Recursion in C#

 Recursion 

Recursion is one of the most useful aspects of subroutines; that is the ability of the procedure or subroutine to call itself.


Learn Python  here

Download: Application to calculate your days on Earth 

This article will use a rather ancient puzzle known as the Tower of Hanoi originated from Hindu.
Tower of Hanoi
Diagram Tower of Hanoi 
The rules of this puzzle are:


  1. We are interested in moving the rings from A to B, perhaps using  C in the process. 
  2. Also by the rules of the game, rings are to be moved one at a time
  3.  At no point may the larger ring be placed on top a smaller one.
This puzzle can be solved following these 7 steps:
  • move A to  B;
  • move A  to C;
  • move B  to C;
  • move A to  B;
  • move C  to A;
  • move C  to B; 
  • move A  to B;

Algorithm


subroutine move N from A to B using C;
  1. if N is 1 then print "move A to B";
  2. else( If N is greater than 1) do the following:                 
            2.1 call move N - 1 from  A to C using B;
            2.2 call  move 1   from A to B using  C;
            2.3 call move N - 1 from  C to B using A;
    3. return


 Algorithm

 We have 3 rings on Peg A, therefore, our N = 3, which is greater than 1.
 After the function; below are the 3 Steps our code follows:
 P(3, A, C, B) means  call move 3 from A to B using C
 Step1: P(N - 1, Beg, End, Aux)  
 Step2: P(1,       Beg,  Aux, End)
 Step3: P(N - 1, Aux, Beg, End)


 Below also are the meaning of the variables selected:

 P = denotes procedure/subroutine
 N = numbers of ring
 Beg = Initial stage of moving the ring
 End = destination 
 Aux = auxiliary output through which we move rings

If N is greater than 1:
Step1  says: move top (N -1) rings from Beg to Aux peg.
Step2  says: move 1 ring from Beg to End peg.
Step3 says: move top (N-1) rings from Aux to End peg.

Let us see in code:
namespace TowerOfHanoi
{
class Program
{
static void Main(string[] args)
{
char beg_fromPeg = 'A';       // Begining of the tower in output where we move from
char dest_Peg = 'B';            //  end tower in output where we move to
char via_PegtoDest = 'C';   // auxilliary tower in output through which we move
int disks = 3;                    // number of disks to move around
solverHanoiTowers(disks, beg_fromPeg, via_PegtoDest, dest_toPeg);
}
private static void solverHanoiTowers(int n, char beg_fromPeg, char via_PegtoDest, char dest_toPeg)
{
if ( n == 1)
{

Console.WriteLine("move" + beg_fromPeg + "to" + dest_Peg);

}
else
{
solverHanoiTowers(n - 1, beg_fromPegdest_Pegvia_PegtoDest);
solverHanoiTowers(1, beg_fromPegvia_PegtoDest, dest_Peg);
solverHanoiTowers(n - 1, via_PegtoDest, beg_fromPegdest_Peg);

}

Console.Read();
}
}
}

OUTPUT
move A to B;
move A to C;
move B to C;
move A to B;
move C to A;
move C to B;
move A to B;

These processes below is the sequential flow that moves all the rings in peg A to B recursively.

P( 3 , A, B, C)                             
       /                                            1st Chain                    2nd Chain           3rd Chain
P(2, A, C, B) - Step 1,2,3.    P(2 , A, C, B)          P(1,A, B, C)= A to C    P(2, B, A, C)
 /                                            /                                                                     /
P(1, A, B,  C)  - Step 2.        P(1, A, B, C) = A to C                               P(1,B,C,A)= B to A
 /                                             /                                                                    /
P(2, B, A, C)  -  Step 1,2,3.   P(1, A, C, B)= A to B                              P(1,B,A,C)= B to C
                                              /                                                                    /
                                            P(1, C, A, B)= C to B                             P(1, A, B, C) = A to C

Here what happened is that we applied those 3 steps on P(3, A, B, C) and those are the chain we got out of it that gave us the accurate result in code.

Happy reading! 
Follow maxybyte on social media.

Read: Class and Object -Object-Oriented Programming


5 comments:

  1. Thanks for posting

    ReplyDelete
  2. This is easy to understand tutorial, thanks for sharing.

    ReplyDelete
  3. Here's [a link](https://www.maxybyte.com/p/counter-in-vhdl-with-debouncer.html)! that might help

    ReplyDelete

Note: only a member of this blog may post a comment.

New Post

New style string formatting in Python

In this section, you will learn the usage of the new style formatting. Learn more here . Python 3 introduced a new way to do string formatti...