p118.py

def solve(part, j, S, S_set, S_all_sets, P):
    if j == len(part):
        S_all_sets.append(S_set)
        return S_set
    for x in P[part[j]]:
        if all(S[int(i)] + 1 != 2 for i in str(x)):
            SS = [S[k] for k in range(10)]
            for i in str(x):
                SS[int(i)] += 1
            if x == max(S_set + [x]):
                solve(part, j + 1, SS, S_set + [x], S_all_sets, P)

def Method1():
    P = [[] for _ in range(10)]

    for k in range(1, 10):
        for x in itertools.permutations("123456789", k):
            v = int("".join(x))
            if is_prime(v):
                P[k].append(v)
        
    total = 0
    for part in partition(9, [1,2,3,4,5,6,7,8,9]):
        
        S_all_set = []
        S = [1,0,0,0,0,0,0,0,0,0]
        solve(part[::-1], 0, S, [], S_all_set, P)
        total += len(S_all_set)
                
    return total
  
def Method2():
    P = [[] for _ in range(10)]

    for k in range(1, 10):
        for x in itertools.permutations("123456789", k):
            v = int("".join(x))
            if is_prime(v):
                P[k].append("".join(x))
    
    total = 0
    for part in partition(9, [1,2,3,4,5,6,7,8,9]):
        for a in itertools.product(*[P[i] for i in part]):
            v = "".join(a)
            v1 = [int(j) for j in a][::-1]
            if v1 == sorted(v1):
                if all([str(i) in v for i in range(1, 10)]):
                    total += 1
                
    return total