一个貌似比较吊的递归转换为loop--总算成功了.

class Stack(object):
    """
    A class to hold arguements and state data.
    """
    def __init__(self,**kwargs):
        self.__dict__.update(kwargs)

    def __repr__(self):
        extra = "|i:%s"%self.i if hasattr(self,'i') else ''
        return "n:%s|stage:%s%s"%(self.n,self.stage,extra)
    
def memory(function):
    """
    A decorator to help a no-side-effect function avoid
    repeative calculation.
    """
    cache = {}
    def memofunc(*nkw,**kw):
        key=str(nkw)+str(kw)
        if key not in cache:            
            cache[key] = function(*nkw,**kw)
        return cache[key]
    return memofunc

def is_equal(rg,*funclist):
    """
    to test whether or not a list of one-arguement functions
    have the same output if given same arguement.
    """
    for n in rg:
        rst=[]
        for func in funclist:
            rst.append(func(n))
            assert len(set(rst))==1

@memory
def hanoi_recur(n):
    """
    n -> (i,v)
    a recursive function to get the smallest number i
    and correspondent value.
    """
    if n==1:
        return 1,1
    psb=[]
    for i in range(n-1,0,-1):
        _, min_v = hanoi_recur(n-i)
        psb_v = 2*min_v+2**i-1
        psb.append((i,psb_v))
    return min(psb,key=lambda x:x[1])

@memory
def