1import numpy as np
 2from wedge_pool import all_pairs_dist, wedge_split, connected, sse
 3from collections import deque
 4
 5
 6def connected_graph(adj):
 7    seen={0}; q=deque([0])
 8    while q:
 9        v=q.popleft()
10        for z in adj[v]:
11            if z not in seen: seen.add(z); q.append(z)
12    return len(seen)==len(adj)
13
14
15def main():
16    rng=np.random.default_rng(123)
17    failures=[]; checks=0
18    for trial in range(500):
19        n=int(rng.integers(5,14))
20        adj=[set() for _ in range(n)]
21        # random connected backbone plus extra edges
22        for i in range(1,n):
23            j=int(rng.integers(i)); adj[i].add(j); adj[j].add(i)
24        for i in range(n):
25            for j in range(i):
26                if rng.random()<.18: adj[i].add(j); adj[j].add(i)
27        adj=[sorted(x) for x in adj]
28        R=list(range(n)); D=all_pairs_dist(adj,R)
29        for u in range(n):
30            for w in range(u+1,n):
31                A,B=wedge_split(adj,R,u,w,D)
32                if A and B:
33                    checks+=1
34                    if not connected(adj,A) or not connected(adj,B):
35                        failures.append((trial,n,u,w,A,B)); break
36            if failures: break
37        if failures: break
38    # Independent mean identity: SSE around c = SSE around mean + |R| ||c-mu||^2.
39    X=rng.normal(size=(17,3)); R=list(range(17)); c=rng.normal(size=3)
40    cost,mu=sse(X,R); lhs=float(((X-c)**2).sum()); rhs=cost+len(R)*float(((c-mu)**2).sum())
41    print({'random_graph_split_checks':checks,'connectivity_failures':len(failures),
42           'first_failure':failures[:1], 'mean_identity_abs_error':abs(lhs-rhs),
43           'mean_cost':cost,'arbitrary_cost':lhs})
44
45if __name__=='__main__': main()