Implement day 7 solver

puzzles/4.py

@@ -1,6 +1,5 @@
 from typing import Iterator
 
-
 test_input = """
 MMMSXXMASM
 MSAMXMSMSA

puzzles/5.py

@@ -1,6 +1,5 @@
 from typing import Iterator
 
-
 test_input = """
 47|53
 97|13

puzzles/6.py

@@ -1,6 +1,5 @@
 from typing import NamedTuple
 
-
 test_input = """
 ....#.....
 .........#

puzzles/7.py

@@ -0,0 +1,84 @@
+from functools import partial
+from typing import Callable, Iterator, NamedTuple
+from math import log
+
+
+test_input = """
+190: 10 19
+3267: 81 40 27
+83: 17 5
+156: 15 6
+7290: 6 8 6 15
+161011: 16 10 13
+192: 17 8 14
+21037: 9 7 18 13
+292: 11 6 16 20
+""".strip()
+
+test_solution_p1 = 3749
+test_solution_p2 = 11387
+
+
+def solve_p1(puzzle_input: str) -> int:
+    equations = _parse_equations(puzzle_input)
+    calibration_guard = partial(
+        _is_calibrated,
+        [
+            int.__add__,
+            int.__mul__,
+        ],
+    )
+    return sum(equation.target for equation in filter(calibration_guard, equations))
+
+
+def solve_p2(puzzle_input: str) -> int:
+    equations = _parse_equations(puzzle_input)
+    calibration_guard = partial(
+        _is_calibrated,
+        [
+            int.__add__,
+            int.__mul__,
+            _concat_ints,
+        ],
+    )
+    return sum(equation.target for equation in filter(calibration_guard, equations))
+
+
+class Equation(NamedTuple):
+    target: int
+    factors: tuple[int, ...]
+
+
+def _parse_equations(puzzle_input: str) -> Iterator[Equation]:
+    for line in puzzle_input.split("\n"):
+        if line:
+            result_string, _, factors_string = line.partition(": ")
+            yield Equation(
+                int(result_string),
+                tuple(map(int, factors_string.split(" "))),
+            )
+
+
+Operator = Callable[[int, int], int]
+
+
+def _is_calibrated(operators: list[Operator], equation: Equation) -> bool:
+    def _eval_permutations(factors: tuple[int, ...]) -> Iterator[int]:
+        assert len(factors) > 0
+        tail = factors[-1]
+        if len(factors) == 1:
+            yield tail
+            return
+        for head in _eval_permutations(factors[:-1]):
+            if head > equation.target:
+                continue
+            for operator in operators:
+                yield operator(head, tail)
+
+    return any(
+        result == equation.target for result in _eval_permutations(equation.factors)
+    )
+
+
+def _concat_ints(a: int, b: int) -> int:
+    return 10 ** int(log(b, 10) + 1) * a + b