#........#.#........#.#........#
#.##...#...#.##...#...#.X#...#...#.##...#...#.##...#...#.##...#...
#...##....##...##....##...#X....##...##....##...##....##...##....#
.#..#...#.#.#..#...#.#.#..#...X.#.#..#...#.#.#..#...#.#.#..#...#.#  --->

Part 1

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?

Part 2

Time to check the rest of the slopes - you need to minimize the probability of a sudden tree stop, after all.

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:

Right 1, down 1.
Right 3, down 1. (This is the slope you already checked.)
Right 5, down 1.
Right 7, down 1.
Right 1, down 2.

Solution your_name_here

There are a few different solutions, each with different complexities.

# Insert solution here