【算法】递归法实现汉诺塔问题

递归法实现汉诺塔问题

这里的汉诺塔问题稍加改动：从“左”不能直接到“右”，必须先从“左”到“中”，再从“中”到“右”；从“右”到“左”同理；即只能在相邻的柱子间移动。

思路：

• process(int num, String from, String to)函数，实现了第num块，从from柱子到to柱子的移动过程
• 移动分为两类，相邻柱子的移动，不相邻柱子的移动（如果是传统的汉诺塔问题则不用如此分类）
• 相邻柱子的移动：从"左"到"中"，从"右"到"中"，从"中"到"左"，从"中"到"右"
• • 1. 上面的num - 1层，从from移到另一个柱子，即除了from和to的另一根柱子
• • 1. 然后第num块从from到to
• • 1. 上面的num - 1层从另一个柱子到to
• 不相邻柱子的移动：从"左"到"右"，从"右"到"左"
• • 1. 上面的num - 1层从from到to
• • 1. 第num块，从from移到middle
• • 1. 然后第num - 1块从to到from
• • 1. 第num块，从middle移到to
• • 1. 上面的num - 1层从from到to

package com.lilydedbb;

/**
 * Created by dbb on 2016/12/24.
 */
public class HanoiProblemByRecursion {

    private static String left = "left  ";
    private static String mid = "middle";
    private static String right = "right ";

    public static int hanoiProblem(int num){
        if (num < 1)
            return 0;
        return process(num, left, right);
    }

    // 返回的是步数
    public static int process(int num, String from, String to){

        // 只有一个的时候
        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 middle");
                System.out.println("move 1 from middle to " + to);
                return 2;
            }
        }

        // 从"左"到"中"，从"右"到"中"，从"中"到"左"，从"中"到"右"
        if(from.equals(mid) || to.equals(mid)){
            String another = (from.equals(left) || to.equals(left)) ? right : left;
            int part1 = process(num - 1, from, another);
            int part2 = 1;
            System.out.println("move " + num + " from " + from + " to " + to);
            int part3 = process(num - 1, another, to);
            return part1 + part2 + part3;
        } else { // 从"左"到"右"，从"右"到"左"
            int part1 = process(num - 1, from, to);
            int part2 = 1;
            System.out.println("move " + num + " from " + from + " to middle");
            int part3 = process(num - 1, to, from);
            int part4 = 1;
            System.out.println("move " + num + " from middle to " + to);
            int part5 = process(num - 1, from, to);
            return part1 + part2 + part3 + part4 + part5;
        }
    }

}

测试程序及测试结果如下：

int steps = HanoiProblemByRecursion.hanoiProblem(2);
System.out.println("The Minimum step is " + steps);

move 1 from left   to middle
move 1 from middle to right 
move 2 from left   to middle
move 1 from right  to middle
move 1 from middle to left  
move 2 from middle to right 
move 1 from left   to middle
move 1 from middle to right 
The Minimum step is 8

Process finished with exit code 0