【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 middlemove 1 from middle to right move 2 from left   to middlemove 1 from right  to middlemove 1 from middle to left  move 2 from middle to right move 1 from left   to middlemove 1 from middle to right The Minimum step is 8Process finished with exit code 0