2021: d24: ex2: add solution

2021/d24/ex2/ex2.py

@@ -0,0 +1,111 @@
+#!/usr/bin/env python
+
+import enum
+import functools
+import sys
+from typing import List, Literal, NamedTuple, Optional, Union, cast
+
+import z3
+
+Register = Literal["w", "x", "y", "z"]
+
+
+class InstructionType(enum.Enum):
+    INPUT = "inp"
+    ADD = "add"
+    MULTIPLY = "mul"
+    DIVIDE = "div"
+    MODULO = "mod"
+    EQUAL = "eql"
+
+
+class Instruction(NamedTuple):
+    type: InstructionType
+    destination: Register
+    source: Optional[Union[Register, int]]
+
+
+def solve(input: List[str]) -> int:
+    def parse() -> List[Instruction]:
+        def parse_instruction(line: str) -> Instruction:
+            type, *registers = line.split()
+
+            assert registers[0] in ("w", "x", "y", "z")  # Sanity check
+            destination = cast(Register, registers[0])
+
+            source: Optional[Union[Register, int]] = None
+            if type != "inp":
+                if registers[1] in ("w", "x", "y", "z"):
+                    source = cast(Register, registers[1])
+                else:
+                    source = int(registers[1])
+
+            return Instruction(InstructionType(type), destination, source)
+
+        return [parse_instruction(line) for line in input]
+
+    def run_z3(instructions: List[Instruction]) -> int:
+        solver = z3.Optimize()
+
+        BITS = 64
+
+        digits = [z3.BitVec(f"input_{i}", BITS) for i in range(14)]
+        next_input = iter(digits).__next__
+
+        for d in digits:
+            solver.add(z3.And(1 <= d, d <= 9))
+
+        zero, one = z3.BitVecVal(0, BITS), z3.BitVecVal(1, BITS)
+
+        registers = {r: zero for r in ("w", "x", "y", "z")}
+
+        for i, instr in enumerate(instructions):
+            if instr.type == InstructionType.INPUT:
+                registers[instr.destination] = next_input()
+                continue
+
+            assert instr.source is not None  # Sanity check
+
+            value = registers[instr.destination]
+            if isinstance(instr.source, int):
+                source = z3.BitVecVal(instr.source, BITS)
+            else:
+                source = registers[instr.source]
+
+            res = z3.BitVec(f"result_{i}", BITS)
+            if instr.type == InstructionType.ADD:
+                solver.add(res == (value + source))
+            elif instr.type == InstructionType.MULTIPLY:
+                solver.add(res == (value * source))
+            elif instr.type == InstructionType.DIVIDE:
+                solver.add(source > zero)  # Sanity check
+                solver.add(res == (value / source))
+            elif instr.type == InstructionType.MODULO:
+                solver.add(value >= zero)  # Sanity check
+                solver.add(source > zero)  # Sanity check
+                solver.add(res == (value % source))
+            elif instr.type == InstructionType.EQUAL:
+                solver.add(res == z3.If(value == source, one, zero))
+            else:
+                assert False  # Sanity check
+            registers[instr.destination] = res
+
+        solver.add(registers["z"] == zero)
+
+        model_number = functools.reduce(lambda a, b: a * 10 + b, digits)
+
+        solver.minimize(model_number)
+        assert solver.check() == z3.sat  # Sanity check
+
+        return solver.model().eval(model_number)
+
+    return run_z3(parse())
+
+
+def main() -> None:
+    input = [line.rstrip("\n") for line in sys.stdin.readlines()]
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()