Task $1(20\backslash \%)$

Problem: Write a recursive program that prints the steps for solving "reverse" Tower of Hanoi. The rules are explained using the figure below.

Key points

$-$ As depicted in the above figure, the pegs are upside down and the disks are held at the top using magnets.

$-$ The order of disks in a tower is the same: smallest disk at the top, largest disk at the bottom.

$-$ The movement of disks is reversed: you can only move the largest disk from the bottom of one tower to the bottom of a smaller disk in another tower $($or onto an empty peg$).$

$-$ You will implement the reverseToH$(...)$ method. Do not change the signature for this method. This method needs to be recursive.

Hint: You will find that this problem looks similar to the original Tower of Hanoi puzzle. Solution to the Tower of Hanoi puzzle is a recursive algorithm, and it is covered in Week $15($see recording for Week $15-$ Lecture $1).$

The listing below shows the output that your program needs to print $($Lines $6-12$ below$)$ for the sample input given in Run.java $($Lines $1-4$ below$).$ The first three steps are depicted in the above figure.

$```$

Task$1$ t$1=$ new Task$1()$;

int size $=3$;

t$1.$setTowerSize$($size$)$;

t$1.$reverseToH$($size $,1,3)$;

Move Disk $3$ from Peg $1$ to Peg $3$

Move Disk $2$ from Peg $1$ to Peg $2$

Move Disk $3$ from Peg $3$ to Peg $2$

Move Disk $1$ from Peg $1$ to Peg $3$

Move Disk $3$ from Peg $2$ to Peg $1$

Move Disk $2$ from Peg $2$ to Peg $3$

Move Disk $3$ from Peg $1$ to Peg $3$

$```$