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--- Day 24: Arithmetic Logic Unit ---
Magic smoke starts leaking from the submarine's arithmetic logic unit (ALU). Without the ability to
perform basic arithmetic and logic functions, the submarine can't produce cool patterns with its
Christmas lights!
It also can't navigate. Or run the oxygen system.
Don't worry, though - you [1m[97mprobably[0m have enough oxygen left to give you enough time to build a new
ALU.
The ALU is a four-dimensional processing unit: it has integer variables w, x, y, and z. These
variables all start with the value 0. The ALU also supports [1m[97msix instructions[0m:
- inp a - Read an input value and write it to variable a.
- add a b - Add the value of a to the value of b, then store the result in variable a.
- mul a b - Multiply the value of a by the value of b, then store the result in variable a.
- div a b - Divide the value of a by the value of b, truncate the result to an integer, then store
the result in variable a. (Here, "truncate" means to round the value toward zero.)
- mod a b - Divide the value of a by the value of b, then store the [1m[97mremainder[0m in variable a. (This
is also called the modulo operation.)
- eql a b - If the value of a and b are equal, then store the value 1 in variable a. Otherwise,
store the value 0 in variable a.
In all of these instructions, a and b are placeholders; a will always be the variable where the
result of the operation is stored (one of w, x, y, or z), while b can be either a variable or a
number. Numbers can be positive or negative, but will always be integers.
The ALU has no [1m[97mjump[0m instructions; in an ALU program, every instruction is run exactly once in order
from top to bottom. The program halts after the last instruction has finished executing.
(Program authors should be especially cautious; attempting to execute div with b=0 or attempting to
execute mod with a<0 or b<=0 will cause the program to crash and might even damage the ALU. These
operations are never intended in any serious ALU program.)
For example, here is an ALU program which takes an input number, negates it, and stores it in x:
inp x
mul x -1
Here is an ALU program which takes two input numbers, then sets z to 1 if the second input number is
three times larger than the first input number, or sets z to 0 otherwise:
inp z
inp x
mul z 3
eql z x
Here is an ALU program which takes a non-negative integer as input, converts it into binary, and
stores the lowest (1's) bit in z, the second-lowest (2's) bit in y, the third-lowest (4's) bit in x,
and the fourth-lowest (8's) bit in w:
inp w
add z w
mod z 2
div w 2
add y w
mod y 2
div w 2
add x w
mod x 2
div w 2
mod w 2
Once you have built a replacement ALU, you can install it in the submarine, which will immediately
resume what it was doing when the ALU failed: validating the submarine's [1m[97mmodel number[0m. To do this,
the ALU will run the MOdel Number Automatic Detector program (MONAD, your puzzle input).
Submarine model numbers are always [1m[97mfourteen-digit numbers[0m consisting only of digits 1 through 9. The
digit 0 [1m[97mcannot[0m appear in a model number.
When MONAD checks a hypothetical fourteen-digit model number, it uses fourteen separate inp
instructions, each expecting a [1m[97msingle digit[0m of the model number in order of most to least
significant. (So, to check the model number 13579246899999, you would give 1 to the first inp
instruction, 3 to the second inp instruction, 5 to the third inp instruction, and so on.) This means
that when operating MONAD, each input instruction should only ever be given an integer value of at
least 1 and at most 9.
Then, after MONAD has finished running all of its instructions, it will indicate that the model
number was [1m[97mvalid[0m by leaving a 0 in variable z. However, if the model number was
[1m[97minvalid[0m, it will leave some other non-zero value in z.
MONAD imposes additional, mysterious restrictions on model numbers, and legend says the last copy of
the MONAD documentation was eaten by a tanuki. You'll need to [1m[97mfigure out what MONAD does[0m some other
way.
To enable as many submarine features as possible, find the largest valid fourteen-digit model number
that contains no 0 digits. [1m[97mWhat is the largest model number accepted by MONAD?[0m
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