2022-2023年Bebras挑战练习题-Embroidery Machine(绣花机)

Havel has a programmable sewing machine. The machine can sew a  stitch or a   stitch and can also move the fabric forward 1 stitch space.哈维尔有一台可编程的缝纫机。这台机器可以缝制 1 针或 2 针,还能将布料向前移动 1 针的距离。

The sewing machine can sew both of these stitches in the same place (in any order), to get a stitch.缝纫机可以在同一位置缝这两种针脚(顺序不限),从而得到一种针脚。

The program for the machine consists of a sequence of characters +x and .该机器的程序由一系列字符 、x 和 → 组成。

The machine keeps repeating the program while the pedal of the sewing machine is held down.只要踩住缝纫机的踏板,机器就会不断重复这个程序。

Example:例子:

Running the program + → + x → x → will sew this pattern: 运行此程序 → x → x → 将会缝制出这种图案:

2022-2023年Bebras挑战练习题-Embroidery Machine(绣花机)

Question:问题:

Which program did Havel enter into the machine to get the following pattern?哈维尔输入了哪个程序到机器里才得到了下面这个图案?

 

 

 

 

 

 

Explanation 解释

Answer: 答案:

x → x → x + → x → + x →

Explanation: 解释:

Looking at the program, we see that the repeating pattern is .

查看该程序,我们发现重复的模式是

The first stitch is , after which the fabric should be moved, so the program starts with x →.

第一针缝完后,应移动布料,因此程序以 x → 开始。

The same for the second  stitch.

第二个针脚也是如此。

Then we have to sew a star - which can be done by sewing x and + on the same place (the order does not matter) and only then the fabric is moved.

然后我们要缝制一颗星——这可以通过在相同位置缝制 x 和 来完成(顺序无关紧要),只有这样布料才会移动。

To do this, we add x + → or + x → to our program.要做到这一点,我们在程序中添加 x → 或者 x → 。

Another cross is "made" by commands x → and another star by the + x → or x + → commands.

另一个十字是通过命令 x → 来“制作”的,而另一颗星则是通过 x → 或 x → 命令来生成的。

So the whole program is x → x → x + → x → + x →.

所以整个程序就是 x → x → x → x → x → 。

Option A: x → x → x + → x → + x → x → x → is incorrect, because it sews a sequence of  which is not the pattern that Havel got.

选项 A:x → x → x → x → x → x → x → 是错误的,因为它拼接了一个序列,这并非哈维尔所得到的模式。

Option B: x → x → x + → x → x → is incorrect, because the resulting pattern is , which is not the pattern Havel was aiming for.

选项 B:x → x → x → x → x → 是错误的,因为这样得到的模式是 ,这并非哈维尔所期望的模式。

Option D: + x → + x → x → + x → x → is also incorrect. The beginning of the program + x → + x → will sew  which is not in Havel's pattern.

选项 D:x → x → x → x → x → 也是错误的。程序的开头 x → x → 会缝合出 ,这不符合哈维尔模式。

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