罗马数字和数字的转化和一个puzzle

1. 罗马数字和数字的转化
下面两段代码出自

def to_roman(x):
    anums = [1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1]
    rnums = "M CM D CD C XC L XL X IX V IV I".split()
    ret=[]
    for a,r in zip(anums,rnums):
        n,x=divmod(x,a)
        ret.append(r*n)
    return "".join(ret)

def test_to_roman():
    test=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,25,30,40,
        50,60,69,70,80,90,99,100,200,300,400,500,600,666,700,800,900,
        1000,1009,1444,1666,1945,1997,1999,2000,2008,2010,2011,2500,
        3000,3999)

    for i in test:
        print("number {} to roman is {}".format(i,to_roman(i)))

#test_to_roman()

def to_arabic(x):
    decoder=dict(zip('MDCLXVI',(1000,500,100,50,10,5,1)))
    result=0
    for r,r1 in zip(x,x[1:]):
        rd,rd1=decoder[r],decoder[r1]
        if rd < rd1:
            result+=-rd
        else:
            result+=rd
    return result+decoder[x[-1]]

def test_to_arabic():
    ll='MCMXC MMVIII MDCLXVI'.split()
    for i in ll:
        print(to_arabic(i))

test_to_arabic()

下面的代码是我自己写的。 和别人的比，果然是差很多了。

def to_arabic2(s):
    #s: sequence
    decoder=dict(zip('MDCLXVI',(1000,500,100,50,10,5,1)))
    result=0
    for i in range(len(s)-1):
        value=decoder.get(s[i])
        vnext=decoder.get(s[i+1])
        if value < vnext:
            result+=-value
        else:
            result+=value
    return result+decoder.get(s[-1])

def test_to_arabic2():
    ll='MCMXC MMVIII MDCLXVI'.split()
    for i in ll:
        print(to_arabic2(i))

test_to_arabic2()

2. 一个puzzle ,出自： Puzzle:
A merchant has a 40 kg weight which he used in his shop. Once, it fell from his hands and was broken into 4 pieces. But surprisingly, now he can weigh any weight between 1 kg to 40 kg with the combination of these 4 pieces.
So question is, what are weights of those 4 pieces?
这个哥们的代码写的太通用了，还加上pieces. 即N个pieces，sum(n)==L, 同时可以表示1->L，很有趣的题目

import itertools as it
def find_weights(weight,pieces):
    full=range(1,weight+1)
    all_nums=set(full)
    comb=[x for x in it.combinations(full,pieces) if sum(x)==40]
    funcs=(lambda x: 0, lambda x: x, lambda x: -x)
    for c in comb:
        sums=set()
        for fmap in it.product(funcs,repeat=pieces):
            s=sum(f(x) for x,f in zip(c,fmap))
            if s>0:
                sums.add(s)
                if sums==all_nums:
                    return c


print(find_weights(40,5))