2018: d25: ex1: add solution

2018/d25/ex1/ex1.py

@@ -0,0 +1,111 @@
+#!/usr/bin/env python
+
+import collections
+import itertools
+import sys
+from collections.abc import Iterable
+from typing import Generic, Hashable, NamedTuple, TypeVar
+
+
+class Point(NamedTuple):
+    x: int
+    y: int
+    z: int
+    t: int
+
+
+class UnionFind:
+    _parent: list[int]
+    _rank: list[int]
+
+    def __init__(self, size: int):
+        # Each node is in its own set, making it its own parent...
+        self._parent = list(range(size))
+        # ... And its rank 0
+        self._rank = [0] * size
+
+    def find(self, elem: int) -> int:
+        while (parent := self._parent[elem]) != elem:
+            # Replace each parent link by a link to the grand-parent
+            elem, self._parent[elem] = parent, self._parent[parent]
+        return elem
+
+    def union(self, lhs: int, rhs: int) -> int:
+        lhs = self.find(lhs)
+        rhs = self.find(rhs)
+        # Bail out early if they already belong to the same set
+        if lhs == rhs:
+            return lhs
+        # Always keep `lhs` as the taller tree
+        if self._rank[lhs] < self._rank[rhs]:
+            lhs, rhs = rhs, lhs
+        # Merge the smaller tree into the taller one
+        self._parent[rhs] = lhs
+        # Update the rank when merging trees of approximately the same size
+        if self._rank[lhs] == self._rank[rhs]:
+            self._rank[lhs] += 1
+        return lhs
+
+    def sets(self) -> dict[int, set[int]]:
+        res: dict[int, set[int]] = collections.defaultdict(set)
+        for elem in range(len(self._parent)):
+            res[self.find(elem)].add(elem)
+        return dict(res)
+
+
+# PEP 695 still not supported by MyPy...
+T = TypeVar("T", bound=Hashable)
+
+
+class DisjointSet(Generic[T]):
+    _values: list[T]
+    _to_index: dict[T, int]
+    _sets: UnionFind
+
+    def __init__(self, values: Iterable[T]) -> None:
+        self._values = list(values)
+        self._to_index = {v: i for i, v in enumerate(self._values)}
+        self._sets = UnionFind(len(self._values))
+
+    def find(self, elem: T) -> T:
+        return self._values[self._sets.find(self._to_index[elem])]
+
+    def union(self, lhs: T, rhs: T) -> T:
+        return self._values[self._sets.union(self._to_index[lhs], self._to_index[rhs])]
+
+    def sets(self) -> dict[T, set[T]]:
+        sets = self._sets.sets()
+        return {
+            self._values[r]: {self._values[i] for i in values}
+            for r, values in sets.items()
+        }
+
+
+def solve(input: str) -> int:
+    def parse(input: list[str]) -> list[Point]:
+        return [Point(*map(int, line.split(","))) for line in input]
+
+    def dist(lhs: Point, rhs: Point) -> int:
+        return sum(abs(l - r) for l, r in zip(lhs, rhs))
+
+    def count_constellations(points: list[Point]) -> int:
+        sets = DisjointSet(points)
+
+        for a, b in itertools.combinations(points, 2):
+            if dist(a, b) > 3:
+                continue
+            sets.union(a, b)
+
+        return len(sets.sets())
+
+    points = parse(input.splitlines())
+    return count_constellations(points)
+
+
+def main() -> None:
+    input = sys.stdin.read()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()