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Required fields*

Rev

Required fields*

Fibonacci domino tiling

There's classic combinatorial result that the number of ways to tile a 2*n strip by 1*2 dominoes is the n^th Fibonacci number. You goal is to print all the tilings for a given n, drawn with dashes and vertical lines like these 8 tilings for n=5:

|————
|————
——|——
——|——
|||——
|||——
————|
————|
||——|
||——|
|——||
|——||
——|||
——|||
|||||
|||||

You are to provide a program or named function that take n as input and prints the required output. Fewest bytes wins.

Input

A number n between 1 and 10 inclusive via STDIN or function input.

Output

Print every possible domino tilings of the 2*n strip, drawn horizontally. The tilings may be in any order, but each should appear exactly once. They must be separated by a blank line.

A vertical domino is made of two vertical bars (|) and a horizontal domino is made of two em dashes (—). You may use hyphens (-) in place of em dashes to stay in ASCII.

You can do anything with whitespace as long as the printed output looks the same.

Answer*

# J - 54 char

Function taking `n` as argument on the right.

 0{::(];'--'&,"1@[,'|',"1])&>/@[&0&((1 2,ドル:)&.>'';,'|')

The main root of this golf is the `(];'--'&,"1@[,'|',"1])&>/`. This takes a list of tilings of length (N-2) and (N-1), and returns a list of tilings of length (N-1) and N. This is the standard Fibonacci recurrence, à la linear algebra. `];` returns the right list as the new left (as there is no change). `'--'&,"1@[` adds `--` tiles to the left list, while `'|',"1]` adds `|` tiles to the right list, and those together are the new right list.

We iterate that over and over `n` times (that's the `@[&0`) and start with the empty tiling and the single tiling of length 1. Then we return the first of the pair with `0{::`. Meaning, if we run it zero times, we just return the first i.e. the empty tiling. If we run it `n` times, we calculate up to the `n` and (`n`+1) pair, but discard the latter. It's extra work but less characters.

The `(1 2,ドル:)` is something J has to do in order to make the tilings in the lists easily extendable. We make the left starting list be a 1-item list of a 2-row matrix of characters, each row having length 0. The right starting list is the same, but has the rows be of length 1, filled with `|`. Then, we add the new tiles to each row, and append the lists of matrices when we're joining the two sets of tilings together. It's a simple application of a concept J calls rank: essentially manipulating the dimensionality of its arguments, and implicitly looping when necessary.

 0{::(];'--'&,"1@[,'|',"1])&>/@[&0&((1 2,ドル:)&.>'';,'|')5
 ----|
 ----|
 
 --|--
 --|--
 
 --|||
 --|||
 
 |----
 |----
 
 |--||
 |--||
 
 ||--|
 ||--|
 
 |||--
 |||--
 
 |||||
 |||||

Try it for yourself at [tryj.tk](https://a296a8f7c5110b2ece73921ddc2abbaaa3c90d10.googledrive.com/host/0B3cbLoy-_9Dbb0NaSk9MRGE5UEU/index.html#code=0%7B%3A%3A%28%5D%3B%27--%27%26%2C%221%40%5B%2C%27%7C%27%2C%221%5D%29%26%3E%2F%40%5B%260%26%28%281%202%24%2C%3A%29%26.%3E%27%27%3B%2C%27%7C%27%295).

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