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  • 用python编写一个程序,得到汉诺塔的解决方案

            古代有一座汉诺塔,塔内有3个座A、B、C,A座上有n个盘子,盘子大小不等,大的在下,小的在上,如图所示。

    有一个和尚想把这n个盘子从A座移到C座,但每次只能移动一个盘子,并且自移动过程中,3个座上的盘子始终保持大盘在下,小盘在上。在移动过程中可以利用B座来放盘子。

      现在我编写一个程序(其实就是运用了递归思想)输入一个正整数,表示汉诺塔内的盘子个数n1<=n<=64)然后输出移动的步骤。

    步骤一:代码如下:

    def move(x,y):
    
    print("%s --> %s"%(x,y))
    
    def hanoi(n,one,two,three):
    
    if n==1:
    
    move(one,three)
    
    else:
    
    hanoi(n-1,one,three,two)
    
    move(one,three)
    
    hanoi(n-1,two,one,three)
    
    def main():#main函数
    
    m=int(input())#输入盘子个数
    
    hanoi(m,'A','B','C')
    
    main()
    

      

    步骤二:执行代码,现在我输入4,即4个盘子,看看搬运的步骤是怎么样的:

    附:用turtle画出步骤则更直观,也更有趣,下面用turtle画出搬运过程

    import turtle
     
    class Stack:
        def __init__(self):
            self.items = []
        def isEmpty(self):
            return len(self.items) == 0
        def push(self, item):
            self.items.append(item)
        def pop(self):
            return self.items.pop()
        def peek(self):
            if not self.isEmpty():
                return self.items[len(self.items) - 1]
        def size(self):
            return len(self.items)
     
    def drawpole_3():#画出汉诺塔的poles
        t = turtle.Turtle()
        t.hideturtle()
        def drawpole_1(k):
            t.up()
            t.pensize(10)
            t.speed(100)
            t.goto(400*(k-1), 100)
            t.down()
            t.goto(400*(k-1), -100)
            t.goto(400*(k-1)-20, -100)
            t.goto(400*(k-1)+20, -100)
        drawpole_1(0)#画出汉诺塔的poles[0]
        drawpole_1(1)#画出汉诺塔的poles[1]
        drawpole_1(2)#画出汉诺塔的poles[2]
     
    def creat_plates(n):#制造n个盘子
        plates=[turtle.Turtle() for i in range(n)]
        for i in range(n):
            plates[i].up()
            plates[i].hideturtle()
            plates[i].shape("square")
            plates[i].shapesize(1,8-i)
            plates[i].goto(-400,-90+20*i)
            plates[i].showturtle()
        return plates
     
    def pole_stack():#制造poles的栈
        poles=[Stack() for i in range(3)]
        return poles
     
    def moveDisk(plates,poles,fp,tp):#把poles[fp]顶端的盘子plates[mov]从poles[fp]移到poles[tp]
        mov=poles[fp].peek()
        plates[mov].goto((fp-1)*400,150)
        plates[mov].goto((tp-1)*400,150)
        l=poles[tp].size()#确定移动到底部的高度(恰好放在原来最上面的盘子上面)
        plates[mov].goto((tp-1)*400,-90+20*l)
     
    def moveTower(plates,poles,height,fromPole, toPole, withPole):#递归放盘子
        if height >= 1:
            moveTower(plates,poles,height-1,fromPole,withPole,toPole)
            moveDisk(plates,poles,fromPole,toPole)
            poles[toPole].push(poles[fromPole].pop())
            moveTower(plates,poles,height-1,withPole,toPole,fromPole)
     
    myscreen=turtle.Screen()
    drawpole_3()
    n=int(input("请输入汉诺塔的层数并回车:
    "))
    plates=creat_plates(n)
    poles=pole_stack()
    for i in range(n):
        poles[0].push(i)
    moveTower(plates,poles,n,0,2,1)
    myscreen.exitonclick()#代码参考https://blog.csdn.net/beerbread134/article/details/69226991
    

      

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  • 原文地址:https://www.cnblogs.com/daydayup12138/p/10588712.html
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