CTCI 1, 3.4

In the classic problem of the towers of Hanoi, you have 3 towers and ndisks of different sizes which can slide onto any tower. the puzzle starts with disks sorted in ascending order of size from top to bottom (I. E ., each disk sits on top of an even larger one ). you have the following constraints:
(1) only one disk can be moved at a time.
(2) A disk is slid off the top of one tower onto the next tower.
(3) A disk can only be placed on top of a larger disk.
Write a program to move the disks from the first tower to the last using stacks.

Use recursion to implement the algorithm. assume we are moving from A to C, with an additional B Tower. if there is only one plate, directly move it from A to C, Else, we first move the n-1, which n is the total plates on a from A to B using C as buffer, then move the last nth plate from A to C, then move the rest n-1 plates from B to C using a as buffer. in my implement, I use a inner class "Tower ". However, when instantiation a tower VaR in a static call, We need to first instantiation the outer class!

/* Using the recursion to implement the algorithm*/import java.util.*;public class Hanoi {    public void recursehanoi(int n, Tower a, Tower b, Tower c) {        if(n == 1) {             System.out.println("Move the " + a.peek() + "th plate from " + a.name + " to " + c.name);            c.add(a.remove());         }        else {            //Move the top n-1 plates from a to b using c as buffer            recursehanoi(n-1, a, c, b);            //Move the last n from a to c            System.out.println("Move the " + a.peek() + "th plate from " + a.name + " to " + c.name);            c.add(a.remove());             //Move the rest n-1 plates from b to c using a as buffer            recursehanoi(n-1, b, a, c);        }    }    public class Tower {        public String name;        public Stack<Integer> plates = new Stack<Integer>();        public Tower(String name) {            this.name = name;        }        public void add(int plate) {            plates.push(plate);        }        public int peek() {            return plates.peek();        }        public int remove() {            return plates.pop();        }    }    public static void main(String[] args) {        Hanoi ha = new Hanoi();        Hanoi.Tower a = new Hanoi().new Tower("a"); a.add(3); a.add(2); a.add(1);        Hanoi.Tower b = new Hanoi().new Tower("b"); Hanoi.Tower c = new Hanoi().new Tower("c");        ha.recursehanoi(3, a, b, c);    }}