Chapter 280 The end is the beginning of victory
Excluding all kinds of invalid information, the bottom line of this question is:
There are two pipes up and down, and beads of two colors are arranged in the pipes. Taking out the beads in a certain order can form an output sequence. Different bead-retrieving methods can form the same output sequence. Suppose the number of bead-retrieving methods of a certain output sequence is a[i], and the task is to find the square of Σa[i] of all output sequences.
What exactly does the last requested formula mean? This is a big difficulty.
It cannot be calculated directly. This mathematical formula that appears very suddenly needs to be given the meaning of actual physical operations.
If you don’t get this step right, you won’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 froze. If he hadn't kept moving his mouse over the question stem, he wouldn't have even noticed it.
As soon as the invigilator saw Li Yan raising her hand, she almost jogged 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 Li Yan’s computer broke during the test, which put a lot of pressure on them. Unexpectedly, there was still a problem in the main game.
So even though the air conditioner was on, the guys who were troubleshooting were still sweating.
Seeing that the repair could not be completed within a few minutes, the invigilator quickly comforted Li Yan.
But I saw this first-year junior high school kid, with his eyes closed and concentrating, sitting as straight as a pine tree.
"You're in such a good mood?"
Director Jin and Dong Chengliang were not in a good mood. They were anxiously running around in the team leader's room. Director Jin had already called the organizing committee to request that Li Yan be replaced due to maintenance. It's time.
Dong Chengliang sighed repeatedly, "This interruption of the train of thought is not enough to make up for the same amount of time!"
"Old Dong, this is called a great responsibility given to this person by heaven. " said another team leader from Linjiang, a teacher from Xin'an Middle School.
“I don’t like to hear this sentence.” Dong Chengliang waved his hand, “Geniuses should have a better and more stable space to develop. Even if this child is a flower in the greenhouse, it is the most beautiful one. ”
The maintenance lasted fourteen minutes. While waiting for the computer to turn on, the invigilator wiped his sweat and said to Li Yan: "I will go to the organizing committee to make up for the missing time. If you have written a program before and it is lost this time, I will also tell the group The committee applied for extra time."
"No need." Li Yan nodded politely, "I haven't written it yet, and...it shouldn't be necessary."
It doesn't matter. After several people's shocked reactions, Li Yan found the path to this question in his meditation just now.
This formula can be understood as: If there are two identical devices that perform the operation of taking beads at the same time, how many options are there for the two devices to obtain the same sequence.
Two people play the game of fetching beads together.
This sentence... there is no problem!
Go directly to the moving rules, but the four-dimensional moving rules do not allow it regardless of time or space.
Two people have the same sequence, and the number they take must be the same, so that dimensionality reduction can be performed, and then state transfer and recursion are considered...
"This recursion is always to the next state. Transfer, use the scrolling array directly for the outermost loop, it’s done.”
Li Yan was thinking silently and started typing frantically at the keyboard.
I originally wanted to look at the third question again, but according to the organizing committee's academic understanding of the "finale", I am afraid that the question of picking up beads is still the most difficult one.
From understanding the formula to using transfer, it is a bit difficult for Li Yan.
The middle is a great test of the "induction" ability, from abstract mathematical formulas to specific physical operations, and then abstracting mathematical logic from physical operations.
As long as your mind goes a little bit wrong at every step, you will encounter a natural chasm.
"It seems that combinatorial mathematics can also be used..." Li Yan only hesitated for a moment and then gave up.
It is the choice of a wise person to avoid making the same mistakes again.
He must take advantage of his continuous thinking about this question and get out of the way in a hot state, otherwise if he turns back and loses his train of thought, he may not be able to turn around some corners.
Writing the program took more time than he expected. Fortunately, Li Yan did not need to do any checks.
He was cautious about letting the program run through - although it didn't take much time.
The third question comes up: "Little A has loved mathematics since he was a child. He is very smart and likes to study some small mathematical problems."
Then do your own research.
So Li Yan went back to the first question and stopped the program.
Then he looked at the third question again. Li Yan said contemptuously: "It seems that Little A is not smart enough and hasn't solved it yet."
As the name suggests, the question is just a stroke problem. The questions are very specific and the solutions are straightforward.
It’s Simpsons.
The difficulty is that the amount of code is very large. If you want to complete an error-free program, the requirements for basic skills and concentration are very important.
Probably similar to the final question of the physics exam, each number must be calculated to four decimal places. The idea is not difficult, but getting it right is not.
Li Yan felt that today’s set of questions really tortured others while tapping the keyboard quickly.
end.
He completed the exam and submitted it half an hour early - plus the ten minutes lost due to repairing the computer, it should be about three quarters of an hour early.
In fact, compared to the various fastest legends he has ever created, this advance is not bad.
But the difficulty of this set of questions is also the top one he has ever experienced.
It is rare to feel like your brain is hot and your eyes are sore after writing a question.
Still hungry.
It seems that it is right not to continue to use combinatorial mathematical solutions.
If you want to show off, you need to be calm after all.
It was rare that I didn’t take it easy today, but it was unexpectedly very pleasurable.
After the exam ended, wailing echoed in the examination room.
Chen Fan, who was waiting outside, was smiling. It seemed that he was determined to win the junior high school competition.
The game was over, and everyone had no worries at lunch, and the discussion was lively.
Li Yan noticed that everyone had a little more rice.
As soon as the four of them in the same dormitory sat down, Lai Yining took Deng Yudi to occupy the last two positions of the small table.
The status of "core group members" gives them a special sense of belonging.
"Are you done?" Lai Yining asked.
He received unanimous nods from Li Yan, He Zixiang and Deng Yudi.
This actually surprised Li Yan. He thought that someone would fail today.
Hu Junxi covered his face and put food into his mouth in big gulps.
“Which question is the most difficult?” Lai Yining continued to ask.
Everyone agreed that it was to get the beads.
Hu Junxi chewed white rice and asked: "Dear masters, isn't the last question not difficult for you?"
"Simpson." He Zixiang said.
"I know, damn, knowing how to do it is one thing. With Simpson's amount of code, I changed it four times and still can't get the result."
"Knowing how to do it... That’s it,” Deng Yudi said.
Seeing the serious expressions on the four people's faces, Hu Junxi waved to Chen Fan, "I don't dare to talk to them anymore, junior, how are you today?"
"It's okay, I've tested it, and there's nothing wrong with it. Maybe I'll deduct some points for the steps."
"...The white rice is so fragrant."
"It seems like I might It’s the worst performance today.” Deng Yudi sighed, “I’ll search directly after taking the beads.”
“The search should only have a basic score, and there is no clue to optimize to get a high score.” Li Yan responded.
"Di Shen's words are heartbreaking. I used dp, but it got stuck in the middle. Maybe it's not as high as your explosive search score." Lai Yining's mouth was full of oil, and he seemed to be hungry. "The key is that you scored 285 yesterday. You got the basic score for today's question. You got the other two. Plus the written test, you still got 500+. You are firmly in the top ten."
"I feel that this year's Au line should be 35336. The three of you scored yesterday. Even if you failed the second question today, you will be safe in entering the defense." He Zixiang also said one after another, "Yanshen, what are you thinking? ”
“Move the rules and transfer the equations”
Everyone stopped eating.
"How did you come up with it?" He Zixiang was very excited.
"ai is the number of options that make up the i-th sequence, so it is natural that the square of ai is the number of options that both devices can use to obtain the i-th sequence." Li Yan had already finished his lunch like a storm. , while wiping his mouth, he said, "This is simple. f[i][j][k] means that i beads have been taken. The first device has taken j beads from the first row, and the second device has taken the first row. After taking k numbers, the resulting sequence is the same number of solutions, and the transfer equation is obvious. ”
"Of course..."
"Simple..."
"Obvious..."
Then the three high school students sighed in unison.
Chen Fan had an inexplicable feeling of secret joy.
(End of this chapter)