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 di…

CC150-3.4.java

package POJ;

import java.util.Stack;


public class Main{

	/**
	 * 
	 *  3.4 In the classic problem of the Towers of Hanoi, you have 3 towers and N disks 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.
	 *  
	 *  Solution:
	 *  To move N disks from tower A to tower B:
	 *  1. move top N -1 disks from tower A to tower C
	 *  2. move N'th disk from tower A to tower B
	 *  3. move top N-1 disks from tower C to tower B
	 *  
	 *  @Runtime & spaces
	 * 	runtime: O(2^n) 
	 * 	space: O(n)
	 * 
	 */
	public static void main(String[] args) throws Exception {
		// TODO Auto-generated method stub
		int diskNumber = 3;
		Tower[] myTower = new Tower[3];
		for (int i = 0; i < 3; i++) {
			myTower[i] = new Tower(i);
		}
		for (int i = diskNumber - 1; i >= 0; i--) {
			myTower[0].add(i);
		}
		myTower[0].moveDisks(diskNumber, myTower[1], myTower[2]);
	}
}

class Tower {
	int index;
	Stack<Integer> disks;

	public Tower(int i) {
		// TODO Auto-generated constructor stub
		disks = new Stack<Integer>();
		index = i;
	}

	public void moveDisks(int diskNumber, Tower buffer, Tower destination)
			throws Exception {
		// TODO Auto-generated method stub
		if (diskNumber > 0) {
			moveDisks(diskNumber - 1, destination, buffer);
			moveTo(destination);
			buffer.moveDisks(diskNumber - 1, this, destination);
		} else
			return;
	}

	private void moveTo(Tower destination) throws Exception {
		// TODO Auto-generated method stub
		int t = disks.pop();
		destination.add(t);
		System.out.println("Now moving " + t + "from " + this.index + " to "
				+ destination.index);
	}

	public void add(int val) throws Exception {
		// TODO Auto-generated method stub
		if ((!disks.isEmpty()) && disks.peek() < val) {
			throw new Exception("Error placing disk " + val);
		} else {
			disks.push(val);
		}
	}

}