Xueba starts with change

Chapter 175 The End of the Show
Zhang Zhongyuan looked a little subtle, waved his hand, and signaled Chen Zhou to sit down.

Now, stealing my words again...

After Chen Zhou sat down, he looked at Zhang Zhongyuan with interest.

He didn't think that, as others said, Zhang Zhongyuan had nothing to say.

as predicted.

Zhang Zhongyuan coughed lightly, and then said: "Student Chen Zhou has explained to us the meaning of the sequence verification method in detail, and by the way, he also gave examples to illustrate its shortcomings."

"However, just because it has flaws, it doesn't mean that it has no research significance."

Zhang Zhongyuan's words directly attracted the eyes of all the students to him again.

Seeing this, Zhang Zhongyuan smiled slightly, turned around and wrote a few words on the whiteboard [Ignore even numbers, do not record].

However, for some reason, when he was writing these words, he suddenly thought of the topic discussion when Chen Zhou participated in the project for the first time.

Suppressing this inexplicable thought, Zhang Zhongyuan turned around, glanced at Chen Zhou first, and then continued: "The example Chen Zhou gave just now is a general term for even numbers, so if we ignore even numbers and only use odd numbers, we can How to verify it?"

Hearing Zhang Zhongyuan's words, except for Chen Zhou, the other students were lost in thought.

Zhao Qiqi beside Chen Zhou even tilted his head and asked Li Li, "It seems to work if you simply verify odd numbers?"

Li Li didn't say anything, just passed Zhao Qiqi and glanced at Chen Zhou.

Chen Zhou naturally knew about this new verification method, but it also had flaws.

Chen Zhou has been looking at Zhang Zhongyuan, he hopes to see Zhang Zhongyuan give a different idea.

Zhang Zhongyuan picked up the wolfberry soaked on the table, took a sip, and checked the time by the way.

There was just enough time for him to finish this part of the content, and by the way, he would spread out the ideas of the students.

Covering the lid of the cup and putting the quilt on the desk, Zhang Zhongyuan said: "Just start verification from odd numbers, and you need to consider the first odd number to be verified."

"It may be an odd number that is divisible by 3, or it may be an odd number that is not divisible by 3. However, after 3x+1, the second odd number reached, the third odd number, the fourth, and the fifth , etc. Every odd number reached in the whole process must not be divisible by 3 any more.”

"However, if we start from the odd numbers that are divisible by 3, every odd number reached on the hail range must not be divisible by 3, and can be reduced to 1 in the end, then all odd numbers must be traversed."

Following Zhang Zhongyuan's narration, the students' thoughts that had just been pulled back fell into thinking again.

Chen Zhou still looked at Zhang Zhongyuan. He knew all these contents, and he was still waiting for Zhang Zhongyuan's next words.

However, Zhang Zhongyuan clearly grasped the time, he did not immediately interrupt the students' thinking.

Chen Zhou felt someone touch him, and he turned his head to look at Zhao Qiqi in doubt.

Zhao Qiqi asked in a low voice: "Brother Chen, what does traversal mean?"

Chen Zhou was taken aback for a moment, and immediately explained: "Traversal is the concept of discrete mathematics, which refers to visiting each node in turn along a certain search route, which is what Professor Zhang said to reach. Well, in the sophomore The book "Data Structures" has this content."

"Oh." Zhao Qiqi nodded again and again, a little ashamed.

He hasn't seen this textbook yet...

Chen Zhou's answer also explained for other students who didn't know the word traversal.

Naturally, they turned their heads to look at Chen Zhou again.

There is admiration and envy in the eyes.

Although he knew that Chen Zhou had already taken the final exams of all grades in the Department of Mathematics, but it was a different feeling to really feel this powerful strength.

On the podium, Zhang Zhongyuan glanced at the time and said again: "I just mentioned odd numbers that are divisible by 3. You must have thought of odd numbers that are not divisible by 3."

"If the verification starts from an odd number that is not divisible by 3, then every odd number reached on the hail range is also impossible to be divisible by 3, and they all end up at 1."

Speaking of this, Zhang Zhongyuan glanced at Chen Zhou again, and then continued to say: "In fact, in the process of verification, for odd numbers that cannot be divisible by 3, there are infinitely many odd numbers in the previous step. "

"Among them, about 1/3 of them are odd numbers divisible by 3, and about 2/3 of them are odd numbers not divisible by 3. And this phenomenon, think about it, what is it similar to?"

As soon as Zhang Zhongyuan finished speaking, Chen Zhou stood up and said, "It's very similar to the natural numbers."

Hearing Chen Zhou's words, Zhao Qiqi next to him suddenly realized: "Yes, it is very similar to natural numbers, why didn't I think of it?"

Li Li glanced at Zhao Qiqi: "Do you want to know why?"

Zhao Qiqi: "Why?"

Li Li: "Because you don't read as much as he does."

Zhao Qiqi was taken aback, not understanding the meaning of this sentence, he muttered: "You might as well say that I am not as smart as Brother Chen..."

Li Li glanced at him and stopped talking.

Instead, the classmate in front of Zhao Qiqi looked back at him with complicated eyes and said, "I think that's what he meant..."

Zhao Qiqi: "..."

Zhang Zhongyuan raised his hand to stop the noise, and motioned for Chen Zhou to sit down. He replied, "Student Chen Zhou is right. This phenomenon is surprisingly coincident with the natural numbers."

After speaking, he noticed that Chen Zhou was still standing there, and asked, "Chen Zhou, do you have any questions?"

Zhang Zhongyuan's words also attracted the attention of all the students.

Under everyone's gaze, Chen Zhou said softly, "Professor, this new verification method has obvious flaws."

Zhang Zhongyuan nodded with a smile: "Well, tell me?"

Zhang Zhongyuan's thought at the moment was that this small class was all taken by this kid.

However, he didn't care.

After all, Chen Zhou has always been a student he values ​​very much.

More importantly, this kid is very similar to him when he was young...

Chen Zhou didn't think too much about it, and said directly: "The calculation of this verification method is discontinuous, and it is very troublesome to verify the process of climbing or descending. When climbing, you need to factorize 2, and when descending, It is also necessary to calculate the Nth power of 3 first.”

After a pause, Chen Zhou continued: "Of course, this method also has advantages. The advantage is that it can be directly replaced when it is verified that the climb is almost infinite. Well, let me give you an example."

When Chen Zhou said that he would give an example, Zhang Zhongyuan's brows twitched, and he thought of the first topic discussion.

At that time, Chen Zhou also gave an example to supplement Shen Jing's research ideas...

However, Chen Zhou's voice brought Zhang Zhongyuan's thoughts back to the classroom.

“比如说2n-1乘以2的一亿次方再减1的验证过程，就是把一亿个2换成一亿个3，也就是2n-1乘以3的一亿次方再减一，通过一次性替换，我们需要把3的一亿次方给计算出来。”

"If you follow the traditional verification method, you need to multiply 2n-1 by 2 to the 1 millionth power and then subtract 1 to calculate it, and then calculate [-] million minus [-] step to get this result."

When Chen Zhou finished speaking, the bell outside the classroom rang.

Zhang Zhongyuan glanced at the time, it was almost time, and Chen Zhou's performance was over, get out of class could be over...

After leaving a thinking question at the end of "summarizing the odd numbers divisible by 3 and the odd numbers not divisible by 3, and calculating through the general term formula", this small class officially ended.

(End of this chapter)