added 2021/09-15

Author: kajott

2021/09/README.md

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+# 2021, Day 9: Smoke Basin
+
+These caves seem to be [lava tubes](https://en.wikipedia.org/wiki/Lava_tube). Parts are even still volcanically active; small hydrothermal vents release smoke into the caves that slowly settles like rain.
+
+If you can model how the smoke flows through the caves, you might be able to avoid it and be that much safer.
+
+## Part 1
+
+The submarine generates a heightmap of the floor of the nearby caves for you (your puzzle input).
+
+Smoke flows to the lowest point of the area it's in. For example, consider the following heightmap:
+
+    2199943210
+    3987894921
+    9856789892
+    8767896789
+    9899965678
+    
+
+Each number corresponds to the height of a particular location, where `9` is the highest and `0` is the lowest a location can be.
+
+Your first goal is to find the _low points_ - the locations that are lower than any of its adjacent locations. Most locations have four adjacent locations (up, down, left, and right); locations on the edge or corner of the map have three or two adjacent locations, respectively. (Diagonal locations do not count as adjacent.)
+
+In the above example, there are _four_ low points, all highlighted: two are in the first row (a `1` and a `0`), one is in the third row (a `5`), and one is in the bottom row (also a `5`). All other locations on the heightmap have some lower adjacent location, and so are not low points.
+
+The _risk level_ of a low point is _1 plus its height_. In the above example, the risk levels of the low points are `2`, `1`, `6`, and `6`. The sum of the risk levels of all low points in the heightmap is therefore _`15`_.
+
+Find all of the low points on your heightmap. _What is the sum of the risk levels of all low points on your heightmap?_
+
+Your puzzle answer was `577`.
+
+## Part 2
+
+Next, you need to find the largest basins so you know what areas are most important to avoid.
+
+A _basin_ is all locations that eventually flow downward to a single low point. Therefore, every low point has a basin, although some basins are very small. Locations of height `9` do not count as being in any basin, and all other locations will always be part of exactly one basin.
+
+The _size_ of a basin is the number of locations within the basin, including the low point. The example above has four basins.
+
+The top-left basin, size `3`. <br>
+The top-right basin, size `9`. <br>
+The middle basin, size `14`. <br>
+The bottom-right basin, size `9`.
+
+Find the three largest basins and multiply their sizes together. In the above example, this is `9 * 14 * 9 = `_`1134`_.
+
+_What do you get if you multiply together the sizes of the three largest basins?_
+
+Your puzzle answer was `1069200`.
+
+
+## Solution Notes
+
+For part 1, the task description already contains the implementation approach. For code golf, the usual "dictionary with complex numbers as keys" trick does the job admirably.
+
+Part 2 adds an additional flood fill step to the mix, which I implemented by means of breadth-first search. After implementing that, I noticed that the BFS doesn't need to start at a low point; the whole idea of the flood fill is that the whole basin is filled, so the start location doesn't matter. Thus, instead of identifying low points first, a simple list of all open deeper-than-9 points in the map can be used.
+
+* Part 1, Python: 185 bytes, <100 ms
+* Part 2, Python (using low point seeds): 328 bytes, <100 ms
+* Part 2, Python (using arbitrary seeds): 311 bytes, ~100 ms

2021/09/aoc2021_09_part1.py

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+E,M,Q=enumerate,{},lambda q:M.get(q,9)
+for y,l in E(open("input.txt")):
+ for x,i in E(l.strip()):M[x+1j*y]=int(i)
+print sum(M[p]+1for p in M if M[p]<min(Q(p+1),Q(p-1),Q(p-1j),Q(p+1j)))

2021/09/aoc2021_09_part2.py

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+E,M,Q=enumerate,{},lambda q:M.get(q,9)
+for y,l in E(open("input.txt")):
+ for x,i in E(l.strip()):M[x+1j*y]=int(i)
+def A(p):
+ v,q={p},{p}
+ while q:
+  v|=q;q=set()
+  for p in v:q|={x for x in(p+1,p-1,p+1j,p-1j)if Q(x)<9}-v
+ return len(v)
+b=sorted(A(p)for p in M if M[p]<min(Q(p+1),Q(p-1),Q(p-1j),Q(p+1j)))
+print b[-3]*b[-2]*b[-1]

2021/09/aoc2021_09_part2_try2.py

@@ -0,0 +1,12 @@
+E,M,Q=enumerate,{},lambda q:M.get(q,9)<9
+for y,l in E(open("input.txt")):
+ for x,i in E(l.strip()):M[x+1j*y]=int(i)
+a,b={p for p in M if Q(p)},[]
+while a:
+ p=a.pop();v,q={p},{p}
+ while q:
+  v|=q;q=set()
+  for p in v:q|={x for x in(p+1,p-1,p+1j,p-1j)if Q(x)}-v
+ b+=[len(v)];a-=v
+b.sort()
+print b[-3]*b[-2]*b[-1]

2021/09/input.txt

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