import numpy as np, time
def gap(w,pattern,T):
    n=2*w+1; N=1<<n; L=n+2*T+4; off=T+2
    idx=np.arange(N,dtype=np.int64)
    X=np.zeros((N,L),dtype=np.uint8)
    for j in range(n): X[:,off+j]=(idx>>j)&1
    X=X[(idx & 1)|(idx>>(n-1))&1 >0] if False else X
    alive=np.ones(N,bool); last=np.full(N,-1)
    for t in range(T):
        c=X[:,off+w]
        ok=(c==pattern[t%len(pattern)])
        newly=alive&~ok; last[newly]=t-1; alive&=ok
        if not alive.any(): break
        l=np.roll(X,1,axis=1); r=np.roll(X,-1,axis=1); X=l^(X|r)
    last[alive]=T
    nz=idx!=0
    return int(last[nz].max())
t0=time.time()
for pat in ((0,1),(1,0)):
    row=[]
    for w in range(1,11):
        g=gap(w,pat,4*w+20)
        row.append(f"w={w}: {g} ({g-w:+d})")
        if time.time()-t0>200: break
    print(f"centre pattern {''.join(map(str,pat))}...: longest match (steps past width): "+"  ".join(row))