# A Teacher Looks at Advent of Code 2020 - day 16

Today's problem was a fun one to solve. Why was it fun? Stay tuned,

The basic gist is that you have a plane ticket which is a set of numbers but you don't know which number maps to which category - row, seat, gate, etc. You also know the number ranges for each category. For example, row might be a number between 6 and 11 or 33 through 44 while a seat might be 13 through 40 or 45 through 50.

Finally, you also can see a number of nearby tickets - each also as tring of numbers.

For part 1 you had to determine how many of the nearby tickets are valid. A ticket is valid if all the numbers on it fall into at least one category range.

See the full description for all the details.

First up - parsing - a little cumbersome but not too bad.

1. Split the input into the three main sections - categories, your ticket, nearby tickets
2. Convert the categories into a usable form
3. Convert your ticket into a list of numbers
4. Convert the nearby tickets into a list of tickets each one being a list of numbers.

Taking each step in turn and it's not too bad - particularly if you're comfortable with regular expressions.

## part 1

Representing the categories leads us to our first interesting decision. How will we test to see if a ticket is valid and based on that how will we represent the categories?

Each category has two ranges connected with an or:

```row: 6-11 or 33-44
seat: 13-40 or 45-50
```

One could make a construct to hold the bounds, loop through the nearby tickets and for each value, run an if statement with the two ranges connected by an or.

This is where a class can talk about code vs data - a topic I'm really fond of.

Instead of taking the above range and having some test like:

``````for number in ticket:
if (number >= low1 and number <= high1) or \
(number >= low2 and number <= high2):
do something``````

or specifically for the row example:

``````for number in ticket:
if (number >= 6 and number <= 11) or \
(number >= 33 and number <= 44):
do something``````

you could make a set with all the possible seats and then just test to see if the seat was in the set:

``````r1 = set( range(low1,high+1))
r2 = set( range(low2,hight2+1))
valid_seats = r1.union(r2)

# then later
if seat in valid_seats:
do something``````

I just find this more elegant.

For part 1 I just made a big set with all the valid seats and then checked each ticket to see if each if its numbers were in the valid seats.

## part 2

For part 2 first you had to remove all the invalid tickets from the nearby tickets. Since you figured out how to identify a valid ticket in part one this shouldn't be too ahrd.

Then we have to sleuth out which column from the tickets represented which category. This would make a great group activity in a class, particularly with an interactive language. This is a great data exploration and representation problem.

To get more data, I thought I'd write a routine to pull all of one column from the nearby tickets. Then I could see if all the values in that row were valid for a particular category. For example, are all the first numbers of all the tickets valid numbers for row. If so, that column could represent row. Of course it could also represent something else as well.

Now that i could test to see if a column is valid for a category I decided to build some data. I built a list of all the possible categories for each row.

Part of it looked sort of like this (but in clojure):

``````[ [17, ["wagon","arrival-station"] ],
[7, ["wagon","arrival-station","route","train","row"]]
...
]``````

Examining this table, I noticed that one row had only one category, another had only 2 then one three etc. Great - we can now solve this by plugging in the row we know, then the next one, then the next etc.

The explorations led to an easy answer. I sorted the list and looped through. At each iteration I:

1. Added the current category and its associated row to the solution set.
2. Removed that category from the rest of the lines

When done we had a dictionary with a mapping from category to row. From there it was pretty simple to find the part 2 answer.

Lots of good stuff here. I love the data explorations and the way it can lead to a pretty straightforward solution.

Full solution in clojure can be found here: https://adventofcode.com/2020/day/16

So far I've managed to complete each day - 32 stars. That beats my 31 from last year adn my top year of 40 back in 2016. Tomorrow I give my last exams and grading ca really begin so we'll see if I can keep going but so it's been a fun Advent of Code year so far.