Python (Not C...)
(Posting from an alt because SDF is having issues)
A graph problem ๐ฌโ. There are well-known algorithms but none trivial to implement in C.
I tried dividing the nodes into two groups and then moving the node with the worst in-group/out-group edge balance - a Wish version of the Kernighan-Lin algorithm. As expected, it got stuck in a local optimum for the real input and random prodding didn't help.
Programming is programming and libraries are fair game so I went to Python and used NetworkX which was my first time using the library but so easy to use! Maybe I'll go back and do it in C someday and implement the algorithm myself.
#!/usr/bin/env python3
import sys
import re
from networkx import Graph
from networkx.algorithms.community import greedy_modularity_communities
G = Graph()
for line in sys.stdin.readlines():
words = re.findall("\\w+", line)
for to in words[1:]:
G.add_edge(words[0], to)
coms = greedy_modularity_communities(G, best_n=2)
print("25:", len(coms[0]) * len(coms[1]))
https://github.com/sjmulder/aoc/tree/master/2023/python/day25.py