## \-\-- Day 18: Duet \-\--

You discover a tablet containing some strange assembly code labeled
simply \"[Duet](https://en.wikipedia.org/wiki/Duet)\". Rather than
bother the sound card with it, you decide to run the code yourself.
Unfortunately, you don\'t see any documentation, so you\'re left to
figure out what the instructions mean on your own.

It seems like the assembly is meant to operate on a set of *registers*
that are each named with a single letter and that can each hold a single
[integer](https://en.wikipedia.org/wiki/Integer). You suppose each
register should start with a value of `0`.

There aren\'t that many instructions, so it shouldn\'t be hard to figure
out what they do. Here\'s what you determine:

-   `snd X` *[plays a
    sound]{title="I don't recommend actually trying this."}* with a
    frequency equal to the value of `X`.
-   `set X Y` *sets* register `X` to the value of `Y`.
-   `add X Y` *increases* register `X` by the value of `Y`.
-   `mul X Y` sets register `X` to the result of *multiplying* the value
    contained in register `X` by the value of `Y`.
-   `mod X Y` sets register `X` to the *remainder* of dividing the value
    contained in register `X` by the value of `Y` (that is, it sets `X`
    to the result of `X`
    [modulo](https://en.wikipedia.org/wiki/Modulo_operation) `Y`).
-   `rcv X` *recovers* the frequency of the last sound played, but only
    when the value of `X` is not zero. (If it is zero, the command does
    nothing.)
-   `jgz X Y` *jumps* with an offset of the value of `Y`, but only if
    the value of `X` is *greater than zero*. (An offset of `2` skips the
    next instruction, an offset of `-1` jumps to the previous
    instruction, and so on.)

Many of the instructions can take either a register (a single letter) or
a number. The value of a register is the integer it contains; the value
of a number is that number.

After each *jump* instruction, the program continues with the
instruction to which the *jump* jumped. After any other instruction, the
program continues with the next instruction. Continuing (or jumping) off
either end of the program terminates it.

For example:

    set a 1
    add a 2
    mul a a
    mod a 5
    snd a
    set a 0
    rcv a
    jgz a -1
    set a 1
    jgz a -2

-   The first four instructions set `a` to `1`, add `2` to it, square
    it, and then set it to itself modulo `5`, resulting in a value of
    `4`.
-   Then, a sound with frequency `4` (the value of `a`) is played.
-   After that, `a` is set to `0`, causing the subsequent `rcv` and
    `jgz` instructions to both be skipped (`rcv` because `a` is `0`, and
    `jgz` because `a` is not greater than `0`).
-   Finally, `a` is set to `1`, causing the next `jgz` instruction to
    activate, jumping back two instructions to another jump, which jumps
    again to the `rcv`, which ultimately triggers the *recover*
    operation.

At the time the *recover* operation is executed, the frequency of the
last sound played is `4`.

*What is the value of the recovered frequency* (the value of the most
recently played sound) the *first* time a `rcv` instruction is executed
with a non-zero value?

Your puzzle answer was `8600`.

## \-\-- Part Two \-\-- {#part2}

As you congratulate yourself for a job well done, you notice that the
documentation has been on the back of the tablet this entire time. While
you actually got most of the instructions correct, there are a few key
differences. This assembly code isn\'t about sound at all - it\'s meant
to be run *twice at the same time*.

Each running copy of the program has its own set of registers and
follows the code independently - in fact, the programs don\'t even
necessarily run at the same speed. To coordinate, they use the *send*
(`snd`) and *receive* (`rcv`) instructions:

-   `snd X` *sends* the value of `X` to the other program. These values
    wait in a queue until that program is ready to receive them. Each
    program has its own message queue, so a program can never receive a
    message it sent.
-   `rcv X` *receives* the next value and stores it in register `X`. If
    no values are in the queue, the program *waits for a value to be
    sent to it*. Programs do not continue to the next instruction until
    they have received a value. Values are received in the order they
    are sent.

Each program also has its own *program ID* (one `0` and the other `1`);
the register `p` should begin with this value.

For example:

    snd 1
    snd 2
    snd p
    rcv a
    rcv b
    rcv c
    rcv d

Both programs begin by sending three values to the other. Program `0`
sends `1, 2, 0`; program `1` sends `1, 2, 1`. Then, each program
receives a value (both `1`) and stores it in `a`, receives another value
(both `2`) and stores it in `b`, and then each receives the program ID
of the other program (program `0` receives `1`; program `1` receives
`0`) and stores it in `c`. Each program now sees a different value in
its own copy of register `c`.

Finally, both programs try to `rcv` a *fourth* time, but no data is
waiting for either of them, and they reach a *deadlock*. When this
happens, both programs terminate.

It should be noted that it would be equally valid for the programs to
run at different speeds; for example, program `0` might have sent all
three values and then stopped at the first `rcv` before program `1`
executed even its first instruction.

Once both of your programs have terminated (regardless of what caused
them to do so), *how many times did program `1` send a value*?

Your puzzle answer was `7239`.

Both parts of this puzzle are complete! They provide two gold stars:
\*\*

At this point, you should [return to your Advent calendar](/2017) and
try another puzzle.

If you still want to see it, you can [get your puzzle
input](18/input).