"""R628：有限网格方法与解析不可行证书；fallback必须重新验约束。"""
from itertools import product
from math import isfinite,isclose

ASSETS=['A','B','C'];SECTOR={'A':'Tech','B':'Tech','C':'Health'}
RET=[.08,.06,.03];VAR=[.04,.01,.0025]


def valid(weights,caps,required=1.,asset_cap=.6,min_return=.055):
    if set(caps)-set(SECTOR.values()) or any(not isfinite(cap) or cap<0 for cap in caps.values()):return False
    if not isfinite(required) or required<0 or not isfinite(asset_cap) or asset_cap<0 or not isfinite(min_return):return False
    if len(weights)!=3 or any(not isfinite(x) or x<0 for x in weights):return False
    if abs(sum(weights)-required)>1e-10:return False
    if any(x>asset_cap+1e-10 for x in weights):return False
    if any(sum(w for s,w in zip(ASSETS,weights) if SECTOR[s]==sector)>cap+1e-10 for sector,cap in caps.items()):return False
    return sum(w*r for w,r in zip(weights,RET))>=min_return-1e-10


def solve(caps,solver_available=True,data_ok=True):
    if not data_ok:return {'status':'insufficient_data','weights':None}
    if set(caps)-set(SECTOR.values()):raise ValueError('unknown constrained sector')
    if any(not isfinite(v) or v<0 for v in caps.values()):raise ValueError('invalid cap')
    if set(caps)=={'Tech','Health'} and sum(caps.values())<1-1e-10:
        return {'status':'proven_infeasible','weights':None,'conflict':['full_investment','Tech_cap','Health_cap']}
    if not solver_available:
        fallback=[1/3]*3
        return {'status':'solver_unavailable_fallback' if valid(fallback,caps) else 'fallback_rejected',
                'weights':fallback if valid(fallback,caps) else None,'optimized':False}
    candidates=[list(w) for w in product([i/10 for i in range(11)],repeat=3) if valid(w,caps)]
    if not candidates:return {'status':'no_grid_candidate','weights':None}
    chosen=min(candidates,key=lambda w:(sum(v*x*x for v,x in zip(VAR,w)),w))
    assert valid(chosen,caps)
    return {'status':'grid_optimum','weights':chosen,'optimized':True}


caps={'Tech':.7,'Health':.6};answer=solve(caps)
assert answer['weights']==[.2,.5,.3]
assert isclose(sum(w*r for w,r in zip(answer['weights'],RET)),.055,rel_tol=0,abs_tol=1e-12)
assert isclose(sum(v*w*w for v,w in zip(VAR,answer['weights'])),.004325,rel_tol=0,abs_tol=1e-12)
assert solve({'Tech':.4,'Health':.4})['status']=='proven_infeasible'
# 该证书是极小冲突：取消任一行业帽或全投资要求，都有构造性可行点。
assert valid([.3,.3,.4],{'Health':.4},min_return=0)
assert valid([.2,.2,.6],{'Tech':.4},min_return=0)
assert valid([0,0,0],{'Tech':.4,'Health':.4},required=0,min_return=0)
assert solve(caps,False)['status']=='solver_unavailable_fallback'
assert solve({'Tech':.6,'Health':.6},False)['status']=='fallback_rejected'
assert solve(caps,data_ok=False)['status']=='insufficient_data'
assert solve({'Tech':.65,'Health':.35})['status']=='no_grid_candidate'
assert valid([.4,.25,.35],{'Tech':.65,'Health':.35})
assert not valid([float('nan'),.5,.5],caps)
assert not valid([float('inf'),0,0],caps)
invalid_constraints=[]
for name,changes in [
    ('NaN_sector_cap',{'caps':{'Tech':float('nan'),'Health':.6}}),
    ('NaN_required',{'required':float('nan')}),
    ('NaN_asset_cap',{'asset_cap':float('nan')}),
    ('infinite_sector_cap',{'caps':{'Tech':float('inf'),'Health':.6}}),
    ('infinite_required',{'required':float('inf')}),
    ('infinite_asset_cap',{'asset_cap':float('inf')}),
    ('unknown_sector',{'caps':{'Unknown':.7}}),
    ('negative_sector_cap',{'caps':{'Tech':-.1}}),
    ('NaN_min_return',{'min_return':float('nan')}),
]:
    options={'caps':caps};options.update(changes)
    if valid([.2,.5,.3],**options):invalid_constraints.append(name)
assert not invalid_constraints,invalid_constraints
print('grid_weights='+str(answer['weights'])+' expected_return=5.500000% variance=0.004325')
print('sector_caps_0.4_0.4=proven_infeasible conflict=full_investment,Tech_cap,Health_cap')
print('solver_missing=explicit_fallback fallback_constraints_rechecked=True invalid_fallback=rejected data_missing=distinct NaN=rejected')
print('no_grid_candidate=not_a_continuous_infeasibility_certificate')