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‎README.md

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| 6 | [source](src/advent_2021_clojure/day06.clj) | [blog](docs/day06.md) |
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| 7 | [source](src/advent_2021_clojure/day07.clj) | [blog](docs/day07.md) |
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| 8 | [source](src/advent_2021_clojure/day08.clj) | [blog](docs/day08.md) |
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| 9 | [source](src/advent_2021_clojure/day09.clj) | [blog](docs/day09.md) |

‎docs/day09.md

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# Day Nine: Smoke Basin
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* [Problem statement](https://adventofcode.com/2021/day/9)
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* [Solution code](https://github.com/abyala/advent-2021-clojure/blob/master/src/advent_2021_clojure/day09.clj)
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---
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## Preamble
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This year, I seem to be on a quest to replace anonymous functions of the form `#(foo %)` with partial functions and
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the use of `juxt` and `comp`. I'm not sure why that is, but it seems to be a pattern. I have discussed `partial`,
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`juxt`, and `comp` in previous problems this season, so I won't be explaining them anymore, so feel free to look back
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if things are starting to look funny.
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---
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## Part 1
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When exploring underwater caves, one does run the risk of running into
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[liquid hot magma](https://www.youtube.com/watch?v=UNJU-5vCrJc), which apparently we have done today. We need to
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navigate the cave carefully. In part 1, we need to identify all points within the cave that are local minima (smaller
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than all cardinal neighbors), increment their heights and add the results together.
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In most such problems, I tend to convert the entire input into one giant map of coordinates to values, in the shape of
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`{[x y] v}`, but for a change of pace I decided to go old-school and use nested vectors. So my core data structure
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is simply `[[values]]`. Thus to parse the cave from the initial input, I split the input string into a sequence of
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strings for each line, and then we have a fun line `(mapv (partial mapv (comp parse-int str)) line)`. So let's piece
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this together. The outer `mapv` says we're going to create a vector from mapping each line to the internal function;
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we need `mapv` to ensure we get an outer vector, since we'll be accessing it by index. The inner function can be
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partial because we're calling `(mapv (comp parse-int str) line)` where `line` is fed in from the outer `mapv`. Each
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inner line is a numeric string, so we need to convert each character to its integer value. I implemented a `char->int`
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function in the `utils` package to perform this.
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```clojure
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; advent-2021-clojure.utils namespace
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(defn char->int [c] (- (int c) 48))
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; advent-2021-clojure.day09 namespace
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(defn parse-cave [input] (->> (str/split-lines input)
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(mapv (partial mapv utils/char->int))))
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```
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Next, we need to find all of the lowest points in the cave, so we'll need four functions to get there. First, the
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`neighbors` function in the `advent-2021-clojure.point` namespace will return the coordinates of the four points
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adjacent to a single point. This is one of those instances of using `(mapv f coll1 coll2)` instead of the normal
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`(mapv f coll)`, where the mapping function gets applied to the nth instance of multiple collections. This lets us
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add the `x` and `y` coordinates of two points together.
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The `lowest-point?` function checks if a single point in a cave is a local low point. This is the first of several
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instances where we'll be calling `(get-in cave point)`. `get-in` takes in a collection and a vector of nested values
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to apply to get to a sub-value in a collection, or `nil` if that value does not exist in the collection. So
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`(get-in {:name {:first "Franklin" :middle "Delano" :last "Roosevelt"}} [:name :middle])` returns `"Delano"`, and for
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vectors, `(get-in [:a :b [:c :d :e]] [2 2])` returns `:e`. Thus we get the value of a point (which is a vector) within
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the cave by calling `(get-in cave point)`. Then we find all neighbors to the given point, keep the ones that exist
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within the cave by calling `keep`, and then ensure that the point's height is lower than all of its neighbors.
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With that function, it's easy to find all of the lowest points. `all-coords` will return all `[y x]` coordinates in
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the cave; note that we use `[y x]` instead of `[x y]` because the outer vector of our `[[values]]` data structure is
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the row, which is indexed by `y`, and the inner vector is the column, which is indexed by `x`. Finally, in
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`lowest-points`, we take all of the coordinates in the cave, and filter them to the ones that pass `lowest-point?`.
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```clojure
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; advent-2021-clojure.point namespace
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(defn neighbors [point]
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(map (partial mapv + point) [[0 1] [0 -1] [-1 0] [1 0]]))
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; advent-2021-clojure.day09 namespace
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(defn lowest-point? [cave point]
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(let [height (get-in cave point)]
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(->> (neighbors point)
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(keep (partial get-in cave))
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(every? (partial < height)))))
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(defn all-coords [cave] (for [y (-> cave count range)
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x (-> cave first count range)]
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[y x]))
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(defn lowest-points [cave]
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(filter (partial lowest-point? cave) (all-coords cave)))
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```
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Finally, we're ready to write `part1`. Starting with the coordinates of all of the lowest points in the cave, we map
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them to their actual values, increment each one, and add them together.
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```clojure
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(defn part1 [input]
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(let [cave (parse-cave input)]
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(->> (lowest-points cave)
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(map (partial get-in cave))
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(map inc)
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(apply +))))
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```
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Have we reached the low point of our problem today? Let's find out.
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---
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## Part 2
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Now we need to find all of the "basins" in the cave, a section whose phrasing I found incredibly misleading. The
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instructions say, in part, "A basin is all locations that eventually flow downward <u>to a single low point</u>"
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(emphasis added). That last part is untrue. What the problem seems to mean is "a basin is all locations that are
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fully enclosed by either the outer wall or a 9." It appears that a basin can happily contain two or more low points.
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So the way I want to find the basins is to go to each lowest point, and find the basin around it by moving outward
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until we hit either a wall or a 9. For this, we'll first start with a `high-point?` function, which just returns
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whether a coordinate in the cave equals the max value of 9.
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Then, the `basin-around` function takes in a cave and a low point, and returns the set of all coordinates within that
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basin. We'll use the recursive `loop-recur` construct, in which I often use the bindings of `candidates` (what I'm
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looping over) and `found` (the accumulated values). If there are candidate points to inspect, which we can tell by
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calling `(if-some [point (first candidates)])`, then we continue to the loop, and if not then we return the set of
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found points. When looping, we remove the current point from the `candidates` with `(rest candidates)`, and then add
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the all neighbors of that point that are in the cave, but which are not either already found or are themselves high
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points.
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```clojure
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(def max-height 9)
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(defn high-point? [cave point] (= max-height (get-in cave point)))
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(defn basin-around [cave lowest-point]
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(loop [candidates #{lowest-point}, found #{}]
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(if-some [point (first candidates)]
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(recur (reduce conj (rest candidates) (->> (point/neighbors point)
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(filter (partial get-in cave))
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(remove (some-fn found (partial high-point? cave)))))
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(conj found point))
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found)))
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```
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And then we're ready to build `part2`. Starting from each of the lowest points, we map each one first to its basin
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(expressed as its set of points), which we then convert to the number of points within the basin. Then
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`(sort-by -)` puts them in reverse size order, from which we take the top three and multiply those values together.
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```clojure
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(defn part2 [input]
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(let [cave (parse-cave input)]
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(->> (lowest-points cave)
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(map (comp count (partial basin-around cave)))
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(sort-by -)
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(take 3)
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(apply *))))
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```

‎resources/day09_data.txt

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‎src/advent_2021_clojure/day09.clj

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(ns advent-2021-clojure.day09
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(:require
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[advent-2021-clojure.point :as point]
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[advent-2021-clojure.utils :as utils :refer [parse-int]]
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[clojure.string :as str]))
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(defn parse-cave [input] (->> (str/split-lines input)
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(mapv (partial mapv utils/char->int))))
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(defn lowest-point? [cave point]
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(let [height (get-in cave point)]
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(->> (point/neighbors point)
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(keep (partial get-in cave))
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(every? (partial < height)))))
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(defn all-coords [cave] (for [y (-> cave count range)
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x (-> cave first count range)]
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[y x]))
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(defn lowest-points [cave]
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(filter (partial lowest-point? cave) (all-coords cave)))
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(defn part1 [input]
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(let [cave (parse-cave input)]
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(->> (lowest-points cave)
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(map (partial get-in cave))
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(map inc)
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(apply +))))
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(def max-height 9)
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(defn high-point? [cave point] (= max-height (get-in cave point)))
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(defn basin-around [cave lowest-point]
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(loop [candidates #{lowest-point}, found #{}]
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(if-some [point (first candidates)]
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(recur (reduce conj (rest candidates) (->> (point/neighbors point)
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(filter (partial get-in cave))
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(remove (some-fn found (partial high-point? cave)))))
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(conj found point))
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found)))
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(defn part2 [input]
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(let [cave (parse-cave input)]
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(->> (lowest-points cave)
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(map (comp count (partial basin-around cave)))
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(sort-by -)
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(take 3)
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(apply *))))

‎src/advent_2021_clojure/point.clj

+3
Original file line numberDiff line numberDiff line change
@@ -27,3 +27,6 @@
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(defn vertical-line?
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([[point1 point2]] (vertical-line? point1 point2))
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([[x1 _] [x2 _]] (= x1 x2)))
30+
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(defn neighbors [point]
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(map (partial mapv + point) [[0 1] [0 -1] [-1 0] [1 0]]))

‎src/advent_2021_clojure/utils.clj

+3-1
Original file line numberDiff line numberDiff line change
@@ -16,4 +16,6 @@
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(defn summation [n]
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(-> (* n (inc n))
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(/ 2)))
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(/ 2)))
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(defn char->int [c] (- (int c) 48))

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