universal data

Chapter 147 Simple Solution of One-stroke Painting

"Seven Bridges of Euler?"

Ying Yingying's face was cute, "This... I just heard about it, but I don't know exactly what it is."

Just when Cheng Nuo was about to explain, Li Shiye, who had been sitting silently, slowly spoke.

"In Königsberg, Prussia, at the beginning of the eighteenth century, there was a river through which there were two small islands, and seven bridges connected the two islands to the river bank. A man asked a question: how can a walker not repeat , Walk through seven bridges without omission, and finally return to the starting point. This is the famous Euler's Seven Bridges problem. But the Euler's Seven Bridges problem itself is unsolvable."

"At that time, the famous mathematician Euler transformed the problem of Euler's Seven Bridges and formed a new concept-one-stroke painting! And proposed two sufficient conditions to satisfy all one-stroke graphics."

"One, all the points on the graph are even points."

"Second, the graph has only two singular points, and all the remaining points are even points."

"The same goes for converting flat graphics into three-dimensional graphics." Li Shiye raised his chin and pointed at the two people on the screen who were participating in the challenge. "So, the two of them don't need to convert each graphic in their minds. , go through the route of each point. You only need to observe whether the points of the irregular three-dimensional polygon are even points or singular points to judge whether it can be drawn in one stroke!"

Cheng Nuo next to him had black lines.

Girl, you’ve already pretended that you don’t have any pussy, so why should I pretend?

"But..." Li Shiye finally changed his tone, "Even so, the difficulty of this project is still very high. The two of them need to confirm every point on the irregular three-dimensional polygon before they can make their own judgments .”

"Although the difficulty of this challenge project is not as complicated as it seems on the surface, it is definitely not worth only 8 points!"

Obviously, what Li Shiye said was to Cheng Nuo.

"But I just think this challenge project is very easy!" Cheng Nuo said flatly, looking like I was wronged.

Li Shiye was also amused by Cheng Nuo, pointing to the screen in front of him and said, "Okay, since you think this project is simple, please tell me, Cheng Nuo, the three-dimensional polygon that Sun Meng is observing now. , is it a one-stroke three-dimensional polygon?"

On the screen, Sun Meng from Peking University was standing in front of a three-dimensional polygon, frowning in thought.

Although it is only necessary to judge whether all the points on the three-dimensional polygon are even points, or whether there are only two singular points, it is still a lot of work for the brain of ordinary people.

There are at least seventeen or eighteen points on a three-dimensional polygon.

Players need to observe every point.See if the number of line segments connected by this point is odd or even.

is an odd number, this point is a singularity.If it is an even number, the point is an even point.

If you count the line segments like this, if there are too many, a three-dimensional polygon, the contestant needs to count more than 100 line segments, which is quite a big number!
The shape of the polygon in front of Sun Meng is obviously a bit more complicated than the others observed.

Therefore, Sun Meng's observation took longer.

In the lounge, Cheng Nuo simply glanced at the screen, and the data about the irregular three-dimensional polygon that Sun Meng was observing appeared in Cheng Nuo's mind.

There are 26 points, 38 line segments, 24 even points, and 2 odd points.

Looking at the data, it meets the second one-stroke condition.The number of singularities is 2.

and so……

Cheng Nuo replied casually, "This polygon can be drawn in one stroke."

Li Shiye glanced at Cheng Nuo suspiciously. Because the camera on the screen switched quickly, he didn't have time to verify Cheng Nuo's answer, and he didn't know whether Cheng Nuo was right or not.

"What about this one?" Li Shiye continued to ask.

The camera on the screen has switched to Zhang Zheng, who is also frowning and observing in front of an irregular three-dimensional polygon.

Cheng Nuo simply glanced at the screen again, as if he hadn't done much observation and calculation, and gave his answer in the next second, "This can't be drawn with one stroke."

Li Shiye glanced sideways at Cheng Nuo.Since the camera stayed on Zhang Zheng for a relatively long time this time, it was enough for Li Shiye to judge whether the three-dimensional figure on the screen could be drawn in one stroke.

Seven or eight seconds later, Li Shiye had already got the answer, turned to look at Cheng Nuo, and let out a sigh of relief, "You're right."

Just now he observed a total of five points of this irregular three-dimensional polygon.It is found that three are singular points and two are even points.

The result is already obvious that this three-dimensional polygon cannot be drawn with one stroke!

What puzzled Li Shiye was that it took him seven or eight seconds to figure it out.

But why did Cheng Nuo give an answer in an instant with just a glance?

This is not scientific!

On the screen, Zhang Zheng, a student from Tsinghua University, observed the irregular three-dimensional polygon in front of him for nearly 20 seconds before slowly shaking his head and denying the answer.

At this time, the camera cuts to the sky, giving a panoramic view of the 200 irregular three-dimensional polygons.

A huge stream of data slowly emerged in Cheng Nuo's eyes, and then transmitted to Cheng Nuo's brain.

No. 1 three-dimensional polygon has 21 points, 29 line segments, 6 odd points, and 15 even points.

No. 2 three-dimensional polygon has 18 points, 25 line segments, 2 odd points, and 16 even points.

…………

No. 200 three-dimensional polygon has 26 points, 35 line segments, 4 odd points, and 24 even points.

The lens only gives two or three seconds of panorama time.

But two or three seconds was enough for Cheng Nuo.

Soon, the camera switched to Sun Meng of Peking University again.

Li Shiye, who was sitting by the side, wanted to speak and repeat the previous question, but was interrupted by Cheng Nuo in advance. "Student Li Shiye, I know what you want to ask me."

"In order to prevent you from asking questions one by one, I will answer you all at once."

Cheng Nuo smiled lightly, and said unhurriedly, "Among the 200 irregular three-dimensional polygons on the field, there are a total of 45 that meet the requirements of one-stroke painting."

"The numbers are No. 2, No. 6, No. 11,... No. 198!"

"How about it, student Li Shiye, are you satisfied with this answer?"

Cheng Nuo looked at Li Shiye and said with a smile.

"You..." Li Shiye looked at Cheng Nuo blankly. He was silent for a long time before holding back a sentence, "You... couldn't you have made it all up?"

It wasn't that Li Shiye had to think this way, but Cheng Nuo's performance was a bit too much.

That's 200 three-dimensional polygons!

If it's him, observe them all, it's impossible without more than ten, twenty or ten minutes!

But how long has Cheng Nuo used it?Just a few seconds!
How is it possible to observe all 200 graphics in a few seconds?

Faced with Li Shiye's questioning, Cheng Nuo just shrugged, "Whether what I said is true or not, you will know in a while."

…………

Every haircut is like a gamble, this time... I lost the bet!
so ugly~~~
(End of this chapter)