Deep Space Fleet

振 Li Zhendong glanced at Zhang Yuan to see that he smiled with honey on the mobile phone, and his heart was stunned.

I'm fine, I'm looking for someone.

Hold a gossip heart burning.

I glanced secretly, wasn't it, I was doing a super brain?

Li Zhendong had to pinch his nose, and said badly, "Did you work so hard?"

"Boring, do some pastimes. Look at this integral, how beautiful the solution is. There are very few integral formulas that can really calculate analytical solutions."

Recreational ...

Recreational ...

Dispel ...

振 Li Zhendong's forehead was jumping wildly and his breathing was short. Think of Zhang Yuan as a diligent dog like he was in college, and he was not criticized by his parents.

看看 "Look at him, look at you again!" Father's judgment sounded in his ears.

振 Li Zhendong's heart can't help getting irritated. After graduating from the university, not only does it not converge, it actually gets worse. Problem solving has become a high-level pastime, is it so awesome? !!

"Wait a minute, there is a game that my sister can't play, a puzzle game. If you are bored, try it."

Game?

"Let's take a look."

Seeing the other person's unwilling eyes, Zhang Yuan has a little interest. How difficult is it for a child's gadgets?

The little girl 拿着 took a learning machine and handed it over. There was a small program called "Light Off Game" on it.

The problem is this: the panel is lit with a 4 * 4 square of electric lights, and each time you operate an electric light, it even changes its state with the surrounding up, down, left, and right lights (lights become dark, and dark becomes bright. )

If you let all these lights go out through a series of operations, even if the game passes.

"This is easy."

Zhang Yuan lighted a few times casually, all the lights went out and passed.

Another image jumped out on the screen, and it turned into a 5 * 5 electric light matrix, and several electric lights in the middle have gone out.

"The difficulty has increased."

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

Obviously, with the increase of the square of electric lights, the game will become more and more difficult.

"My opinion is……"

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

Zhang Yuan scratched his head and said with a smile, "Your sister has a mathematical mind, this universal algorithm, oh, I think ..."

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

"Brother ~ I'm smarter than you ~"

哪里 "Where are you smarter than me?"

振 Li Zhendong smiled with a smile on his lips.

题目 This problem is difficult.

Why is it difficult?

Because he Li Zhendong thought for a while, he didn't make it.

So, brother Zhang who loves to do the subject, slowly you think about it, it's dark, day and night are upside down ...

Let the good friend shame in front of his sister, he is very happy! Very deflated!

"I'll take a shower first. Do it slowly."

The little girl looked at Zhang Yuan with anticipation. Anyway, she definitely couldn't do it.

I am just as proud as the person who made the question.

Zhang Yuan's reaction was beyond their expectation. He was a little embarrassed: "No, you don't have to take a shower first.

what?

Unlocked?

Li Zhendong's eyes were about to stare out, ran out of the bathroom, and wore his underwear back again.

Zhang Yuan talked eloquently: "According to the topic: Pressing the switch once, along with itself and the lights up, down, left, and right all change the state. So we can get a conclusion: for an electric lamp, the effect of switching on an odd number of times, and pressing The effect of one switch is the same; the effect of pressing an even switch is equivalent to not pressing, which is 0. "

interesting.

所以 "So, if the problem is solved, each lamp can only be operated at most once, or not operated."

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

I just heard such a few words, Li Zhendong's head was about to burst, and inspiration was flowing like spring water!

Wait a minute.

It seems like this ...

Very simple subject.

怎么 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!"

Li even looked at Li Zhendong's mother and found out that they were not doing anything. She shook her head and returned to the kitchen.

"Let's do that. Did junior high school students learn multivariate equations?"

The little girl nodded her head. The binary one-time equations are indeed the content of junior high school. The elimination method and substitution method can solve it.

Three yuan once and four yuan once are acceptable.

Zhang Yuan continued: "Suppose Aij is the number of times to adjust the jth lamp in the ith column. Obviously, according to what I just said, Aij is either 1 or 0."

"Let's take the simplest 2 * 2 matrix as an example, let's set the light off state to 0 and the light on to 1."

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

【1-0】

【0-0】 ”

"Then four equations can be written:

A11⊕A12⊕A21 = 1

A11⊕A12⊕A22 = 0

A11⊕A21⊕A22 = 0

A12⊕A21⊕A22 = 0 ”

"The solution is A21 = A11 = A12 = 1, A22 = 0. So you only need to operate the three lamps A21, A11, and A12 in order, and the order doesn't matter ~ www.novelmtl.com ~ All N * N matrix problems Calculated this way, and there must be a solution. But the N * M problem does not necessarily have a solution. The reason is this ... "

振 Li Zhendong wanted to cry without tears, watching her sister's eyes a little admired, and even a little star popped up!

Although he knows that his sister probably doesn't understand ...

But, however, girls of this age are innocent and simple, with only learning in their eyes, they have no resistance to Xueba!

When I was finished, my sister's admiration for her brother was taken away by others!

I only heard my sister asked, "Why 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 XOR operation in the computer field ... If you use ordinary plus sign, it will calculate a negative number."

"Brother Zhang, you know so much!"

所以 "So try hard, otherwise, like your brother, gifted but not honored, smart and useless ..."

Livestock, but also hurt me!

Go-die!

"Brother Zhang, help me do the math problems, I don't know many problems. My brother doesn't help me."

"Fine."

妹妹 My sister is still young!

Let go of your paw!

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

What?

Zhang Yuan scratched his head.

The little girl could not help but froze and rolled her eyes. She has already attended junior high school and knows a lot of things. Even if she falls in love, she will not be opposed by her family.

She feels that her brother is really having a brain problem, or is this brother Zhang Yuan more normal ...