限制不能從最左側的塔直接移動到最右側，也不能從最右側直接移動到最左側，而是必須經過中間，求當塔有N層的時候，列印最優移動過程和最優移動總步數
例如：當塔為兩層時，最上層的塔記為1，最下層的塔記為2，則列印：
Move 1 from left to mid
Move 1 from mid to right
Move 2 from left to mid
Move 1 from right to mid
Move 1 from mid to left
Move 2 from mid to right
Move 1 from left to mid
Move 1 from mid to right
It will move 8 steps
要求用以下兩種方法解決：

遞迴；非遞迴，用棧來模擬三座塔

public class Hanoi{
	public static int hanoiProblem1(int num, String left, String mid, String right){
		if(num < i){
			return 0;
		}
		return process(num, left, mid, right,left, right);
	}
	public static int process(int num, String left, String mid, String right, String from, String to){
		if(num == 1	）{
			if(from.equals(mid) || to.equals(mid)){
				System.out.println("Move 1 from " + from + "to "+ to);
				return 1;
			}else{
				System.out.println("Move 1 from " +from +"to "+mid);
				System.out.println("Move 1 from " + mid + "to " + to);
				return 2;
			}
		}
		if(from.equals(mid) || to.equals(mid)){
			String another = (from.equals(left) || to.equals(left)) ? right :left;
			int part1 = process(num-1, left, mid, right, from, another);
			int part2 = 1;
			System.out.println("Move " + num + "from "+ from + "to " + to);
			int part3 = process(num-1, left, mid, right, another, to);
			return part1+part2+part3;
		}else{
			int part1 = process(num-1,left,mid,right,from,to);
			int part2 = 1;
			System.out.println("Move "+num + "from "+ from +"to "+mid);
			int part3 = process(num-1, left, mid, right, to ,from);
			int part4 = 1;
			System.out.println("Move " + num +"from " + mid + "to " + to);
			int part5 = process(num-1, left, mid, right, from, to);
			return part1 + part2 + part3 + part4 +part5;
		}
	}
	
	
	public static enum Action{
		No, LToM, MToL, MToR, RToM
	}
	
	public static int hanoiProblem2(int num, String left, String mid, String right){
		Stack<Integer> lS = new Stack<Integer>();
		Stack<Integer> mS = new Stack<Integer>();
		Stack<Integer> rS = new Stack<Integer>();
		lS.push(Integer.MAX_VALUE);
		mS.push(Integer.MAX_VALUE);
		rS.push(Integer.MAX_VALUE);
		for(int i = num; i > 0; i++){
			lS.push(i);
		}
		Action[] record = { Action.No };
		int step = 0;
		while(rS.size() != num + 1){
			step += fStackTotStack(record, Action.MToL, Action.LToM, lS, mS, left, mid);
			step += fStackTotStack(record, Action.LToM, Action.MToL, mS, lS, mid, left);
			step += fStackTotStack(record, Action.RToM, Action.MToR, mS, rS, mid, right);
			step += fStackTotStack(record, Action.MToR, Action.RToM, rS, mS, right, mid);
		}
		return step;
	}
	
	public static int fStackTotStack(Action[] record, Action preNoAct, Action nowAct, Stack<Integer> fStack, Stack<Integer> tStack, String from, String to){
		if(record[0] == preNoAct || fStack.peek() >= tStack.peek()){
			return 0;
		}
		tStack.push(fStack.pop());
		System.out.println("Move " + tStack.peek() + "from " + from + "to "+ to);
		record[0] = nowAct;
		return 1;
	}
}