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n(1<=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