70分享（81）：Java实战中的汉诺塔

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Java实战中的汉诺塔

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Java Practice: Tower of Hanoi

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在Java中，汉诺塔是一个经典的递归问题。它通常被用来教导递归的概念，且问题的解决方法基于将一个大问题分解为更小的子问题。下面是汉诺塔问题的基本描述和如何用Java来实现。

In Java, the Tower of Hanoi is a classic recursive problem. It is commonly used to teach the concept of recursion, and the solution to the problem is based on breaking down a larger problem into smaller subproblems. Below is the basic description of the Tower of Hanoi problem and how to implement it in Java.

1.汉诺塔问题描述

1. Description of the Tower of Hanoi problem

汉诺塔由三根柱子和若干个不同大小的圆盘组成，最初所有圆盘都按大小顺序从小到大叠放在其中一根柱子上。目标是将所有的圆盘从起始柱子移动到目标柱子上，同时遵守以下规则：

The Tower of Hanoi consists of three rods and a number of disks of different sizes, initially all stacked on one rod in ascending order of size from top to bottom. The objective is to move all the disks from the starting rod to the target rod while adhering to the following rules:

一次只能移动一个圆盘。

Only one disk can be moved at a time.

每次只能将圆盘从一个柱子移到另一个柱子上。

Each move consists of taking the upper disk from one of the stacks and placing it on top of another stack.

任何时刻，一个柱子上的大圆盘不能在小圆盘的下面。

At no time may a larger disk be placed on top of a smaller disk.

2.递归思路

2.Recursive approach

将除最底下的圆盘外的所有圆盘从起始柱子移动到辅助柱子。

Move all disks except the bottommost one from the starting rod to the auxiliary rod.

将最底下的圆盘从起始柱子移动到目标柱子。

Move the bottommost disk from the starting rod to the target rod.

将剩下的圆盘从辅助柱子移动到目标柱子。

Move the remaining disks from the auxiliary rod to the target rod.

3.Java实现

3.Java Implementation

下面是一个简单的Java代码实现来解决汉诺塔问题。

Here is a simple Java code implementation to solve the Tower of Hanoi problem.

public class Hanoi {

// 汉诺塔递归算法

public static void moveDisks(int n, String fromPole, String toPole, String auxPole) {

// 基本情况：只有一个圆盘时，直接从起始柱子移动到目标柱子

if (n == 1) {

System.out.println("Move disk 1 from " + fromPole + " to " + toPole);

return;

}

// 第一步：将n-1个圆盘从起始柱子移动到辅助柱子

moveDisks(n - 1, fromPole, auxPole, toPole);

// 第二步：将第n个圆盘从起始柱子移动到目标柱子

System.out.println("Move disk " + n + " from " + fromPole + " to " + toPole);

// 第三步：将n-1个圆盘从辅助柱子移动到目标柱子

moveDisks(n - 1, auxPole, toPole, fromPole);

}

public static void main(String args) {

int n = 3; // 圆盘数量

moveDisks(n, "A", "C", "B"); // 从柱子A移动到柱子C，辅助柱子为B

}

4.输出

4.Output

对于3个圆盘，程序会输出如下的移动步骤：

For 3 disks, the program will output the following movement steps:

Move disk 1 from A to C

Move disk 2 from A to B

Move disk 1 from C to B

Move disk 3 from A to C

Move disk 1 from B to A

Move disk 2 from B to C

汉诺塔问题是一个经典的递归问题，通过递归的方式将问题分解为子问题来解决。Java中的实现通过递归调用来依次移动圆盘，遵循汉诺塔的规则。递归问题通常具有一个简单的基本情况（在这个问题中就是只有一个圆盘时直接移动），并通过不断减少问题的规模来解决。

The Tower of Hanoi problem is a classic recursive problem, which is solved by decomposing the problem into subproblems through recursion. The implementation in Java involves recursively calling methods to move the disks sequentially, adhering to the rules of the Tower of Hanoi. Recursive problems typically have a simple base case (in this problem, directly moving a single disk) and are solved by progressively reducing the problem's scale.

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翻译来源于百度翻译