Stepping on a horse (one stroke)

Catalog

One , The rules of the game

Two , Simple analysis

1, Nature of the problem

2, The starting point

3、 ... and , Strategic thinking

1, Circle Division

2, Partial solution

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One , The rules of the game

The rule of the game is , According to the Japanese character of Ma Zou , Go out of a circle .

  

For those with numbers 2 Of , To go 2 Time , In fact, that is 2 The intersection of cycles .

  

The resulting graph does not quite show the full path , So I added it manually .

Two , Simple analysis

1, Nature of the problem

The problem can be broken down into two problems , First of all , Look for a circle , second , Draw a circle with one stroke .

（1） Find a cycle in an undirected graph , Make the number of times each point passes the same as the given number .

Most of the given numbers are 1, A few are 2

（2） Draw a circle with one stroke , A circle may be self intersecting , It is composed of several circles .

2, The starting point

Because it's a circle , So any point can be the starting point .

But for those with numbers 2 Of , Use numbers 2 It is easier to find the answer by using the point of .

3、 ... and , Strategic thinking

1, Circle Division

  

2, Partial solution

（1） The point with the lowest degree

The point with the lowest degree , Only 2 A neighbor , Such as B My neighbor is AC, be ABC It must be part of the circle .

（2） Path splicing

For simple circles , As long as the two paths have common endpoints , Can be put together into a path . For self intersecting circles , If the public endpoint is not 1, Not necessarily .

Yes 2 And above is the self intersecting circle , Only 1 Is a simple circle .

All in all , If two paths have common endpoints , And this endpoint is not 1, Can be put together to form a path .

   

  such , Look for the rest , It's easier .

In fact, the problem itself has not been greatly simplified , The main thing is that it looks clearer .