Rebirth 07: Start adding points from elementary school students

Chapter 280 The End is the Beginning of Victory

Eliminating all invalid information, this question boils down to:
There are two pipes, one above the other, with beads of two colors arranged in them. By taking out the beads in a certain order, an output sequence can be formed. Different ways of taking out beads can form the same output sequence. Let the number of ways of taking out beads for a certain output sequence be a[i]. The task is to find the square of ∑a[i] for all output sequences.

A big difficulty is what the final formula means.

It is impossible to calculate it directly. We need to give this mathematical formula, which appears very suddenly, the meaning of actual physical operation.

If this step is not completed, I don’t know how to proceed later.

Fortunately, thinking speed is not a problem for Li Yan, and there is still plenty of time.

But suddenly, his computer crashed, and he wouldn't have even noticed if he hadn't been moving the mouse over the questions.

As soon as the invigilator saw Li Yan raise her hand, he almost ran over.

The maintenance work was carried out in a hurry, and Li Yan vaguely heard a staff member muttering "Murphy's Law" in a low voice.

In short, this law means that whatever you fear will come to you.

It seems that the fact that Li Yan's computer broke down during the test brought them a lot of pressure, and they didn't expect that there would be problems in the main competition.

So even though the air conditioner was on at the scene, the guys who were troubleshooting the problem were still sweating profusely.

Seeing that the repairs could not be completed within a few minutes, the invigilator hurriedly comforted Li Yan.

But I saw this first-grade student was sitting upright like a pine tree with his eyes closed.

"You're in such a good mood?"

Director Jin and Dong Chengliang were in a bad mood and were running around the team leader's room anxiously. Director Jin had already called the organizing committee to ask them to make up for the time Li Yan lost due to maintenance.

Dong Chengliang sighed repeatedly, "This interruption of my train of thought cannot be made up for in the same amount of time!"

"Boss, this is what we call God giving great responsibilities to this person." Another leader of Linjiang, a teacher from Xin'an Middle School said.

"I don't like to hear that." Dong Chengliang waved his hand. "A genius should have a better and more stable space to perform. Even if this child is a flower in a greenhouse, he is still the most beautiful one."

The repair lasted fourteen minutes. While waiting for the computer to boot up, the invigilator wiped his sweat and said to Li Yan: "I will ask the organizing committee to make up for the missing time. If you have written a program before and lost it this time, I will also ask the organizing committee to give you extra time."

"No need." Li Yan nodded politely, "I haven't written it yet, and... I don't think I need to add more time."

Ignoring the surprised reactions of these people, Li Yan found the solution to this problem in his previous meditation.

This formula can be understood as: if there are two identical devices taking beads at the same time, how many ways are there for the two devices to obtain the same sequence?

Two people play the game of getting beads together.

There is nothing wrong with this sentence...
Directly use the motion rule, but the four-dimensional motion rule does not allow it in either time or space.

If two people have the same sequence, the number of items they take must be the same, so we can reduce the dimension, consider the state transfer and perform recursion...

"This recursion always moves to the next state. For the outermost loop, just use the rolling array. That's it."

Li Yan was muttering to himself and had already started typing frantically on the keyboard.

I originally wanted to take a look at the third question, but according to the organizing committee’s academic understanding of the “finale”, I’m afraid the question of picking the beads is still the most difficult one.

From understanding the formula to using the transfer, it was a bit difficult for Li Yan.

The ability of "induction" is greatly tested in the process, from abstract mathematical formulas to specific physical operations, and then abstracting mathematical logic from physical operations.

If your thinking is just a little bit off at every step, you will encounter an insurmountable obstacle.

"It seems that the method of combinatorial mathematics can also be used..." Li Yan hesitated for a moment and then gave up.

Avoiding repeating the same mistakes is the smart choice.

He had to take advantage of the continuous thinking on the problem and solve it in one second with a fiery state of mind, otherwise once his train of thought was interrupted, he might not be able to turn around.

Writing the program took longer than he expected, but fortunately Li Yan didn't need to do any checks.

He was being cautious by just running the program once - although it wouldn't take long.

The third question came up: "Little A has loved mathematics since he was young. He is smart and especially likes to study some small mathematical problems."

Then go research it yourself.

So Li Yan went back to the first question and solved the program in seconds.

Then he looked at the third question again and said contemptuously, "It seems that Xiao A is not smart enough and hasn't solved it yet."

As the title suggests, it is a question of outlining. The question is very specific and the solution is also very surprising.

The Simpson.

The difficulty lies in the large amount of code. In order to complete a program without errors, it requires a lot of basic skills and concentration.

It's probably similar to the last question in a physics exam, where you have to calculate every number to four decimal places. The idea is not difficult, but it is not easy to do it right.

Li Yan typed quickly on the keyboard while lamenting that today's set of questions was really torturous.

end.
He finished the exam and submitted it half an hour ahead of schedule - including the ten minutes lost due to computer repairs, it should be about three quarters of an hour ahead of schedule.

In fact, compared with the various fastest legends he had created, this advance time was not so bad.

But the difficulty of this set of questions is also the top 1 he has ever experienced.

It's rare to feel my brain burning and my eyes sore after finishing a question.

Still hungry.

It seems that it is right not to continue to work on the combinatorial mathematics solution.

If you want to show off, you need to be calm after all.

Today was a rare day when I wasn't able to be relaxed, but it was surprisingly enjoyable.

After the exam, wailing echoed in the examination room.

Chen Fan, who was waiting outside, had a smile on his face. It seemed that he was determined to win the junior high school group competition.

The competition was over, and during lunch everyone had no reservations and had a heated discussion.

Li Yan noticed that everyone had more rice.

As soon as the four roommates sat down, Lai Yining and Deng Yudi occupied the last two seats at the small table.

The identity of “core group members” gives them a special sense of belonging.

"Are you done?" Lai Yining asked.

Li Yan, He Zixiang and Deng Yudi nodded in unison.

This surprised Li Yan a little. He thought that someone would fail today.

Hu Junxi covered his face and ate big mouthfuls of food.

"Which question is the most difficult?" Lai Yining continued to ask.

Everyone agreed that it was to take the pearls.

Hu Junxi chewed his rice and asked, "Masters, is the last question not difficult for you?"

"Simpson." He Zixiang said.

"I know. Damn, knowing how to do it is one thing. The Simpson code is so huge that I changed it four times and still can't get it to work."

"As long as you know how to do it... that's enough." Deng Yudi said.

Seeing the four people's serious expressions, Hu Junxi waved at Chen Fan, "I don't dare to talk to them. Junior, how are you today?"

"It's OK. I've tested it all. There's no problem. Maybe I'll deduct some points for the steps."

"…White rice smells really good."

"It seems that I may have performed the worst today." Deng Yudi sighed, "I will take the beads and search them directly."

“The search should only have a basic score, and there is no clue of optimizing to get a high score.” Li Yan responded.

"God, what you said hurts my heart. I used DP, but it got stuck in the middle. Maybe my explosive search score is not as high as yours." Lai Yining's mouth was full of oil, and he seemed to be very hungry. "The key is that you scored 285 yesterday. You can get the basic score for this question today, and you can get full marks for the other two. With the written test, you can still get 500+. You will definitely be in the top ten."

"I feel that the Au score this year should be 350-360. With the scores you three got yesterday, even if you fail the second question today, you will definitely make it to the defense." He Zixiang also said one after another, "God Yan, what's your idea?"

"Motion rules, transfer equations."

Everyone stopped eating.

"How did you come up with this idea?" He Zixiang was very excited.

"If ai is the number of solutions that make up the i-th sequence, then it stands to reason that the square of ai is the number of solutions that both devices can obtain the i-th sequence," Li Yan finished his lunch like a whirlwind and said as he wiped his mouth. "This is simple. f[i][j][k] means that i beads have been taken, j beads have been taken from the first row of the first device, and k beads have been taken from the first row of the second device. The resulting sequences are the same number of solutions, and the transfer equation is obvious."

“Of course…”

"Simple……"

"It's obvious..."

Then the three Gao Yitians sighed in unison.

Chen Fan inexplicably felt secretly happy.

(End of this chapter)