MTL - Scholar’s Advanced Technological System-Chapter 23 Classic modeling problem with businessmen and followers

Looking at the two people in the classroom, Professor Liu Xiangping squinted and smiled and asked: "Only two people? I heard that there is one."

"...I called her and asked her." Wang Xiaodong stunned and took the phone and went outside.

The teacher was not in a hurry, unscrewed the thermos cup, took a sip of hot water, and walked slowly to the side of Lu Zhou. He smiled and asked: "What is the configuration of your team?"

Lu Zhou put down his mobile phone and smiled and replied: "I am responsible for modeling, Wang Xiaodong is responsible for programming, and Lin Yuxiang is responsible for writing papers and defenses."

"Modeling, programming, writing, standard configuration," Liu smiled and continued. "Say, you are the one-three-year Lu Zhou. I read that paper, it is really good." Article."

Lu Zhou’s eyes lit up: “Do you also engage in mathematics?”

"That's right, but my research direction is biased towards physics. Mathematical papers are rarely sent." Teacher Liu blinked and looked at the door of the classroom. He continued with a smile. "You lesbians don't seem to be reliable. what."

Lu Zhouyi smiled politely and politely.

Teacher Liu also smiled. She didn’t say anything on this issue. After a pause, she continued: “With regard to the configuration of your team, I suggest that you can adjust it slightly. Modeling and papers are the responsibility of the same person, and the rest. Two people are responsible for programming. The advantage of this is that the person responsible for modeling has a strong grasp of the whole topic and the text is more fluent. However, of course, there are also disadvantages, that is, your burden will be heavy. Three days, this means that you must start writing the paper immediately after you have completed the modeling."

Lu Zhou thoughtfully: "... Are two people responsible for programming?"

Teacher Liu licked the tea and said slowly: "Yes."

Lu Zhou smiled and did not immediately give a reply: "I will consider it again. After all, this matter has to be discussed with my teammates."

At this time, the footsteps of the trot came from outside the corridor, and the last teammate was finally late.

"Sorry, I am a little late, really really sorry!" and Wang Xiaodong walked into the classroom together, Lin Yuxiang looked down and smiled at the teacher.

"Nothing, since people are coming together, he will start soon." Teacher Liu Xiangping smiled casually, did not blame her lateness, turned and walked to the podium, inserted the U disk into the computer, and opened The projector, released his PPT.

“Before starting the lecture, I hope that you will come to see an example. This question is not difficult in itself, but it can be used as a case for mathematical modeling. I hope that through this case, you can understand that mathematical modeling is what?"

Said, he pressed the mouse and turned the ppt to the next page.

"Three merchants each take a boat to cross the river, a boat can only accommodate two people, followers secretly, on any shore of the river, once the number of followers is more than the merchants, killing people, but how to cross the river by boat The power of the people is in the hands of the merchants. Q: How can the merchants cross the river safely?"

Indeed, there is no difficulty with this question.

Even without relying on the power of the system, Lu Zhou quickly came up with the answer and replied.

"The first round, two followers, one follower."

"The second round, two more followers, one follower."

"In the third round, two businessmen passed, a follower and a businessman came back."

"In the fourth round, two businessmen passed and one followed."

"The fifth round, two followers, one follower."

"The sixth round, the last two follow the past, successfully crossing the river!"

"Hey!" Lin Yuxiang patted his little hand and snorted, his face full of worship.

The expression on Wang Xiaodong's face is not moved, the appearance of a worldly high man.

In his opinion, this question is really not difficult. Although he didn't think about it, he believed that his IQ was at the same time and he took a little time to solve it.

“Exactly correct.” Teacher Liu smiled and continued, “Even if you don’t need any mathematics, you can solve this problem simply by logic analysis. But what if you extend the problem to N merchants?”

This problem is indeed somewhat difficult, but it is not difficult to be in mathematics, but it is difficult to solve this problem by abstracting it into a mathematical problem.

Lu Zhou seriously thought for a while, and he already had a general idea in his mind.

"Can I use the blackboard?"

"Of course," Professor Liu Xiangping smiled and made a gesture of asking.

Lu Zhou stepped forward and picked up the chalk to start the blackboard on the blackboard.

[1 number of merchants on the shore before the kth crossing the river is Xk. The following numbers are Yk, k=1, 2, ..., Xk, Yk=0, 1, 2, 3. The two-dimensional vector Sk=(Xk, Yk) is defined as a state, and the state set under the safe crossing condition is a set of allowed states, which is denoted as S.

S={(X,Y)|X=0, Y=0,1,2,3; X=3, Y=0,1,2,3; X=Y=1,2}

The number of merchants on the kth ferry is 2 Uk, and the number of followers is Vk. The two-dimensional vector Dk=(Uk, Vk) is defined as a decision. Allow the decision set to be recorded as D, which is known by the boat capacity: D={(U,V)|1≤U+V≤V, U,V=0,1,2}

3 Combining the above conclusions, the variation law of state Sk with Dk is: S(k+1)=Sk+(-1)^k*Dk

】

"It's so powerful..." Looking at the blackboard on the blackboard with a blank look, Lin Yuxiang slightly opened his mouth and looked at Lu Zhou, who came down from the podium, and whispered in surprise. "You don't need to draft a draft?"

"Played in my heart." Lu Zhou said with a smile.

Wang Xiaodong was as silent as ever and did not speak.

However, from his expression, this arrogant schoolmaster is completely convinced of Lu Zhou’s mathematical ability.

After looking at the process on the blackboard, Professor Liu Xiangping nodded with a smile: "Exactly! But from the perspective of mathematical modeling, this work can only be completed in half. After the modeling is completed, we still Need a program to implement this model. Of course, this model is very simple, I believe that with the ability of our classmates, this level of program is definitely a handy, not to waste valuable time here."

Wang Xiaodong pushed the glasses, and the expression on his face was still indifferent, and that was the way of course.

Although there is no chance to show his programming skills on the spot, he is a little regretful.

After a pause, Mr. Liu continued, “Data modeling is actually a process of simplifying a practical problem into a problem that can be expressed in terms of data and very short language, and then solving the problem through mathematical tools.”

“So the key is what the actual problems your team is facing?”

"Modeling is neither about the ability of the team to study, nor the ability to examine mathematics, but to examine the ability to translate practical problems into data language and solutions. You must remember this."

"I don't have much advice about the modeling itself. There is no more shortcut than to practice and broaden the knowledge. As far as programming is concerned, I can say two things."

"The four main types of software are commonly used, Matlab, Mathematica, Lingo and SAS. You don't need to master all of them. At least you can master one of them. The key is to use the software that suits you to solve the actual problem." Professor Liu Xiangping is watching Wang Xiaodong.

Because of this sentence, the main thing is to say to him.

Wang Xiaodong pushed the glasses and nodded: "I have used Matlab and SAS, and the problem is not big."

Professor Liu nodded. "These two softwares are basically enough. These things require you to teach yourself. What I can do is provide guidance when you don't understand."

"The last is about reference books. I recommend that you can read some books on mathematical modeling, such as Mathematical Models, Mathematical Modeling Algorithms and Applications, and Mathematical Modeling Basics."

"I have some handouts and materials inside the school. You can copy them back and read them, but remember not to pass them outside, and you can't upload them online. Understand?"

"Understand!" Three people have the same voice.

Professor Liu smiled and said: "Oh, I will be here today. I have nothing else to say. I mainly rely on you. I need the information to download it. When I am finished, I will go back to review English. ""