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 hanoi_loop(n): """ The loop version of hanoi_recur. """ if n==1: return 1,1 stack = [Stack(n=n,stage=0,)] cache={1:1} while stack: crt=stack.pop() if crt.n in cache: psb_v = 2*cache[crt.n]+2**crt.i-1 crt.prt.psb.append((crt.i,psb_v)) continue if crt.stage==0: crt.stage, crt.pgs, crt.psb= 1, 0, [] stack.append(crt) continue if crt.stage==1: if crt.pgs != crt.n - 1: crt.pgs += 1 stack.append(crt) chd = Stack(n=crt.pgs, stage=0, i=crt.n-crt.pgs, prt=crt) stack.append(chd) else: crt.stage=2 stack.append(crt) continue if crt.stage==2 and hasattr(crt,'prt'): #hasattr - the last stack doesn't have attribute 'prt', #so it has to be excluded here. _, min_v = min(crt.psb,key=lambda x:x[1]) psb_v = 2*min_v + 2**crt.i - 1 crt.prt.psb.append((crt.i,psb_v)) cache[crt.n] = min_v continue return min(crt.psb,key=lambda x:x[1]) if __name__=='__main__': is_equal(range(1,300),hanoi_loop,hanoi_recur) print('passed test!')