[LeetCode] 由 “分形" 所想

分形思想和递归思想有区别么？

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一、简单例子

函数调用自己，简化了理解逻辑，但其他到处都是问题。

#%%
def listsum(numList):
    if len(numList) == 1:
        return numList[0]
    else:
        return numList[0] + listsum(numList[1:])

print(listsum([1,3,5,7,9]))

　　

二、分形的思想

中文版本Tutorial: turtle --- 海龟绘图

无限分叉树

import turtle
deftree(branchLen,t):
    if branchLen > 5:
        # 出发后做出一系列动作，最后要回到原点
        t.forward(branchLen)
        t.right(20)
        tree(branchLen-15,t)
        t.left(40)
        tree(branchLen-15,t)
        t.right(20)
        t.backward(branchLen)

def main():
    t = turtle.Turtle()
    myWin = turtle.Screen()
    t.left(90)
    t.up()
    t.backward(100)
    t.down()
    t.color("green")
    tree(100,t)
    myWin.exitonclick()
main()

输出：

谢尔宾斯基三角形

import turtle

def drawTriangle(points,color,myTurtle):
    myTurtle.fillcolor(color)
    myTurtle.up()
    myTurtle.goto(points[0][0],points[0][1])
    myTurtle.down()
    myTurtle.begin_fill()
    myTurtle.goto(points[1][0],points[1][1])
    myTurtle.goto(points[2][0],points[2][1])
    myTurtle.goto(points[0][0],points[0][1])
    myTurtle.end_fill()

def getMid(p1,p2):
    return ( (p1[0]+p2[0]) / 2, (p1[1] + p2[1]) / 2)
#########################################################################
def sierpinski(points,degree,myTurtle):
    colormap = ['blue','red','green','white','yellow', 'violet','orange']
    drawTriangle(points,colormap[degree],myTurtle)
    if degree > 0:
        sierpinski([points[0], getMid(points[0], points[1]), getMid(points[0], points[2])], degree-1, myTurtle)
        sierpinski([points[1], getMid(points[0], points[1]), getMid(points[1], points[2])], degree-1, myTurtle  )
        sierpinski([points[2], getMid(points[2], points[1]), getMid(points[0], points[2])], degree-1, myTurtle)

def main():
    myTurtle = turtle.Turtle()
    myWin = turtle.Screen()
    myPoints = [[-100,-50],[0,100],[100,-50]]
    sierpinski(myPoints,3,myTurtle)
    myWin.exitonclick()

main()

输出：

三、汉诺塔游戏

核心思想

要把fromPole最下面的"盘子“转移到toPole，就先要解决：

要把fromPole的height-1的"盘子“转移到withPole；在此之后：

把withPole的”盘子“也转移到toPole。

对应代码

def moveDisk(fp,tp):
　　print("moving disk from",fp,"to",tp)

def moveTower(height,fromPole, toPole, withPole):
　　if height >= 1:
　　　　moveTower(height-1,fromPole,withPole,toPole)
　　　　moveDisk(fromPole,toPole)
　　　　moveTower(height-1,withPole,toPole,fromPole)

模拟栈帧 之 二叉树遍历

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/* implement */