递归级别和循环计数

Question

我有一个家庭作业，我准备上交，在作业中，我不得不使用递归来绘制 10 层深的嵌套圆圈，在我的头撞了几个小时之后，我终于完成了它。我唯一的问题是，我绘制的图像是 10 层深还是实际上是 11 层？

这个问题来自这样一个事实，即我已经明确说明递归在经过 10 级时结束，但我确实告诉方法绘制原始圆圈然后它会调用自己。这让我觉得它绘制了第一个级别，然后下降 10 个，总共 11 个级别。它创建的图像下降到我无法数出圆圈：/

任何澄清将不胜感激，谢谢！

    // import statements
    import java.awt.*;
    import javax.swing.*;

    public class RecursiveCircles 
    {

public static void main(String[] args) 
{
    // create a new canvas
    RCanvas myCanvas = new RCanvas();

    // create JFrame
    JFrame myJframe = new JFrame();
    myJframe.setTitle("Recursive Circles");

    // set JFrame size, location and close operation
    myJframe.setSize(1500, 500);
    myJframe.setLocation(100, 100);
    myJframe.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

    // and canvas to JFrame and make it visble
    myJframe.getContentPane().add(myCanvas);
    myJframe.setVisible(true);

     } // end main          
   } // end class RecursiveCircles

    /*
     * this class will draw the main circle of the image and will have the recursive
     * method that draws the two outer circles down 10 levels
     */

    class RCanvas extends Canvas 
    {
   // defualt constructor 
   public RCanvas ()
   {}

   public void paint (Graphics graphics)
   { 
       // declare variables
       String title = "Recursive Circles";

       int n = 300; // diamerter of the circle
       int xOrigin = 600; // x location of start of circle (makes circle around the origin I wanted
       int yOrigin = 100; // y location of start of circle (makes circle around the origin i wanted
       int radius = n/2; // radius of circle (half the diamerter

       int level = 10;

       // make canvas background color black
       graphics.setColor(Color.black); // make the background color black
       graphics.fillRect(0, 0, 1500, 500); // rectangle that fills the JFrame

       // put title on canvas
       graphics.setColor(Color.BLUE);
       graphics.drawString(title, 725, 50);

       // draw main circle
       graphics.setColor(Color.WHITE);
       graphics.drawOval(xOrigin, yOrigin, n, n);   

      drawRCircles(graphics,xOrigin,yOrigin,radius,level); // call recrusrive method
       System.out.println(level);

   } // end paint

   /*
    * This is the recursive method that will draw the two circles on the outer sides of the
    * main circle. it will then call itself and repate the process till it is 10 levels deep
    */
   public void drawRCircles(Graphics graphics,int xOrigin,int yOrigin, int radius, int level)
   {

   int newRadius = (radius/2); // radius of smaller circle
   int newXOrigin = xOrigin - (newRadius); // xOrigin of circle on left of the main circle
   int newYOrigin = yOrigin + (newRadius); // yOrigin of circle on the right of the main circle
   int newXOrigin2 = xOrigin + (newRadius*3); // xOrigin of circle on the right of the main circle
   int newYOrigin2 = yOrigin + (newRadius); // yOrigin of circle on the right of the main circle
       if (level > 0) // counts down from 10 to make the recursive image 10 levels deep
       { 
           graphics.drawOval(newXOrigin, newYOrigin, newRadius*2, newRadius*2); // draw recursive circle on the left of main circle
           graphics.drawOval(newXOrigin2, newYOrigin2, newRadius*2, newRadius*2); // draw recursive circle on the right of main circle
           drawRCircles(graphics, newXOrigin, newYOrigin , newRadius, (level-1)); // make recursion of left circle
           drawRCircles(graphics, newXOrigin2, newYOrigin2,newRadius,(level-1)); // make recursion of right circle

       }// end if
   } // end drawRCircles
  }// end class

Answer 1

您的代码绘制了 11 个圆圈，但您对 drawRCircles 本身的调用仅负责其中的 10 个。

更具体地说，这些线画了 1 个圆圈。

    // draw main circle
    graphics.setColor(Color.WHITE);
    graphics.drawOval(xOrigin, yOrigin, n, n);  

无论您是否有drawRCircles 函数，都会绘制这个圆圈。 （尝试删除它并运行您的代码，看看会发生什么。）

然后，您的代码 调用 drawRCircles 函数 11 次，但自上次调用以来仅 绘制 10 个圆圈，级别 = 0 未通过测试 @ 987654325@.

它创建的图像下降到我无法数出圆圈：/

快速提示：由于您想知道在给定最大级别 N 的情况下，它是否会绘制 N 或 N+1 级别的圆圈，您也可以尝试将您的 level 变量更改为更多易于管理（如 2）并目视检查。

回到上面的代码，忽略draw main circle 部分（因为它独立于你的递归圆图）

    drawRCircles(graphics,xOrigin,yOrigin,radius,level); // call recursive method
    System.out.println(level);

在您的 public void drawRCircles(…) 函数中，

    drawRCircles(…,level-1);

让我们用 level = 2 而不是 10 来检查它：

    drawRCircles(…, 2) 
        --> Check if 1 > 0.  
            --> Yes, 1 > 0 so drawRCircles(…, 1) 
                -->  Check if 0 > 0.
                    --> No, 0 = 0, so stop.

层数 = 2 = 绘制的递归圈数。