2024: d23: ex2: add solution

2024/d23/ex2/ex2.py

@@ -0,0 +1,57 @@
+#!/usr/bin/env python
+
+import sys
+from collections import defaultdict
+from collections.abc import Iterator
+
+
+def solve(input: str) -> str:
+    def parse_line(input: str) -> tuple[str, str]:
+        lhs, rhs = input.split("-")
+        return lhs, rhs
+
+    def parse(input: list[str]) -> list[tuple[str, str]]:
+        return [parse_line(line) for line in input]
+
+    def links_to_graph(topology: list[tuple[str, str]]) -> dict[str, set[str]]:
+        graph: dict[str, set[str]] = defaultdict(set)
+        for lhs, rhs in topology:
+            graph[lhs].add(rhs)
+            graph[rhs].add(lhs)
+        return graph
+
+    # Maximum clique solution thanks to [1]
+    # [1]: https://en.wikipedia.org/wiki/Bron%E2%80%93Kerbosch_algorithm
+    def bron_kerbosch(graph: dict[str, set[str]]) -> Iterator[set[str]]:
+        def helper(
+            clique: set[str],
+            candidates: set[str],
+            discarded: set[str],
+        ) -> Iterator[set[str]]:
+            if not candidates and not discarded:
+                yield clique
+            while candidates:
+                v = candidates.pop()
+                yield from helper(
+                    clique | {v},
+                    candidates & graph[v],
+                    discarded & graph[v],
+                )
+                discarded.add(v)
+
+        return helper(set(), set(graph.keys()), set())
+
+    topology = parse(input.splitlines())
+    graph = links_to_graph(topology)
+    cliques = bron_kerbosch(graph)
+    historian_group = max(cliques, key=len)  # MyPy doesn't like it inline in `sorted`
+    return ",".join(sorted(historian_group))
+
+
+def main() -> None:
+    input = sys.stdin.read()
+    print(solve(input))
+
+
+if __name__ == "__main__":
+    main()