Toggle, Print, Repeat

Question

This challenge is loosely inspired by the unimplemented esolang Pada.

Consider an array of 8 bits, all initialised to zero. We'll introduce a very minimalistic instruction set to print arbitrary strings. There are two instructions, both of which take a parameter N which is the index of a bit:

• t N for toggle: This changes the value of bit N.
• p N for print: This interprets all 8 bits as a byte, starting from bit N and wrapping around the end. The character corresponding to this byte is printed to STDOUT.

Let's look an example. We want to print :=. Naively we achieve this as follows (0-based bit indices):

t 2    [0 0 1 0 0 0 0 0]
t 3    [0 0 1 1 0 0 0 0]
t 4    [0 0 1 1 1 0 0 0]
t 6    [0 0 1 1 1 0 1 0]
p 0    [0 0 1 1 1 0 1 0] == 58 == ':'
t 5    [0 0 1 1 1 1 1 0]
t 6    [0 0 1 1 1 1 0 0]
t 7    [0 0 1 1 1 1 0 1]
p 0    [0 0 1 1 1 1 0 1] == 61 == '='

But instead, we can make use of the cyclic feature of p and save two instructions:

t 2    [0 0 1 0 0 0 0 0]
t 3    [0 0 1 1 0 0 0 0]
t 4    [0 0 1 1 1 0 0 0]
t 6    [0 0 1 1 1 0 1 0]
p 0    [0 0 1 1 1 0 1 0] == 58 == ':'
t 1    [0 1 1 1 1 0 1 0]
p 7    [0 1 1 1 1 0 1 0] == [0 0 1 1 1 1 0 1] == 61 == '='
                      ^

So p 7 simply starts reading the byte value from the last bit instead of the first.

The Challenge

Given a non-empty string of printable ASCII characters (0x20 to 0x7E, inclusive), produce an optimal list of instructions (one line per instruction) to print that string with the above system. If there are multiple optimal solutions (which will almost always be the case), generate only one of them.

You may choose between 0-based and 1-based indexing for the bits, but please state your choice.

You may write a program or function, taking input via STDIN (or closest alternative), command-line argument or function argument and outputting the result via STDOUT (or closest alternative), function return value or function (out) parameter. If you don't print the result to STDOUT, it should still be a single newline-separated string.

This is code golf, so the shortest answer (in bytes) wins.

Test Cases

Each test case is a single line containing the input string, followed by the optimal number of instructions, followed by one possible solution.

You should not output the instruction count in your solution - this is only included here so you can check the correctness of your code if it prints a different instruction list.

?
7 instructions
t 2
t 3
t 4
t 5
t 6
t 7
p 0

:=
7 instructions
t 2
t 3
t 4
t 6
p 0
t 1
p 7

0123456789
26 instructions
t 2
t 3
p 0
t 7
p 0
t 6
t 7
p 0
t 7
p 0
t 5
t 6
t 7
p 0
t 7
p 0
t 6
t 7
p 0
t 7
p 0
t 2
t 3
p 3
t 2
p 3

9876543210
28 instructions
t 2
t 3
t 4
t 7
p 0
t 7
p 0
t 0
t 7
p 5
t 4
p 5
t 0
t 5
p 0
t 7
p 0
t 5
t 6
t 7
p 0
t 7
p 0
t 6
t 7
p 0
t 7
p 0

Hello, World!
39 instructions
t 1
t 4
p 0
t 3
t 7
p 2
t 1
t 6
p 2
p 2
t 0
t 1
p 2
t 0
t 1
t 3
p 2
t 6
t 7
p 2
t 0
t 2
t 6
t 7
p 1
t 0
t 1
t 5
p 0
t 2
t 7
p 3
t 2
t 6
p 0
t 4
p 0
t 1
p 3

The quick brown fox jumps over the lazy dog.
150 instructions
t 1
t 3
t 5
p 0
t 1
t 2
p 1
t 1
t 3
t 7
p 0
t 1
t 5
t 7
p 0
t 1
t 3
t 7
p 0
t 5
p 0
t 3
t 4
t 5
p 0
t 4
t 6
p 0
t 4
p 0
t 1
t 4
t 6
t 7
p 0
t 1
t 6
p 0
t 3
p 0
t 0
t 5
p 4
t 0
t 7
p 0
t 1
p 1
t 3
t 5
t 6
t 7
p 0
t 1
t 5
t 6
p 0
t 4
t 7
p 0
t 1
t 2
p 3
t 5
t 6
t 7
p 2
t 1
t 2
t 6
p 0
t 0
p 7
t 0
t 7
p 5
t 3
t 4
t 6
t 7
p 0
t 6
t 7
p 0
t 1
t 3
t 6
t 7
p 0
t 1
t 4
t 5
t 6
t 7
p 0
t 4
p 4
t 6
p 0
t 1
t 6
p 4
t 5
t 6
t 7
p 0
t 1
t 3
t 5
p 0
t 1
p 1
t 1
t 3
t 7
p 0
t 1
t 5
t 7
p 0
t 1
t 4
t 5
p 0
t 1
p 3
t 3
t 7
p 1
t 1
t 5
p 0
t 1
t 3
t 4
t 7
p 0
t 1
t 5
p 0
t 4
t 6
t 7
p 0
t 4
p 0
t 1
t 4
t 7
p 0

The test cases were generated with this CJam reference implementation.

Answer 1

CJam, 67 bytes

U]8*l{i2b8Ue[8,{1$m>2$.^:+}$0=_@m>@1$.^ee{~{"t "op}{;}?}/"p "o\p}/;

Try it online

Explanation:

U]8*    Build start bit array [0 0 0 0 0 0 0 0].
l       Get input.
{       Start loop over input characters.
  i       Convert character to integer.
  2b      Convert to binary array.
  8Ue[    Pad to 8 entries with leading 0.
  8,      Generate list of possible rotation amounts.
  {       Start of sort function block.
    1$      Get bit array of character.
    m>      Rotate by rotation amount.
    2$      Get previous bit array.
    .^      Element-wise xor to get different bits.
    :+      Add elements in result to get count of different bits.
  }$      Sort possible rotations by count of different bits.
  0=      Get first rotation amount in sorted list, which is the one with the
          one that results in the smallest count of different bits.
  _       Copy count. Will use original for "p" output later.
  @       Get the character bit array to top of stack.
  m>      Rotate it, to get optimal rotated bit array.
  @       Get previous bit array to top of stack.
  1$      Copy rotated bit array, will need the original as starting point
          for next character.
  .^      Element-wise xor to get different bits.
  ee      Enumerate array to get pairs of index and bit value.
  {       Loop over bits.
    ~       Unpack index bit pair.
    {       Start of if block for bit value.
      "t "o   Output "t ".
      p  Output index and newline.
    }       End of if block.
    {       Start of else block.
      ;       Pop the index value.
    }?      End of ternary if.
  }/      End loop over bits.
  "p "o   Output "p ".
  \       Swap rotation amount to top.
  p       Print rotation amount and newline.
}/      End loop over input characters.
;       Ppp current bit array off stack to prevent extra output.

Answer 2

Ruby, 171

->w{s=[0]*8
w.chars.flat_map{|c|z=0..7
*m,i=z.map{|j|z.select{|k|s[k]!=z.map{|i|c.ord[i]}.rotate(j)[k]}<<j}.min_by &:size
m.map{|m|s[m]=1-s[m];"t #{7-m}"}+["p #{i}"]}*?\n}

A Ruby function that's only double the size of the reference implementation. :)

Try it online: http://ideone.com/ysYyFP

The program is pretty straighforward: it starts off with the 8 bits set to 0 and iterates through the characters. At each step, it takes the shortest route from the current state to a state that would allow printing the character. It returns a string in the specified format.

The initial (less golfed) version of the program is available here.

Answer 3

CJam, 81 76 bytes

Still a lot to golf.

0]8*q{i2b8Te[8,\fm>:X\_@\f.=::+_$W=#:YX=_@.{=M['tSUN]?U):U;}o0:U;['pSYN]o}/;

Try it online.