用栈来求解汉诺塔问题（offer收割）

问题

  汉诺塔问题比较经典，这里修改一下游戏规则：现在限制不能从最左侧的塔直接移动到最右侧，也不能从最右侧直接移动到最左侧，而是必须经过中间。求当塔有N层的时候，打印最优移动过程和最优移动总步数。

代码

代码1：经典递归算法

package com.iqiyi;

public class Code1_6_1 {
	
	public static void main(String[] args){
		int count=hanoi(5, "left", "right");
		System.out.println(String.format("It will move %d steps.", count));
	}
	
	public static void move(int index,String from,String to){
		System.out.println(String.format("Move %d from %s to %s", index, from, to));
	}
	
	public static int hanoi(int n,String from,String to){
		if(n==1){
			move(1, from, "mid");
			move(1,"mid",to);
			return 2;
		}
		int count1=hanoi(n-1, from, to);
		move(n, from, "mid");
		int count2=hanoi(n-1, to, from);
		move(n, "mide", to);
		int count3=hanoi(n-1, from, to);
		return count1+count2+count3+2;
	}
}

代码2：利用栈的非递归算法

package com.iqiyi;

import java.util.Stack;

public class Code1_6_2 {
	public static int hanoi(int n){
		Stack<Integer> stack1=new Stack<Integer>();
		Stack<Integer> stack2=new Stack<Integer>();
		Stack<Integer> stack3=new Stack<Integer>();
		stack1.push(Integer.MAX_VALUE);
		stack2.push(Integer.MAX_VALUE);
		stack3.push(Integer.MAX_VALUE);
		int t=n;
		while(t>0){
			stack1.push(t);
			t--;
		}
		int count=0;
		int action=1;
		int first=stack1.pop();
		stack2.push(first);
		move(first, action);
		count++;
		while(stack3.size()!=(n+1)){
			if(action==1 || action==2){
				if(stack2.peek()>stack3.peek()){
					first=stack3.pop();
					stack2.push(first);
					action=3;
				}
				else{
					first=stack2.pop();
					stack3.push(first);
					action=4;
				}
			}
			else {
				if(stack1.peek()>stack2.peek()){
					first=stack2.pop();
					stack1.push(first);
					action=2;
				}
				else{
					first=stack1.pop();
					stack2.push(first);
					action=1;
				}
			}
			move(first, action);
			count++;
		}
		return count;
		
	}
	
	public static void move(int index,int action){
		switch (action) {
		case 1:
			System.out.println(String.format("Move %d from 1 to 2", index));
			break;
		case 2:
			System.out.println(String.format("Move %d from 2 to 1", index));
			break;
		case 3:
			System.out.println(String.format("Move %d from 3 to 2", index));
			break;
		case 4:
			System.out.println(String.format("Move %d from 2 to 3", index));
			break;
		default:
			break;
		}
	}
	
	public static void main(String[] args){
		int count=hanoi(5);
		System.out.println(String.format("It will move %d steps.", count));
	}

}