In addition, there are some problems, whether it can be solved within the polynomial time complexity, if you know a possible solution given casually, you can verify whether it is the desired solution within the polynomial time complexity.

Then, this type of problem is called np type problem.

As for why we need to study a question, whether there are algorithms with polynomial time complexity.

This is because the calculation rate of the time complexity of polynomials is a bit too "fast".

As n increases, its calculation amount is much smaller than the time complexity problems such as o(2^n), o(n!), and o(n^n).

It's like the very famous problem of prime factor decomposition of large integers.

Given a 2048-bit binary integer, you need to find out some prime factor of it.

Generally speaking, it may take hundreds of years to complete the solution calculation process by utilizing the world's computing power.

However, if you know a certain prime number.

However, it can be used to determine whether this prime number is a factor of this 2048-bit binary integer in a few seconds.

And this is the difference between different time complexity and in the actual calculation process!

Although it is not good to be fast sometimes, in terms of time complexity, it is still more useful to be faster.

Naturally, all p-class problems belong to np-class problems.

Looking at the content on the draft paper, Chen Zhou had already given this obvious explanation.

[A problem can be solved within the time complexity of polynomials, and of course it can be verified within the time complexity of polynomials.]

However, Chen Zhou, who had finished writing this line of text, added another "?" below.

Next to the question mark, Chen Zhou wrote: "What about it?"

That's right, what's the other way around?

Can a problem that can be verified within the time complexity of polynomials be solved by an algorithm of time complexity of polynomials?

Chen Zhou doesn't know for the time being.

So, he drew two horizontal lines under this rhetorical question.

In fact, if this rhetorical question is, is all np-type problems arising from p-type problems?

And this is the famous np complete problem, that is, "np=p?".

Although Chen Zhou doesn't know the answer to this question yet.

However, Chen Zhou, who is no longer a novice in informatics, naturally knows the answer to this question and the practical significance.

If “np=p?” has no question mark.

This means that any np-class problem that cannot find the p-class algorithm can find the corresponding p-class algorithm.

It also means that the prime factor decomposition problem of large integers has become a p-type problem.

For example, a 2048-bit binary large integer can be used to complete the decomposition of prime factors in a few seconds or even less time using an ordinary computer.

If this is the case, the RSA encryption algorithm, which is now widely used, will be completely invalid.

A large number of bank digital certificates and website SSL encryption will no longer be secure.

Those digital currencies that are now popular will also become mobile wealth that may be taken away at any time.

The entire digital finance will be reshuffled.

At the same time, if np=p, it also means that a large number of problems that are difficult to solve through calculation will be easily solved through algorithm optimization.

Problems such as weather prediction, traffic scheduling, predicting protein structure through amino acid sequences, the most effective transistor layout on computer chips, etc., will all be solved.

It is no exaggeration to say that this is definitely a problem that changes the world.

Chen Zhou was not very excited about these practical meanings.

He just took his gaze from the draft paper and turned back to the computer screen.

Then, I moved my mouse and clicked on the second downloaded document.

The reason why Chen Zhou is like this is not because he has no longing for the idea of ​​changing the world after solving this problem.

In fact, the difficulty of this problem is really a bit too great.

Think about it and know that if it is listed as one of the seven Millennium Awards, will its difficulty be average?

Moreover, from the current academic perspective, most scholars in related fields, including mathematicians, computational theorists, senior algorithm researchers in informatics, etc.

Everyone thinks that np≠p.

This shows the difficulty of this problem.

In addition, the NP complete problem is different from the Yang-Milles standard field existence and mass interval hypothesis problem that Chen Zhou had solved quickly before.

To a certain extent, this problem is that Chen Zhou is conducting his first research on an uncultivated virgin land.

Therefore, Chen Zhou was not in a hurry to achieve success in the NP issue.

He didn't make too much restrictions on the time he gave himself.

As of now, Chen Zhou's research focus is still on normative field theory.

If np is completely problematic, it must be ranked third.

The second one is Zhang Yifan's side, and related research on material dmd-2.

As the literature was gradually downloaded, Chen Zhou no longer thought about it and instead immersed in the sorting of literature.

It was not until twelve o'clock in the evening that Chen Zhou came back to his senses from his immersed research state.

After taking a look, there were still many documents that were being downloaded. Chen Zhou simply screened them again and increased the number of downloads again.

Then organize the information on the desk, get up and go to wash and sleep.

Although he had no intention of retreating to research, Chen Zhou, who returned to his research state, gradually returned to his previous research and life rhythm.

The next morning, before the alarm clock, Chen Zhou got up and went for a morning run with Xiong Hao.

After the morning run, I brought breakfast back to the dormitory.

After quickly resolving breakfast, Chen Zhou returned to the room and at the desk.

Sometimes, Chen Zhou felt that this desk was his world.

These stacks of draft paper and refills were his weapon of conquest.

Chen Zhou, who entered the research state again, could not detect the passage of time at all.

And the following days were spent quickly between the interweaving of paper and pen.

Until September 10, the day when Yan University starts school.

After breakfast, Chen Zhoucai did not choose to return to his desk.

He plans to go to his office and communicate with his students.

Because in the past few days, he has received a lot of emails from these students.

Although these students were all stocked by him.

However, when the stocking is almost the same, let’s take a look at how these children grow up?

In addition, Chen Xiao is also going to report to the Department of Mathematics of Yan University today.

By the way, this kid is going to move out of the dormitory and into the school's student apartment.

This is not Chen Zhou’s request, but Chen Xiao’s own decision.

Chen Xiao doesn't want to be discovered by others' relationship with Chen Zhou.

Chen Zhou naturally had no objection to this.

He also wanted to see how far his younger brother could grow.
Chapter completed!