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| 1 | +# Day One: Report Repair |
| 2 | + |
| 3 | +* [Problem statement](https://adventofcode.com/2020/day/1) |
| 4 | +* [Solution code](https://github.com/abyala/advent-2020-clojure/blob/master/src/advent_2020_clojure/day01.clj) |
| 5 | + |
| 6 | +--- |
| 7 | + |
| 8 | +## Part 1 |
| 9 | + |
| 10 | +This problem requires reading a list of integers, finding the two that add up |
| 11 | +to the value 2020, and then returning the product of those numbers. Pretty |
| 12 | +straightforward problem. |
| 13 | + |
| 14 | +My initial solution (foreshadowing!!) was to calculate this as a single function. |
| 15 | +As a convention for AoC, I tend to name the solution to each part `part1` and |
| 16 | +`part2`, so it's easy to know what to look at. Clojure namespace files require |
| 17 | +compilation in order, so if function `foo` depends on function `bar` and |
| 18 | +they are in the same file, `bar` must appear first. This is quite a change |
| 19 | +from my Java or Kotlin code, where I like to put the most business-relevant, |
| 20 | +low-granulairty methods at the top and then the implementations below. |
| 21 | + |
| 22 | +The first thing I want to do is parse the input. In this case, I'm expecting a |
| 23 | +single string of the integers, separated by new-lines. For my test data, I |
| 24 | +just copy-pasted the data from the website, and for the puzzle data, I stored the |
| 25 | +data in a file and use the `slurp` function to read it all in as a single string. |
| 26 | + |
| 27 | +To parse the data, I use the wonderful `thread-last` macro `->>`, which takes |
| 28 | +in a list of expressions, and supplies the result of each expression as the final |
| 29 | +value of the next expression. So if I wanted to take a numeric value `x`, |
| 30 | +square it, triple the result, and then add 1000, this is much easier to read with |
| 31 | +pipelining/threadng. Being able to read left-to-right, or top-to-bottom instead |
| 32 | +of inside-out makes Lisp much easier to work with: |
| 33 | + |
| 34 | +``` |
| 35 | +; Without threading |
| 36 | +(+ 1000 (* 3 (* x x))) |
| 37 | +
|
| 38 | +; or |
| 39 | +(+ 1000 |
| 40 | + (* 3 |
| 41 | + (* x x))) |
| 42 | +
|
| 43 | +
|
| 44 | +; With threading |
| 45 | +(->> (* x x) |
| 46 | + (* 3) |
| 47 | + (+ 1000))) |
| 48 | +``` |
| 49 | + |
| 50 | +So to parse the data, I use `str/split-lines` to break the string into a sequence |
| 51 | +of strings, separated by the newline character. Then I use the `map` function |
| 52 | +to apply the `Integer/parseInt` function to each value in the sequence, resulting |
| 53 | +in a sequence of integers. Note that this is _the_ `Integer/parseInt` static Java |
| 54 | +method, so you can see the interop is pretty slick. I take the results and bind |
| 55 | +the result to the `expenses` symbol, which is lexically scoped. This is Clojure's |
| 56 | +equivalent of making a local variable within a method. |
| 57 | + |
| 58 | +```clojure |
| 59 | +(let [expenses (->> (str/split-lines input) |
| 60 | + (map #(Integer/parseInt %)))] |
| 61 | + OTHER STUFF HERE) |
| 62 | +``` |
| 63 | + |
| 64 | +Next, I want to find all possible pairs of non-equal values, such that they add |
| 65 | +up to 2020. Once found, return them as a vector, or a two-element tuple. For this, |
| 66 | +we use Clojure's `for` function, which like the `let` macro, takes in a vector |
| 67 | +of bindings and an expression. Here I bind both `x` and `y` to the integer sequence |
| 68 | +created above, so this is pretty close to nested loops. The `:when` keyword |
| 69 | +allows filtering of the `for` bindings, so in this case I use it to restrict the |
| 70 | +pairs to those where x is smaller than y (to avoid duplicates) and where they |
| 71 | +add up to 2020. The evaluated value is just the vector `[x y]`. |
| 72 | + |
| 73 | +```clojure |
| 74 | +(for [x expenses |
| 75 | + y expenses |
| 76 | + :when (and (< x y) |
| 77 | + (= 2020 (+ x y)))] |
| 78 | + [x y]) |
| 79 | +``` |
| 80 | + |
| 81 | +We're almost done. The `for` function returns a sequence of values, and in this |
| 82 | +case I know we only expect one value, so I wrap the results in the `first` function. |
| 83 | +That returns a single `[x y]` vector of integers, so all I need to do is multiply |
| 84 | +the values with each other. The `apply` function takes in 2 or more arguments, |
| 85 | +where the first is the function to apply, and the second is the container of values. |
| 86 | +So my function is just `*` for multiplication, and the expression is everything else |
| 87 | +I just computed. Put all together, the function looks like this: |
| 88 | + |
| 89 | +```clojure |
| 90 | +(defn part1 [input] |
| 91 | + (let [expenses (->> (str/split-lines input) |
| 92 | + (map #(Integer/parseInt %)))] |
| 93 | + (apply * (first (for [x expenses |
| 94 | + y expenses |
| 95 | + :when (and (< x y) |
| 96 | + (= 2020 (+ x y)))] |
| 97 | + [x y]))))) |
| 98 | +``` |
| 99 | + |
| 100 | +But wait -- that last section looks all scary and nested. Can't we pipeline it? |
| 101 | +Sure we can! |
| 102 | + |
| 103 | +```clojure |
| 104 | +(defn part1 [input] |
| 105 | + (let [expenses (->> (str/split-lines input) |
| 106 | + (map #(Integer/parseInt %)))] |
| 107 | + (->> (for [x expenses |
| 108 | + y expenses |
| 109 | + :when (and (< x y) |
| 110 | + (= 2020 (+ x y)))] |
| 111 | + [x y]) |
| 112 | + first |
| 113 | + (apply *)))) |
| 114 | +``` |
| 115 | + |
| 116 | +## Part 2 |
| 117 | + |
| 118 | +This is essentially the same algorithm as part 1, except that we need three |
| 119 | +numbers to add up to 2020, instead of two. The easiest way to solve this is with |
| 120 | +a copy-paste job, adding in the third binding `z` go to along with `x` and `y`. |
| 121 | + |
| 122 | +```clojure |
| 123 | +(defn part2 [input] |
| 124 | + (let [expenses (->> (str/split-lines input) |
| 125 | + (map #(Integer/parseInt %)))] |
| 126 | + (->> (for [x expenses |
| 127 | + y expenses |
| 128 | + z expenses |
| 129 | + :when (and (< x y z) |
| 130 | + (= 2020 (+ x y z)))] |
| 131 | + [x y z]) |
| 132 | + first |
| 133 | + (apply *)))) |
| 134 | +``` |
| 135 | + |
| 136 | +## Rewrite |
| 137 | + |
| 138 | +What I like to do with AoC problems, when feasible, is to refactor part 1 such |
| 139 | +that I get as much reuse as possible between parts 1 and 2. In this case, we can |
| 140 | +see that the only real difference is the desired length of the vectors of ints |
| 141 | +that add up to 2020 -- two for part 1, and three for part 2. Also, I want to be |
| 142 | +a good little functional programmer and pretend that the logic of adding up to |
| 143 | +2020, or multiplying the result, could potentially have business meaning. So |
| 144 | +let's do some decomposition. |
| 145 | + |
| 146 | +The first step is to create a function called `permutations` that takes in a |
| 147 | +desired sequence length and a sequence of data, and provide all permutations of |
| 148 | +data. So for `(permutations 2 [3 4])` we should get back `((3 3) (3 4) (4 3) (4 4))`. |
| 149 | +In theory, if part 3 of this problem asked for the 15 input values that add up to |
| 150 | +2020, we shouldn't have to make a structural change to the design. |
| 151 | + |
| 152 | +For this to work, we use the `iterate` function, which often can take the place of |
| 153 | +a `reduce` function. It takes in a function to apply and some initialization |
| 154 | +data, and it returns an infinite sequence of applying the function to the |
| 155 | +output of the previous iteration. Let's start with the initial data first - |
| 156 | +we use `(map list data)` which takes each value in the `data` sequence and |
| 157 | +turns it into a single element list. So `(map list [1 2 3])` should return |
| 158 | +`((1) (2) (3))`. This is a working base case; if I wanted all single-element |
| 159 | +tuples in a list, I would expect a list of single-element lists. Plus, |
| 160 | +`(map list data)` sounds like I'm confused about data types, but here `map` is |
| 161 | +the mapping function and `list` is a function to create a list. No confusion! |
| 162 | + |
| 163 | +Then the `iterate` function needs to flatmap each input data value onto each of |
| 164 | +these lists. The Clojure equivalent of flatmap is `mapcat`, since we map a |
| 165 | +function to the input data, and then concatenate the values back into a list. |
| 166 | +In this case, the function uses the `for` function only once, since we want to add |
| 167 | +a single value to each incoming list, and we use the `cons` function to add an |
| 168 | +element to the front of another list. Note that since we don't care about ordering, |
| 169 | +let's favor the Clojure list instead of the vector, which means that the mapping |
| 170 | +function will add the new data to the head of the list. |
| 171 | + |
| 172 | +The last piece is to take the `nth` value of the infinite sequence. Calling |
| 173 | +`(nth f 0)` would provide the input data, in this case a list of length 1, so |
| 174 | +we actually want to call `(nth f (dec target-length))`. |
| 175 | + |
| 176 | +```clojure |
| 177 | +(defn permutations |
| 178 | + "Creates a list of lists, containing all permutations of the incoming data, each with |
| 179 | + the intended length." |
| 180 | + [length data] |
| 181 | + (nth (iterate |
| 182 | + (fn [d] (mapcat #(for [x data] (cons x %)) |
| 183 | + d)) |
| 184 | + (map list data)) |
| 185 | + (dec length))) |
| 186 | +``` |
| 187 | + |
| 188 | +Next, we'll make three tiny functions that explain the target functionality |
| 189 | +without getting bogged down in implementation. `all-increasing?` will make sure |
| 190 | +that all elements in a list are strictly increasing, so that we can keep values |
| 191 | +`(10 2010)` and throw out `(2010 10)`. `adds-to-2020?` makes sure the values... |
| 192 | +add up to 2020. And `product-of-all` multiplies all values together. |
| 193 | + |
| 194 | +What I like about these functions is the use of `apply`. Remember that `apply` |
| 195 | +applies a function to all following values. So where in Java you might need |
| 196 | +to say `if ((x < y) && (y < z))`, in Clojure you can say `(if (< x y z))`. |
| 197 | +Again, if we needed to look at a tuple of 15 values, the function doesn't change. |
| 198 | + |
| 199 | +```clojure |
| 200 | +(defn all-increasing? [v] (apply < v)) |
| 201 | +(defn adds-to-2020? [v] (= 2020 (apply + v))) |
| 202 | +(defn product-of-all [v] (apply * v)) |
| 203 | + ``` |
| 204 | + |
| 205 | +Then we get to the key objective -- a nice `solve` function that we can share |
| 206 | +between parts 1 and 2. Let's put the pieces together. |
| 207 | +Using a thread-last pipeline, we split the input String by line, map each String |
| 208 | +value to an Integer, and calculate all permutations of those values given a target |
| 209 | +length. The `keep` function says to apply a mapping function and throw away the |
| 210 | +nulls, like Kotlin's `mapNotNull`. So here we say when we have a matching tuple, |
| 211 | +such that the values are all increasing and add to zero, return the product. |
| 212 | +Finally, returning the first (and only?) value calculated. |
| 213 | + |
| 214 | +```clojure |
| 215 | +(defn solve [length input] |
| 216 | + (->> (str/split-lines input) |
| 217 | + (map #(Integer/parseInt %)) |
| 218 | + (permutations length) |
| 219 | + (keep #(when (and (all-increasing? %) |
| 220 | + (adds-to-2020? %)) |
| 221 | + (product-of-all %))) |
| 222 | + first)) |
| 223 | +``` |
| 224 | + |
| 225 | +We'll know we have a good solution if the `part1` and `part2` functions look |
| 226 | +pretty. Let's see if that's the case: |
| 227 | + |
| 228 | +```clojure |
| 229 | +(defn part1 [input] (solve 2 input)) |
| 230 | +(defn part2 [input] (solve 3 input)) |
| 231 | +``` |
| 232 | + |
| 233 | +I think they won a freaking beauty contest. Day 1 complete with Clojure! |
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