汉诺塔问题的递归解法和非递归解法（python语言实现）

1. 汉诺塔问题的非递归解法（python语言类解法）

#!/usr/bin/env python
#coding:utf-8

import sys
import time
reload(sys)
sys.setdefaultencoding('utf-8')
class Mycolumns(object):
    val=0
    #__slots__ = ['plates','name']
    def __init__(self,name='',plates_num=0):
        self.name = name
        self.plates = []
        if plates_num > 0 :
            for i in range(0,plates_num):
                self.plates.append(n-i)
    @staticmethod
    def fun():
        Mycolumns.val +=1
        print"this is the %d th time to move" %(Mycolumns.val)

【这段可以用类方法代替】

【

@classmethod

    def fun(cls):

        cls.val +=1

        print"this is the %d th time to move" %(cls.val)

】

def initialize(n):
    stack = []
    mycolumn1 = Mycolumns('A',n)
    if n%2 == 0:
        mycolumn2 = Mycolumns('B')
        mycolumn3 = Mycolumns('C')
        index = 2
    else:
        mycolumn2 = Mycolumns('C')
        mycolumn3 = Mycolumns('B')
        index = 1
    stack.append(mycolumn1)
    stack.append(mycolumn2)
    stack.append(mycolumn3)
    return stack,index

def nowcolumn(i,stack):
    for item in stack:
        if i in item.plates:
            return item

def nextcolumn(i,stack):
    for item in stack:
        if i in item.plates:
            if i%2!=0:
                next = (stack.index(item)+1)%3
            else:
                next = (stack.index(item)+2)%3
            #print "%d next column is %s"%(i,stack[next].name)
            return stack[next]

def move(nowcolumn,nextcolumn):
    n = nowcolumn.plates.pop()
    nextcolumn.plates.append(n)
    print "move plate %d from %s to %s" %(n,nowcolumn.name,nextcolumn.name)
    Mycolumns.fun()

def hannuoyi(n):
    stack,index = initialize(n)
    #max = pow(2,n)-1
    #k =0
    #while(k<max):

　　 FINAL = []
　　 for i in range(0,n):
    　　FINAL.append(n-i)
　　 while(stack[index].plates!=FINAL):

        for i in range(1,n+1):
            #print "i value is %d" %(i)
            if(nowcolumn(i,stack).plates.index(i)==len(nowcolumn(i,stack).plates)-1 and (nextcolumn(i,stack).plates==[] or i< nextcolumn(i,stack).plates[-1])):
                move(nowcolumn(i,stack),nextcolumn(i,stack))
                #k = k+1
            else:
                pass
                #print"can not move plate %d" %(i)

    print stack[0].plates,stack[0].name
    print stack[1].plates,stack[1].name
    print stack[2].plates,stack[2].name
if __name__=="__main__":
    n=3
    hannuoyi(n) 

　　2. 汉诺塔问题的非递归解法（python语言过程式解法）

#!/usr/bin/env python

#coding:utf-8

 

import sys

import time

reload(sys)

sys.setdefaultencoding('utf-8')

global a

a =0

def fun():

    global a

    a = a+1

    print"this is the %d th time to move" %(a)

 

def nowcolumn(i,stackA,stackB,stackC):

    if i in stackA:

        return stackA

    elif i in stackB:

        return stackB

    else:

        return stackC

 

def nextcolumn(n,i,stackA,stackB,stackC):

    if n%2==0:

        if i in stackA:

            if i%2!=0:

                newcolumn = stackB

            else:

                newcolumn = stackC

        if i in stackB:

            if i%2!=0:

                newcolumn = stackC

            else:

                newcolumn = stackA

        if i in stackC:

            if i%2!=0:

                newcolumn = stackA

            else:

                newcolumn = stackB

    else:

        if i in stackA:

            if i%2==0:

                newcolumn = stackB

            else:

                newcolumn = stackC

        if i in stackB:

            if i%2==0:

                newcolumn = stackC

            else:

                newcolumn = stackA

        if i in stackC:

            if i%2==0:

                newcolumn = stackA

            else:

                newcolumn = stackB

    return newcolumn

def move(nowcolumn,nextcolumn):

    n = nowcolumn.pop()

    nextcolumn.append(n)

    print "move plate %d" %(n)

    fun()

 

 

def hannuoyi(n):

    stackA = []

    stackB = []

    stackC = []

    FINAL = []

    for i in range(0,n):

        stackA.append(n-i)

        FINAL.append(n-i)

    print stackA,stackB,stackC,FINAL

 

    while(stackC!=FINAL):

        for i in range(1,n+1):

            print "i value is %d" %(i)

            if(nowcolumn(i,stackA,stackB,stackC).index(i)==len(nowcolumn(i,stackA,stackB,stackC))-1 and (nextcolumn(n,i,stackA,stackB,stackC)==[] or i< nextcolumn(n,i,stackA,stackB,stackC)[-1])):

                move(nowcolumn(i,stackA,stackB,stackC),nextcolumn(n,i,stackA,stackB,stackC))

            else:

                print"can not move plate %d" %(i)

            print stackA,stackB,stackC

if __name__=="__main__":

    n=6

    hannuoyi(n)

2. 汉诺塔问题的递归解法（python语言）

#!/usr/bin/env python

#coding:utf-8

 

import sys

 

reload(sys)

sys.setdefaultencoding('utf-8')

global a

a =0

def fun():

    global a

    a = a+1

 

def hannuoyi(n,A,B,C):

    if n==1:

        move(1,A,C)

    else:

        hannuoyi(n-1,A,C,B)

        move(n,A,C)

        hannuoyi(n-1,B,A,C)

 

def move(n,tempA,tempB):

    print "move plate %d from column %s to column %s" %(n,tempA,tempB)

    fun()

if __name__=="__main__":

    hannuoyi(3,'A','B','C')

    print "total:we need %d steps"%(a)