2015 day 24.

src/holt59/aoc/2015/day24.py

@@ -0,0 +1,88 @@
+from typing import Any, Iterator, TypeAlias
+
+from ..base import BaseSolver
+
+TupleOfInts: TypeAlias = tuple[int, ...]
+
+
+def check_n_groups(
+    target: int, groups: tuple[TupleOfInts, ...], numbers: TupleOfInts
+) -> bool:
+    n_groups = len(groups)
+    groups_s = tuple(sum(group) for group in groups)
+
+    if all(target == group_s for group_s in groups_s):
+        return not numbers
+
+    if not numbers:
+        return False
+
+    head, *tail_l = numbers
+    tail, tail_s = tuple(tail_l), sum(tail_l)
+
+    return any(
+        groups_s[i] + head <= target
+        and sum(groups_s[j] for j in range(len(groups)) if i != j) + tail_s
+        >= (n_groups - 1) * target
+        and check_n_groups(
+            target, groups[:i] + ((groups[i] + (head,)),) + groups[i + 1 :], tail
+        )
+        for i in range(len(groups))
+    )
+
+
+def enumerate_single_subset(
+    target: int, numbers: TupleOfInts
+) -> Iterator[tuple[int, TupleOfInts, TupleOfInts]]:
+    """
+    Enumerate subset of numbers whose sum equals target.
+
+    Subset are enumerated in increasing order of length, then product (quantum value).
+
+    Args:
+        target: Target for the sum of the subset.
+        numbers: Tuple of integers to find the subset from.
+
+    Returns:
+        A generator (quantum, subset, remaining) where subset if the subset of numbers
+        whose sum equals target, quantum the product of the subset, and remaining the
+        remaining numbers.
+    """
+    groups: list[tuple[int, TupleOfInts, TupleOfInts]] = [(1, (), numbers)]
+
+    for _ in range(len(numbers)):
+        new_groups: list[tuple[int, TupleOfInts, TupleOfInts]] = []
+
+        for g_quantum, group, remaining in groups:
+            sg = sum(group)
+            for i in range(len(remaining)):
+                if group and remaining[i] <= group[-1]:
+                    continue
+
+                uv = remaining[:i] + remaining[i + 1 :]
+                kv = g_quantum * remaining[i], group + (remaining[i],), uv
+
+                if sg + remaining[i] == target:
+                    yield kv
+                elif sg + remaining[i] < target:
+                    new_groups.append(kv)
+
+        groups = new_groups
+
+
+def find_min_quantum(numbers: tuple[int, ...], n_groups: int):
+    return next(
+        g_quantum
+        for g_quantum, group_1v2, group_234v2 in enumerate_single_subset(
+            sum(numbers) // n_groups, numbers
+        )
+        if check_n_groups(sum(group_1v2), ((),) * (n_groups - 1), group_234v2)
+    )
+
+
+class Solver(BaseSolver):
+    def solve(self, input: str) -> Iterator[Any]:
+        numbers = tuple(map(int, input.split()))
+
+        yield find_min_quantum(numbers, 3)
+        yield find_min_quantum(numbers, 4)

src/holt59/aoc/inputs/holt59/2015/day24.txt

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+1
+3
+5
+11
+13
+17
+19
+23
+29
+31
+41
+43
+47
+53
+59
+61
+67
+71
+73
+79
+83
+89
+97
+101
+103
+107
+109
+113

src/holt59/aoc/inputs/tests/2015/day24.txt

@@ -0,0 +1,10 @@
+1
+2
+3
+4
+5
+7
+8
+9
+10
+11