# t3: Wire crossings

Apparently I solemnly swore in the last p6cc blog post that this blog post would appear sooner than after a two-month break. Apparently I suck at living up to what I solemnly swear. Anyway, kudos to `\$dayjob` for keeping me healthily occupied with things, and a big thanks to all people related to Perl 6 who gently reminded me to keep up with the reviewing.

(Or maybe I didn't specifically mean "the next p6cc blog post", but just "the next blog post"? I wish I could make myself believe that. No, the real answer is that reviewing stuff takes time and effort, and my time and effort have been elsewhere lately.)

Let's talk about crossing wires in elegant ways! Here, I'll let the description refresh your mind:

``````## Arrange wire crossings to rearrange wires

Ten wires are come in from the left. Ten wires leave to the right. Write a
program that, given a permutation of the digits 0..9, arranges crossings on a
grid that places the wires in the order designated by the permutation.

The output consists of a grid whose elements connect the left and right sides.
Each cell of the grid is either *empty* (in that it just lets the wires
through), or a *crossing* (in that it lets the wires trade places). Two
crossings can never be placed vertically adjacent to each other. (This is
equivalent to saying that the wires never split or merge, they only permute.)

Often, solutions require crossings to be spread out not just vertically but
also horizontally. It is considered elegant not to make the grid wider than it
has to be.

Examples:

Input: 1032547698

Output:

0 _  _ 1
\/
1 _/\_ 0

2 _  _ 3
\/
3 _/\_ 2

4 _  _ 5
\/
5 _/\_ 4

6 _  _ 7
\/
7 _/\_ 6

8 _  _ 9
\/
9 _/\_ 8

(This permutation is simply flipping wires pairwise.)

Input: 1234567890

Output:

0 _  _________________ 1
\/
1 _/\  _______________ 2
\/
2 ___/\  _____________ 3
\/
3 _____/\  ___________ 4
\/
4 _______/\  _________ 5
\/
5 _________/\  _______ 6
\/
6 ___________/\  _____ 7
\/
7 _____________/\  ___ 8
\/
8 _______________/\  _ 9
\/
9 _________________/\_ 0

(The simplest way to bubble 0 to the bottom.)

Input: 5012367894

0 _________  _ 5
\/
1 _______  /\_ 0
\/
2 _____  /\___ 1
\/
3 ___  /\_____ 2
\/
4 _  /\_______ 3
\/
5 _/\  _______ 6
\/
6 ___/\  _____ 7
\/
7 _____/\  ___ 8
\/
8 _______/\  _ 9
\/
9 _________/\_ 4

(The simplest way to bubble 4 and 5 simultaneously.)
``````

The reviews are in. To get the full enjoyment out of this blog post, I highly recommend that you read the reviews as well as this post. The solutions are a varied bunch, and there's lots of nice code in there.

How would a program find a nice, short solution to the write-crossing problem? Wait, can we even be sure there always is a solution? If the fundamental operation is crossing two adjacent wires, can we really generate the full space of permutations? (As opposed to, say, only half the space, like in the 15 puzzle.)

We can generate the full space of permutations. The quickest way to convince ourselves of that is to think of sorting algorithms, many of which use "flip two adjacent values" as its fundamental operation. Sorting algorithms can sort anything, hence the wire-crossing problem always has a solution.

(Wouldn't it be weird to live in a world where sometimes you'd pass in a list to be sorted, and the computer would come back and say "sorry, this is one of those unsortable lists of values". What a bummer!)

In fact, many of the solutions took the sorting analogy to heart, producing something like a bubble sort with slightly modified rules. In bubble sort, the same value can be transposed several times during one run, something that isn't possible in the wire universe: you flip two writes, and you then have to wait until the next column to flip either of those wires again. But with that little restriction added, bubble sort seems to solve this problem just fine.

As always, it's nice to see how people's styles differ broadly. I never see two identical solutions, but this time around, it felt especially varied. Maybe because the problem is relatively small, and one wouldn't think there were that much to vary. But just watch as people apply dynamic variables, feed operators, enums, junctions, sequence operators, metaoperators, and many other things to solve the same problem. There Is indeed More Than One Way To Do It.

As of last review post, we were down to five finalists. Now we're down to four.

Next post: pouring water on a block world!