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C'est la Z

Seven Segment Silliness - Advent 2021 Day08

Day 8 took a lot longer than the other days. Not all that much code and not too complex, at least after getting through a scary sounding lead up but going from problem statement to solution took both time and thought.

As I started to read the problem, I wasn't sure I'd finish it let alone have time to write it up.

Take a minute to read over the problem. You can find it [[ ][here.]]

A pretty intimidating wall of text.

You've got a bunch of lines, each looking like this:

be cfbegad cbdgef fgaecd cgeb fdcge agebfd fecdb fabcd edb | fdgacbe cefdb cefbgd gcbe

Each "word" represents a seven segment display. The side to the left of the | is the input for that line and the stuff on the right, the output.

The problem is that each line has the inputs scrambled. We jave to figure out which letter maps to the top segment, which the bottom, etc.

Oh boy.

It turns out that part one really wasn't hard at all. In fact, it could make a nice early CS assignment. If you look at the display for a 1, it has two segment on the right hand side. It's the only number that uses 2 and only 2 of the seven segments. Likewise a 4 is the only four segment letter, 7 is the only one that uses 3 segments, and 8 is the only one that uses all seven segments.

For part 1 you just had to look at all the outputs - that is, the stuff on each line after the | and add up the number of items that are either a 1, 4, 7, or 8. That's easily accomplished by going over each of those items and checking if they have the correct number of characters and then figuring out the total number of these items.

I had already parsed my data into the a two item list where the left item is a list of inputs and the right a list of outputs:

[ ["cg" "cdbga" "bcg" ...] ["geac" "ceag" "faedcb" "cg"]]

So all I had to do go through all the output sides, count the characters in each item and then add up the number of them.

Here's the code:

  (defn myfilter [x]
  "takes a list of numbers and returns only those that are 2,4,3, or 7"
    (filter #(contains? #{2 4 3 7} %) x))

  (defn part1 [  data]
    (let [results (map second data) ;; pull out all the outputs
          counted (map #(map count %) results) ;; turn the "words" into counts of their lengths
          f (map #(myfilter %) counted) ;; only keep the ones that are the right lengths
          total (map #(count %) f) ;; count how many are in each line
      (apply +  total))) ;; add them all up 

  (part1 data)

For part 2 we had to decode all the output lines and then turn them into numbers and add them up.

Sounded really daunting. It required some thought but it wasn't that bad.

I wanted to build a dictionary where the keys were the digits and the values would be the segments for that particular input line that represent that digit.

For a given line, we can do it pretty easily for the unique numbers 2, 4,3, and 7 so we just loop through all the items in a line and when we see an item with the appropriate length, we store the number in our dictionary.

We might have something like this:

key value
1 b e
4 b c e g
7 b d e
8 a b c d e f g

These were the values from the first line of the example data. Also, I used a Clojure set to store the values since that makes the rest of the solution easier.

I then took this dictionary and tried to add to it by figuring out the 5 segment numbers - specifically, 2, 3 and 5. It turns out that of the 5 segment numbers, the 3 is the only one that ovelaps with the two segments from the 1 so we can find that one pretty easily. If the five segment number wasn't a 3, I looked to see if it was a 5. For this, I looked to see if it had the left and middle segments that the 4 had. Finally, if it wasn't a 3 or a 5 then it had to be a 2.

Next, I did the same for the remaining segments which were all 6 segments. You can look at my full code (linked below) for specifics.

Once we had the complet dictionary I flipped it - keys became values and values became keys so we could look up the output numbers. From there, it was easy to convert them to numbers and find the final answer.

The part of this problem that was both fun and challenging was trying to figure out how to decode a given letter given what you already figured out. That took some time but getting the final answers for problems like this are somehow more satisfying than just a straight up "code it" problem.

You can find my full solution here.

I was worried I wasn't going to finished this one when I first read it but I think it's my favorite of the year so far.

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