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--- Day 20: Trench Map ---
With the scanners fully deployed, you turn their attention to mapping the floor of the ocean trench.
When you get back the image from the scanners, it seems to just be random noise. Perhaps you can
combine an image enhancement algorithm and the input image (your puzzle input) to clean it up a
little.
For example:
..#.#..#####.#.#.#.###.##.....###.##.#..###.####..#####..#....#..#..##..##
#..######.###...####..#..#####..##..#.#####...##.#.#..#.##..#.#......#.###
.######.###.####...#.##.##..#..#..#####.....#.#....###..#.##......#.....#.
.#..#..##..#...##.######.####.####.#.#...#.......#..#.#.#...####.##.#.....
.#..#...##.#.##..#...##.#.##..###.#......#.#.......#.#.#.####.###.##...#..
...####.#..#..#.##.#....##..#.####....##...##..#...#......#.#.......#.....
..##..####..#...#.#.#...##..#.#..###..#####........#..####......#..#
#..#.
#....
##..#
..#..
..###
The first section is the [1m[97mimage enhancement algorithm[0m. It is normally given on a single line, but it
has been wrapped to multiple lines in this example for legibility. The second section is the
[1m[97minput image[0m, a two-dimensional grid of [1m[97mlight pixels[0m (#) and [1m[97mdark pixels[0m (.).
The image enhancement algorithm describes how to enhance an image by [1m[97msimultaneously[0m converting all
pixels in the input image into an output image. Each pixel of the output image is determined by
looking at a 3x3 square of pixels centered on the corresponding input image pixel. So, to determine
the value of the pixel at (5,10) in the output image, nine pixels from the input image need to be
considered: (4,9), (4,10), (4,11), (5,9), (5,10), (5,11), (6,9), (6,10), and (6,11). These nine
input pixels are combined into a single binary number that is used as an index in the [1m[97mimage
enhancement algorithm[0m string.
For example, to determine the output pixel that corresponds to the very middle pixel of the input
image, the nine pixels marked by [...] would need to be considered:
# . . # .
#[. . .].
#[# . .]#
.[. # .].
. . # # #
Starting from the top-left and reading across each row, these pixels are ..., then #.., then .#.;
combining these forms ...#...#.. By turning dark pixels (.) into 0 and light pixels (#) into 1, the
binary number 000100010 can be formed, which is 34 in decimal.
The image enhancement algorithm string is exactly 512 characters long, enough to match every
possible 9-bit binary number. The first few characters of the string (numbered starting from zero)
are as follows:
0 10 20 30 [1m[97m34[0m 40 50 60 70
| | | | [1m[97m|[0m | | | |
..#.#..#####.#.#.#.###.##.....###.[1m[97m#[0m#.#..###.####..#####..#....#..#..##..##
In the middle of this first group of characters, the character at index 34 can be found: #. So, the
output pixel in the center of the output image should be #, a [1m[97mlight pixel[0m.
This process can then be repeated to calculate every pixel of the output image.
Through advances in imaging technology, the images being operated on here are [1m[97minfinite[0m in size.
[1m[97mEvery[0m pixel of the infinite output image needs to be calculated exactly based on the relevant pixels
of the input image. The small input image you have is only a small region of the actual infinite
input image; the rest of the input image consists of dark pixels (.). For the purposes of the
example, to save on space, only a portion of the infinite-sized input and output images will be
shown.
The starting input image, therefore, looks something like this, with more dark pixels (.) extending
forever in every direction not shown here:
...............
...............
...............
...............
...............
.....#..#......
.....#.........
.....##..#.....
.......#.......
.......###.....
...............
...............
...............
...............
...............
By applying the image enhancement algorithm to every pixel simultaneously, the following output
image can be obtained:
...............
...............
...............
...............
.....##.##.....
....#..#.#.....
....##.#..#....
....####..#....
.....#..##.....
......##..#....
.......#.#.....
...............
...............
...............
...............
Through further advances in imaging technology, the above output image can also be used as an input
image! This allows it to be enhanced [1m[97ma second time[0m:
...............
...............
...............
..........#....
....#..#.#.....
...#.#...###...
...#...##.#....
...#.....#.#...
....#.#####....
.....#.#####...
......##.##....
.......###.....
...............
...............
...............
Truly incredible - now the small details are really starting to come through. After enhancing the
original input image twice, [1m[97m35[0m pixels are lit.
Start with the original input image and apply the image enhancement algorithm twice, being careful
to account for the infinite size of the images. [1m[97mHow many pixels are lit in the resulting image?[0m
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