narcissus 水仙花數

def num_to_dict(num):
    num = [int(_) for _ in str(num)]
    dic = {}
    for e in num:
        dic[e] = dic.get(e, 0) + 1
    return dic


def my_narcissus(N, M):
    re, power = [], {}
    for num in range(N, M):
        if not num%N or not num%(10**6):
            print('.', end='')
        dic = num_to_dict(num)
        lng = len(str(num))
        cnt = 0
        for key in dic:
            if not (key, lng) in power:
                power[(key, lng)] = key**lng
            cnt += dic[key] * power[(key, lng)]
        if cnt == num:
            re.append(num)
    print()
    return re


import time
scale = 10**6
for l in range(5):
    start_time = time.time()
    print(l+1, '位數', end='')
    t = narcissus(10**l, 10**(l+1))
    time_spend = time.time()-start_time
    print(t)
    print('時間:', time_spend)
    print('時間比例:', time_spend/(9*10**l)*scale, '\n')