Lin Gao Qiming

Chapter 1948 The Mathematical Theory of Troubleshooting

Qian Yuzhi's eyes were the first to be in a trance, and Li Jianai's mind was also distracted when he persisted until here. Only Feng Shan was still listening.

"Binary search to find a specific value from an ordered table is essentially a divide-and-conquer strategy, that is, to divide a large problem into several similar sub-problems, and then either solve it directly or continue to divide. Why does it require an ordered table ?It is to ensure that each operation can solve all sub-problems at the same time. For example, if the median value of the ascending list is less than the value being looked up, I can ensure two conclusions at the same time, one, the value being looked up is not in the first half of the ordered list In, two, the value to be looked up is in the second half of the ordered list - then I can repeat the above operation in the second half of the ordered list."

"Our problem is similar. In terms of probability, first we can reasonably assume that there is one and only one card that is wrong. Then, we count half of all cards known to contain wrong cards at a time. If the statistics The result shows that the wrong card is not in this half, then it must be in the other half, and vice versa. So I narrowed down the "suspect range" of half of the wrong cards. I repeated the halving operation to narrow down the suspect range, and when it narrowed to a certain extent, the problem It's no longer a problem."

"I told you before that the actual capabilities of the punched card computer we are making are not limited to what you see in front of you. My halving operation just now is very mechanical-always divide half, enter it, and then check the result. Take the stack containing the wrong card and repeat."

"So if one day, we design a machine to replace the repetitive mechanical operation I just had, and combine it with the tabulating machine to accomplish more things, many big problems will be broken down into small problems, and then use the same operation process solve."

"The idea of ​​decomposing a seemingly complex problem into smaller problems similar to the original problem, and repeatedly using a series of similar mechanical operations to solve it, so that computers can also complete it, is called 'recursion'. This is what we You have to think carefully about the use of computers as an essential way of thinking. In particular, when thinking about such issues, don’t take into account the speed of existing mechanical computers, thinking that they are not as fast as manpower. The key is to think about it. What kind of problems can be solved by the computer only by following the rules without any intervention. That is, what kind of problems can be solved by the computer, which we call 'computable problems'. As for the speed, that is not a problem - bread will have .”

Feng Nuo stopped and asked Feng Shan to chew on this passage carefully. For her, this way of thinking was similar to mathematics, but quite different from the mathematics she had learned before.And Li Jianai and Qian Yuzhi's mathematics is at the level of the four arithmetic operations, and it is really difficult for them to understand.Because he didn't sleep well last night, he was already very confused at this time, these words were nothing less than a lullaby - Qian Yuzhi was still wondering what this matter had to do with bread while he was confused.

"Okay, you two go to sleep. Let me see what is going on with this card." Feng Nuo put aside Feng Shan, who was still thinking blankly, and said to Qian Yuzhi and Li Jianai. In the middle, "You can sleep on that bed." After finishing speaking, he picked up the card with the wrong hole on the table.

Li Jianai woke up from the bed and found that Qian Yuzhi was still sitting on the chair, leaning against the wall and sleeping soundly.She looked around, Feng Shan was reading a book at the workbench and calculating something, and Feng Yuan was not in the room, so she probably had a meeting somewhere.

She yawned and got out of bed, poked Qian Yuzhi, and said, "Go to bed." Unexpectedly, he just snorted and stopped moving.Li Jianai dragged him to the bed with all his strength - said that the two were on shift, but in fact, Qian Yuzhi stayed up on duty last night much longer than her.

Probably feeling the remaining body temperature on the bed, Qian Yuzhi turned over, as if he wanted to curl up in the depression that Li Jianai had just slept in, and continued to sleep soundly.

Li Jianai walked to the workbench and poured a glass of water to drink.At this time, she saw Feng Shan put down the book and rubbed her eyes, as if she was going to take a rest, so she chatted with her.After a while, they said that they would go to the party of Li Jianai and his classmates from the Faculty of Arts and Sciences next Monday-it is said that several seniors will also attend.

In the next few days, the research team repeatedly improved and tested the duplicator. At the request of Feng Nuo, a card reading mechanism was added to the row of the punching mechanism of the duplicator. This change is not big, but it can make the duplicator The machine also has the function of part of the verification machine (Verifier).After the copying is completed, a small amount of wiring can be changed to make the machine function change to automatically check whether the perforations of the two stacks of cards are consistent, and when the perforations are found to be inconsistent, the machine will stop and turn on the alarm.

No matter how fast the binary search is, it is always faster than not having to go through the machine directly.

In addition, the improved version can also hold a mother card in the card reader mechanism, punch and verify a stack of cards.In practical applications, this function can pre-punch the common hole positions of a batch of cards, reducing the workload of manual punching.

However, although the duplicator has been improved and the problem of punching wrong holes has been fixed, it still occasionally misses punching holes.Finally, the research team reduced the card drive and processing speed and found that the problem disappeared.

"It seems to be a problem with the response speed of the relay." Sun Li threw the pen in his hand on the table, "Slow down and run."

Everyone looked at Feng Nuo "swish", Feng Nuo had no choice but to nod without a word.But the veterans are all practicing thick-skinned now-everyone's level is about the same, so don't laugh at anyone else.The embarrassment quickly recovered, and he proposed a plan to develop a decoding machine.

According to the plan, the tabulation machine should integrate the functions of printing and summary punching. For the purpose of simplifying the complexity of a single machine, the tabulation machine does not include these parts at this stage.Therefore, Feng Nuo plans to build the most basic digital decoding machine first. Since the printing of Latin letters is not considered, it can no longer be called "decoding". Then activate the relay to drive the curved typesetting to print the numbers of 0-9 on the top of the card.Now the development of the replicator is complete, and the decoder is just a matter of course.

The veterans of the mechanical port felt that the problem was not serious, and promised to manufacture a prototype as soon as possible and send it over.

The meeting ended here, and Feng Nuo returned to the office: He thought that he had to prepare lessons today——With the development of mechanical computers, he felt that it was time to teach some mathematical problems related to software engineering in depth——First Almost all programmers of the present generation were mathematicians.

He handled the daily official documents of the data center in the office, and walked around the computer room as usual to do routine equipment maintenance.I browsed through the "to-be-repaired catalog" again, and ticked off a few "immediately imminent" items with a red pencil. These can only be repaired after class at the expense of sleep time—since he got the mechanical computer For the project, the original work has been suppressed a lot.Now Old Fifth Xu has helped him with most of the paperwork, and it would be unreasonable to let this job go unused.

After finally finishing the tasks at hand one by one, he got up and went to the workshop.

Now the "workshop" is full of people.All kinds of "engineering prototypes" manufactured from the machinery factory are filled with this workshop, and some of them are not the products of the "technical meeting" at all, but the products of the brains of some veterans with strong hands-on ability-to say that they are completely Brain holes are not necessarily true, because these things are roughly the different technical ideas in the development of mechanical computers back then.

Naturally, the engineering prototype is not very sophisticated, because the time is tight, and most of them are only to verify whether the design idea is engineering feasibility, so there is no optimization in design and manufacturing, adhering to the usual stupidity of machinery factory products, Many parts of equipment are also exposed, which saves manufacturing time and facilitates troubleshooting and debugging at any time.

The workshop is full of machines with iron teeth and steel teeth, and there are many scattered materials and parts on the ground.So Feng Nuo has been taking care of his three helpers, and he must take good precautions when entering the workshop.He set an example by himself, wearing a rattan helmet, rough work clothes, and safety shoes.

Passing through the equipment area, the other end of the workshop is the research area. A bulky large "Holy Ship" 12-person conference table stands in the center. The table is full of drawings, documents, and draft calculation papers, surrounded by seven or eight folding chair.There is a huge blackboard stand in the corner, and the blackboard is full of formulas and numbers written in chalk.Against the wall is a row of open bookshelves, filled with various technical materials and reference materials layer by layer-in just a few months, so much paperwork has been accumulated.According to the regulations of the Planning Institute, Feng Shan and Li Jianai sorted and bound these materials according to categories - they are all to be archived and provided as a reference for future technical workers.

However, if there is no set of efficient retrieval equipment, these technical materials will only be silent in a corner of the big library and will be slowly forgotten by people.Thinking of this, Feng Nuo felt more and more that he had a heavy responsibility on his shoulders.

The ground in the research area is full of scattered calculation drafts, just like when the old movie gunners were defeated.The research team forgot to sleep and eat all day long, and naturally they didn't care about cleaning.After all, everyone washes their bento boxes and takes them away, otherwise rats will definitely be attracted to this level of sloppiness.

Feng Nuo sat down on the chair, and took out a professional textbook on discrete mathematics—this was reprinted locally in Lingao, and it had been reviewed by the Office of Truth, so there was no need for confidentiality measures, and it could be directly inserted on the bookshelf.

Just as I was about to open it, I suddenly saw that the wastebasket under the table was full of shredded paper—not ordinary shredded paper, but torn and shredded shredded paper. This was not the calculation paper they usually used, but letter paper.It seemed to be densely covered with handwriting.
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The next update will be Chapter 53 of the seventh volume of Guangdong and Guangxi Raiders

(End of this chapter)