Wandering Spaceship in Deep Space Chapter 15: Let go of your paws!

　　 Li Zhendong glanced at Zhang Yuan, and was taken aback when he saw that he smiled honey on the phone.

　　 Very good, I am looking for someone.

　　 A gossip heart is burning.

　　 Secretly glanced at him. No, he's doing a super brain?

　　 Li Zhendong had to pinch his nose, and said, "You worked so hard?"

　　 "It’s boring, do the topic for fun. Look at this integral, the solution is so beautiful, there are very few integral formulas that can really calculate the analytical solution."

　　 Have fun...

　　 Recreational...

　　Cancel...

　　 Li Zhendong's blue veins jumped wildly on his forehead, and he was short of breath. Reminiscent of his college days, Zhang Yuan was like this diligent dog, which caused him to be criticized by his parents.

　　 "Look at him, and then at you!" Father's judgment seemed to ring in his ears.

　　 Li Zhendong couldn't help becoming irritable. After graduating from university, this guy not only didn't converge, but instead got worse. Problem solving has become an advanced pastime, is it so awesome? !

　　 "Wait a minute, my sister has a game that I can’t play, a puzzle game. If you are bored anyway, try it."

　　 game?

　　 "Come and see."

　　 Seeing the other person’s unkind eyes, Zhang Yuan became a little interested. How difficult can children’s stuff be?

　　The little girl took a learning machine and handed it over. There was a small program called "light off game" on it.

　　 The title is like this: There is a 4*4 square array of electric lights on the panel. Every time you operate an electric light, it even brings the surrounding up, down, left, and right lights all change state (bright becomes darker, darker). Brightens.)

　　 If all these lights are turned off through a series of operations, the game will be cleared.

　　 "This is very simple."

　　 Zhang Yuan randomly clicked a few times, all the lights went out, and it passed.

　　 Another image jumped out on the screen, which turned into a 5*5 electric light matrix, and some of the electric lights in the middle were already off.

　　 "The difficulty has increased."

　　 Zhang Yuan thought for a while, clicked a few times, and passed the level again. This time it took more time than the last time.

　　 Obviously, as the number of electric lights increases, the game will become more and more difficult.

　　"My thoughts are..."

　　 The little girl's eyes flickered, and she said timidly: "If there is a very large queue of lights, and the initial state of the lights is arbitrary. Then, is there a mathematical algorithm to solve this problem instead of random Mess..."

　　 Zhang Yuan scratched his head and said with a smile: "Your sister is very mathematically minded, this general algorithm, well, let me think about it..."

　　 "Of course, she has more than half of my IQ!"

　　 "Brother~ I am smarter than you~"

　　 "Why are you smarter than me?"

　　 Li Zhendong smiled and smiled in his heart.

　　 This topic is difficult.

　　 Why is it difficult?

　　 Because of him, Li Zhendong thought for a while, but didn't make it.

　　 So, Brother Zhang, who loves to make questions, think about it slowly, thinking that the sky is dark, day and night are turned upside down...

　　 Make a good friend ashamed in front of his sister, he is very happy! It's so cool!

　　 "I will take a shower first. You do it slowly."

　　 The little girl looked at Zhang Yuan expectantly. Anyway, she would not be able to do this kind of problem.

　　 However, as the author of the question, I am extremely proud of myself.

　　 Zhang Yuan’s reaction was beyond their expectations. He was a little embarrassed: "No, don’t take a shower. It’s already solved."

　　What?

　　 unlocked?

　　 Li Zhendong was about to stare out, ran out of the bathroom, and put on his underwear again sullenly.

　　 Zhang Yuan talked freely: "According to the topic: Pressing the switch once, along with itself and the lights up and down, left and right, all change state. So we can get a conclusion: For a certain light, the effect of pressing the switch on an odd number of times , Has the same effect as pressing the switch once; pressing the switch even times is equivalent to not pressing it, which is 0."

　　 is interesting.

　　"So, if there is a solution to the problem, each lamp should only be operated once at most, or no operation."

　　"First discuss the N*N matrix, which is actually a two-element group and is isomorphic to a full-rank matrix. Since the matrix is ​​full-rank, there must be a unique solution..."

　　 Just after hearing these few sentences, Li Zhendong's head was about to burst, and his inspiration surged like spring water!

　　 wait a minute.

　　 It seems, that's it...

　　 is a very simple topic.

　　 Why didn’t I think of it?

　　 He shouted unwillingly: "How can you use group theory? How can junior high school students understand group theory? You can't do this to my sister!"

　　 Even Li Zhendong’s mother came out to look, and found that they were not doing anything, shook his head again, and went back to the kitchen.

　　 "That's OK. Junior high school students have learned the system of multivariate linear equations?"

　　 The little girl nodded, the two-dimensional linear equations are indeed the content of junior high school, and the elimination method can be solved by the substitution method.

　　 Three yuan once, four yuan once is also acceptable.

　　 Zhang Yuan continued: "Assuming that Aij is the number of adjustments to the jth lamp in the i-th column, obviously, according to what I just said, Aij is not 1, or 0."

　　"Let’s take the simplest 2*2 matrix as an example, set the light off state to 0 at the beginning and 1 to turn on the light."

　　"We assume that the initial state of the matrix is ​​like this:

　　【1-0】

　　【0-0】"

　　"Then you can write four equations:

　　A11⊕A12⊕A21=1

　　A11⊕A12⊕A22=0

　　A11⊕A21⊕A22=0

　　A12⊕A21⊕A22=0"

　　" The solution can be A21=A11=A12=1, A22=0. So just operate the three lights A21, A11, A12 in sequence, the order does not matter~IndoMTL.com~All N*N matrix problems are It can be calculated like this, and there must be a solution. But the N*M problem may not necessarily have a solution, the reason is this..."

　　 Li Zhendong wanted to cry without tears, and watched his sister's eyes a little admiration, and even little stars appeared!

　　 Although he knows that his sister will probably not understand...

　　 But, but, girls at this age are innocent and innocent. They only have learning in their eyes. They have no resistance to schoolmasters!

　　 is over, my sister’s admiration for her brother has been snatched away by others!

　　 I only heard my sister ask again: "Why do you add a circle to this plus sign?"

　　"Because it is a binary field operation, 1⊕1=0, 1⊕0=1, 0⊕0=0, which is called exclusive OR operation in the computer field... If you use a normal plus sign, it will calculate a negative number. "

　　 "Brother Zhang, you know so much!"

　　 "So work harder, otherwise, like your brother, he has talent but hasn't cashed in it, and it's useless to be smart..."

　　 Livestock, even hurt me!

　　go-die!

　　 "Brother Zhang, please help me with Mathematical Olympiad problems. I can't understand many of them. My brother doesn't help me."

　　"Go...Let’s go."

　　My sister is underage!

　　 Let go of your paws!

　　 "Ahem!" Li Zhendong coughed heavily and warned: "I'm going to take a bath, don't mess around, my parents are still at home."

　　 what?

　　 Zhang Yuan scratched his head.

　　 The little girl couldn't help but curled her lips and rolled her eyes. She is already in junior high school and understands many things. Even if she falls in love, she won't be opposed by her family.

　　 She feels that her own brother really has some brain problems, or that Zhang Yuan’s brother is normal...