Algorithm Gossip: 双色、三色河内塔

而三色河内塔则是将下图左上的圆环经移动成为右上的圆环：

在移动的过程中，一样遵守大盘必须在小盘之下的规则，而颜色顺序则无限制。

解法

无论是双色河内塔或是三色河内塔，其解法观念与之前介绍过的河内塔是类似的，同样也是使用递迴来解，不过这次递迴解法的目的不同，我们先来看只有两个 盘的情况，这很简单，只要将第一柱的黄色移动至第二柱，而接下来第一柱的蓝色移动至第三柱。

再来是四个盘的情况，首先必须用递迴完成下图左上至右下的移动：

接下来最底层的就不用管它们了，因为它们已经就定位，只要再处理第一柱的上面两个盘子就可以了。

那麽六个盘的情况呢？一样！首先必须用递迴完成下图左上至右下的移动：

接下来最底层的就不用管它们了，因为它们已经就定位，只要再处理第一柱上面的四个盘子就可以了，这又与之前只有四盘的情况相同，接下来您就知道该如何进行解题了，无论是八个盘、十个盘以上等，都是用这个观念来解题。

那麽三色河内塔呢？一样，直接来看九个盘的情况，首先必须完成下图的移动结果：

接下来最底两层的就不用管它们了，因为它们已经就定位，只要再处理第一柱上面的三个盘子就可以了。

您也可以看看 Towers of Hanoi Page 中有关于河内塔的讨论。

 实作

以下Java演算实例由 http://www.javaworld.com.tw 的 T5555 提供，感谢他的协助，我根据他的实例，转换为C语言的实作部份，您可以参考这个 讨论串 有关于河内塔的讨论。

• 双色河内塔 C 实作

#include <stdio.h>

void hanoi(int disks, char source, char temp, char target) {
    if (disks == 1) {
        printf("move disk from %c to %c\n", source, target);
        printf("move disk from %c to %c\n", source, target);
    } else {
        hanoi(disks-1, source, target, temp);
        hanoi(1, source, temp, target);
        hanoi(disks-1, temp, source, target);
    }
}

void hanoi2colors(int disks) {
    char source = 'A';
    char temp = 'B';
    char target = 'C';
    int i;
    for(i = disks / 2; i > 1; i--) {
        hanoi(i-1, source, temp, target);
        printf("move disk from %c to %c\n", source, temp);
        printf("move disk from %c to %c\n", source, temp);
        hanoi(i-1, target, temp, source);
        printf("move disk from %c to %c\n", temp, target);
    }
    printf("move disk from %c to %c\n", source, temp);
    printf("move disk from %c to %c\n", source, target);
}

int main() {
    int n;
    printf("请输入盘数：");
    scanf("%d", &n);

    hanoi2colors(n);

    return 0;
} 

• 三色河内塔 C 实作

#include <stdio.h>

void hanoi(int disks, char source, char temp, char target) {
    if (disks == 1) {
        printf("move disk from %c to %c\n", source, target);
        printf("move disk from %c to %c\n", source, target);
        printf("move disk from %c to %c\n", source, target);
    } else {
        hanoi(disks-1, source, target, temp);
        hanoi(1, source, temp, target);
        hanoi(disks-1, temp, source, target);
    }
}

void hanoi3colors(int disks) {
    char source = 'A';
    char temp = 'B';
    char target = 'C';
    int i;

    if(disks == 3) {
        printf("move disk from %c to %c\n", source, temp);
        printf("move disk from %c to %c\n", source, temp);
        printf("move disk from %c to %c\n", source, target);
        printf("move disk from %c to %c\n", temp, target);
        printf("move disk from %c to %c\n", temp, source);
        printf("move disk from %c to %c\n", target, temp);;
    }
    else {
        hanoi(disks/3-1, source, temp, target);
        printf("move disk from %c to %c\n", source, temp);
        printf("move disk from %c to %c\n", source, temp);
        printf("move disk from %c to %c\n", source, temp);

        hanoi(disks/3-1, target, temp, source);
        printf("move disk from %c to %c\n", temp, target);
        printf("move disk from %c to %c\n", temp, target);
        printf("move disk from %c to %c\n", temp, target);

        hanoi(disks/3-1, source, target, temp);
        printf("move disk from %c to %c\n", target, source);
        printf("move disk from %c to %c\n", target, source);

        hanoi(disks/3-1, temp, source, target);
        printf("move disk from %c to %c\n", source, temp);
        
        for (i = disks / 3 - 1; i > 0; i--) {
            if (i>1) {
                hanoi(i-1, target, source, temp);
            }

            printf("move disk from %c to %c\n",
                                 target, source);
            printf("move disk from %c to %c\n",
                                 target, source);

            if (i>1) {
                hanoi(i-1, temp, source, target);
            }
            printf("move disk from %c to %c\n", 
                                   source, temp);
        }
    }
}

int main() {
    int n;
    printf("请输入盘数：");
    scanf("%d", &n);

    hanoi3colors(n);

    return 0;
} 

• 双色河内塔 Java 实作

public class Hanoi2Colors { 
    public static void help() {
        System.out.println(
              "Usage: java Hanoi2Colors number_of_disks");
        System.out.println(
              "\t number_of_disks: must be a even number.");
        System.exit(0);
    }
    
    public static void main(String[] args) {
        int disks = 0;        
        try {
            disks = Integer.parseInt(args[0]);
        } catch (Exception e) {
            help();
        }
        if ((disks <= 0) || (disks % 2 != 0)) { 
            help(); 
        }
        hanoi2colors(disks);
    }
     
    public static void hanoi(int disks, 
                      char source, char temp, char target) {
        if (disks == 1) {
            System.out.println("move disk from " 
                               + source + " to " + target);
            System.out.println("move disk from " 
                               + source + " to " + target);
        } else {        
            hanoi(disks-1, source, target, temp);
            hanoi(1, source, temp, target);
            hanoi(disks-1, temp, source, target);
        }
    }
 
    public static void hanoi2colors(int disks) {
        char source = 'A';
        char temp = 'B';
        char target = 'C';
        for (int i = disks / 2; i > 1; i--) {
            hanoi(i-1, source, temp, target);
            System.out.println("move disk from " 
                                   + source + " to " + temp);
            System.out.println("move disk from " 
                                   + source + " to " + temp); 
            hanoi(i-1, target, temp, source);
            System.out.println("move disk from " 
                                   + temp + " to " + target);
        }
        System.out.println("move disk from " 
                                   + source + " to " + temp);
        System.out.println("move disk from " 
                                 + source + " to " + target);
    }
} 

• 三色河内塔 Java 实作

public class Hanoi3Colors {    
    public static void help() {
        System.out.println(
              "Usage: java Hanoi3Colors number_of_disks");
        System.out.println(
      "\tnumber_of_disks: must be a number divisible by 3.");
        System.exit(0);
    }
    
    public static void main(String[] args) {
        int disks = 0;        
        try {
            disks = Integer.parseInt(args[0]);
        } catch (Exception e) {
            help();
        }
        if ((disks <= 0) || (disks % 3 != 0)) { 
            help(); 
        }
        hanoi3colors(disks);
    }
    
    public static void hanoi(int disks, 
                       char source, char temp, char target) {
        if (disks == 1) {
            System.out.println("move disk from " 
                               + source + " to " + target);
            System.out.println("move disk from "
                               + source + " to " + target);
            System.out.println("move disk from "
                               + source + " to " + target);
        } else {        
            hanoi(disks-1, source, target, temp);
            hanoi(1, source, temp, target);
            hanoi(disks-1, temp, source, target);
        }
    }
    
    public static void hanoi3colors(int disks) {
        char source = 'A';
        char temp   = 'B';
        char target = 'C';
        if (disks == 3) {
            System.out.println("move disk from " 
                            + source + " to " + temp);
            System.out.println("move disk from " 
                            + source + " to " + temp);
            System.out.println("move disk from " 
                            + source + " to " + target);
            System.out.println("move disk from " 
                            + temp + " to " + target);
            System.out.println("move disk from " 
                            + temp + " to " + source);
            System.out.println("move disk from " 
                            + target + " to " + temp);
        } else {
            hanoi(disks/3-1, source, temp, target);
            System.out.println("move disk from " 
                            + source + " to " + temp);
            System.out.println("move disk from " 
                            + source + " to " + temp);
            System.out.println("move disk from " 
                            + source + " to " + temp);
            hanoi(disks/3-1, target, temp, source);
            System.out.println("move disk from " 
                            + temp + " to " + target);
            System.out.println("move disk from "
                            + temp + " to " + target);
            System.out.println("move disk from "
                            + temp + " to " + target);
            hanoi(disks/3-1, source, target, temp);
            System.out.println("move disk from " 
                            + target + " to " + source);
            System.out.println("move disk from " 
                            + target + " to " + source);
            hanoi(disks/3-1, temp, source, target);
            System.out.println("move disk from " 
                            + source + " to " + temp);
        
            for (int i = disks / 3 - 1; i > 0; i--) {
                if (i>1) { 
                    hanoi(i-1, target, source, temp); 
                }
                System.out.println("move disk from " 
                         + target + " to " + source);
                System.out.println("move disk from " 
                         + target + " to " + source);
                if (i>1) { 
                    hanoi(i-1, temp, source, target); 
                }
                System.out.println("move disk from " 
                         + source + " to " + temp);
            }
        }
    }
}