recursive function practice, work on a small example to explain the ideas. Write a test case this time.

HTree_practice_Nov29_2017.cs

using System;

class HelloWorld
{
    static void Main()
    {
        DrawHTreeGivenDepthLength(2, 0, 3, 4);
    }
  
    public static void DrawHTreeGivenDepthLength(double x, double y, int depth, double length) // 2, 0, 3, 4
    {
      // base case
      if(depth == 0 || depth < 0) // false
      {
        return; 
      }
      
      // draw h- tree 
      double half = length/2; // 2
      double leftH  = x - half;  // 0 
      double rigthH = x + half; // 4
      
      drawLine(x - half , y, x + half, y);  // horizontal line (0, 0, 4, 0)
      drawLine(leftH,  y + half, leftH,  y - half);  // left one vertical (0, 2, 0, -2)
      drawLine(rigthH, y + half, rigthH, y - half); // (2, 2, 2, -2 )
      
      // call 4 recursive calls for each corners 
      var nextLength = length/ Math.Sqrt(2); // 2/ sqrt(2)
      var nextDepth = depth - 1;  // 2
      
      DrawHTreeGivenDepthLength(leftH,  y + half, nextDepth, nextLength); // (0, 2)  LT
      DrawHTreeGivenDepthLength(leftH,  y - half, nextDepth, nextLength); // (0, -2) LB
      DrawHTreeGivenDepthLength(rigthH, y - half, nextDepth, nextLength); // (2, -2) RB
      DrawHTreeGivenDepthLength(rigthH, y + half, nextDepth, nextLength); // (2, 2)  RT
    }
  
    private static void drawLine(double x1, double y1, double x2, double y2)
    {
      // (x1, y1) to (x2, y2)
      Console.WriteLine(x1 + " " + y1 + " " + x2 + " " + y2) ;
    }
}

// depth = 3
// H -> depth = 2, 4 trees -> 4* 4= 16 , tree 1 + 4 + 4 ^2 + .. + 4^(depth - 1) = (4^depth -1)/ 3
// 3 lines -> time complexity time O(4^depth)
// space -> stack -> depth space O(depth)

/*
from center -> (x, y ), depth, length 
(2, 0),  length 4

x1 (0, 2) x4(4, 2)

_________
0   2    4 -> x axis, y = 0 

x2        x3
(0, -2)  (4, -2), nextlength = length/ sqrt(2)

base case: three lines    0 - 4 y = 0 horizontal
   x1 -> x2, 
   x4 -> x3 
*/