# Day 3: Toboggan Trajectory

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.

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:

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

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:

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

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).

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:

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

In this example, traversing the map using this slope would cause you to encounter 7 trees.

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?

This will need more memory than a default Retro build has, so start by building a version with a much larger memory footprint and support for 64-bit cells:

make CFLAGS="-DIMAGE_SIZE=8000000 -O2 -DBIT64"

I am doing this in a simple way, constructing a large enough map that I can just iterate through.

Some math.

My input file has 323 lines with 31 characters per line. With a horizontal distance of 3 per row, the last position will be at 969 characters out. So the lines need to be a little over 31 times longer than they are by default.

The easy way to do this is to duplicate the pointer and use s:append to concat them until I get it long enough. Five iterations is plenty, but I'll do a bit more since I suspect that I'll need a larger map for the second half.

~~~:extend (s-s)   #7 [ dup s:append ] times s:keep ; ~~~

We also need to raise the limit on temporary string size.

~~~#4096 !TempStringMax ~~~

With this, I can create an array for the inputs:

~~~'input-day-3 'INPUT s:const   (Count_the_number_of_lines) #0 INPUT [ drop n:inc ] file:for-each-line   (Create_the_array,_and_reserve_space) 'MAP d:create dup , allot   (Fill_in_the_array) MAP n:inc INPUT [ extend over store n:inc ] file:for-each-line drop ~~~

Now all that's left is to quickly iterate through it, increasing a counter for the horizontal distance.

~~~#0 #0 MAP [ over + fetch \$# eq? [ &n:inc dip ] if #3 + ] a:for-each   drop n:put nl ~~~

# Part 2

Time to check the rest of the slopes - you need to minimize the probability of a sudden arboreal 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.

In the above example, these slopes would find 2, 7, 3, 4, and 2 tree(s) respectively; multiplied together, these produce the answer 336.

What do you get if you multiply together the number of trees encountered on each of the listed slopes?

This is pretty much the same, except for the last one, which needs to ignore every other line.

I start by just running through each of the trivial slopes, reducing down the products.

~~~'Right var   :calculate   !Right   #0 #0 MAP [ over + fetch \$# eq? [ &n:inc dip ] if @Right + ] a:for-each   drop ;   { #1 #3 #5 #7 } #1 [ calculate * ] a:reduce ~~~

Then create a new MAP, discarding the odd lines.

~~~{ #0 MAP [ swap dup n:odd? [ nip ] if n:inc ] a:for-each } 'MAP const ~~~

And finally run through the final slope, multiplying by the other products to get the final answer.

~~~#0 #0 MAP [ over + fetch \$# eq? [ &n:inc dip ] if #1 + ] a:for-each   drop *   n:put nl ~~~