Updated puzzle commentary for days 13, 14, 15, and 16

README.md

@@ -88,6 +88,40 @@ While parsing the input, we track coordinates of each galaxy, and for each row a
 
 This approach was trivial to adapt for part 2, since all that was needed was another factor that had to be multiplied with the values tracked for the rows and columns before applying the *+1*.
 
+## Day 13: Point of Incidence
+
+<https://adventofcode.com/2023/day/13>
+
+While going through each line, the algorithm keeps updating two lists of mirror candidates, separately for horizontal and vertical mirrors. For horizontal mirrors, a new candidate is added whenever two consecutive lines are identical. After it is added, new lines are each compared against the potentially mirrored earlier line, until the candidate is discarded or the last line successfully mirrored.
+
+For vertical mirrors, all candidates are added during processing of the first line, based on whether they mirror the first line or not. While processing further lines, each candidates is verified against each line or discarded.
+
+To solve part 2 as well, each candidate tracks whether one character was switched or not to successfully mirror all processed lines. If a second character switch is required or no switch had occurred at the end, the candidate is discarded. By setting this tracker as if a switch had already happened even for new candidates, both parts of the puzzle can be solved simultanously.
+
+## Day 14: Parabolic Reflector Dish
+
+<https://adventofcode.com/2023/day/14>
+
+I spent too much time on this one. I had originally implemented a relatively naive algorithm that would do the tilting of the platform by operating directly the string list, swapping out round rocks as it went, which seemed quite slow.
+
+So I reimplemented the whole thing with proper data structures consisting of lists of non-empty intervals between cube-shaped rocks, and lists of rows and columns of rounded rocks, between which the algorithm would alternate, to facilitate a faster computation without string manipulation. This improved the performance of the algorithm, but unfortunately not as much as I had expected.
+
+An essential revelation to make any algorithm for this work is that the formations of the rounded rocks on the platform repeat while spinning it 1,000,000,000 times, so once a previous formation is discovered, the calculation can be severly short-cut.
+
+## Day 15: Lens Library
+
+<https://adventofcode.com/2023/day/15>
+
+Pretty straight-forward implementation of a HASHMAP with custom HASH function.
+
+## Day 16: The Floor Will Be Lava
+
+<https://adventofcode.com/2023/day/16>
+
+Here I calculate how a beam traverses through the grid until it is reflected out of the grid. Everytime it hits a splitter a new beam is put on a stack to be calculated later. I found the difficulty to be to find a good way to track how a beam has already travelled through the grid. This seems essential to detect when calculation for a part of the beam can be aborted, since splitters can create loops. However, two beams could pass through the same tile without meeting. I settled for tracking four energy states for each tile of the grid, one being "not energized", two describing generically the two directions a beam could travel through some tiles, and one for the combination of those two directions, and then using the energy state of the current field and the beam's direction to stop it before it leaves the boundaries of the grid.
+
+Once this was solved for one starting beam in part 1, I just iterated over all possible starting beams to find the maximum for part 2.
+
 ## License
 
 Copyright (C) 2023 Stefan Müller