Difficult.

Yi Cheng frowned, pondering for a long time, he couldn't ride his sister for a hundred years, no, he couldn't figure it out.

This question can be described in one word:

Difficult.

Two words: hard.

Three words: a chicken.

Just reading the question stem is very complicated, and the entire third class, and even 90% of the high school students in the country, are estimated to not understand what the question is about.

But this does not include Yicheng.

He understood the original meaning of this question at a glance:

First of all, you need to draw up a functional equation of ranking points, and the second question is a hint, and it is also the tenderness left by Mr. Ran.

Through Mr. Ran's tenderness, we know:

The variables that need to be applied to this are ranking, survival time, number of kills, ......

Together, they form a function curve of the ranking score.

So there are three variables here.

This function curve then affects the next drawdown, and several of the conditions given in the problem are useful.

The initial score, the performance score, the elimination rate and the initial circle together constitute the shrinkage function.

Then as you can see from the chicken rules, the circle is a two-dimensional figure, a circle to be exact.

The implicit rule is that each shrinkage must be in the previous circle.

That is, there are two ternary functions, one binary function and one unary function.

Now it's time to unify them and string them together with a thread.

It's hard, it's hard.

Yi Cheng stomped his foot anxiously.

It seems that the topic is not beyond the curriculum at all, and the knowledge used is not up to the university curriculum, but the key is that it cannot be broken through.

To put it figuratively, this question is equivalent to stuffing one person into another person's stomach, and you have to flatten this combination into a big pie on the ground.

After that, you have to use good ramen skills to shake the flatbread into a continuous and smooth curve.

That's not all, according to the second question, you still have to pinch a rookie player into a small point so that it can find its place on the upper line......

This kind of operation is really too difficult.

What to do, great Euler, magical Gaussian ...... Or is it......

Hey?

A flash of inspiration suddenly flashed in Yi Cheng's brain.

He suddenly remembered that when the first problem he had done with Lan Bing, the derivation in the cloak of Gaussian function-

Isn't it?

Derivation is the most powerful weapon for weft reduction, and its power is comparable to that of a two-way foil.

Waha, Yi Cheng showed a smug smile, looking like a devil to the others.

He took up his pen and wrote:

Let the ranking be x, the survival time is y, and the number of kills is z.

Of these three variables, only y is a continuously varying irrational number, and the other two are positive integers.

Then there is no doubt that the task of smoothing after that falls on Xiao Y.

The inner product of two vectors with the same dimension is defined as:

（x1，x2，…… x100）^y.（z1，z2，…… z99）^y。

The growth rate of x and z can be indicated by different angles.

Suppose the vector angle between x and z is a, then there is ......

Yi Cheng quickly constructed the first three-dimensional humanoid with a pen, and then continued to write:

The circle radius is ...... Time...... The product of the indentation rule function and the circular function is obtained......

Well, the second figure has been pinched, and ten minutes have passed by this point.

Half an hour left is more than enough.

Yi Cheng hurriedly used the little beauty of [Time] as a seduction, and stuffed the first little man's ternary function into the fat man in the back.

The fat man's body immediately swelled up and became an indescribably great existence in the five-dimensional space.

The fat man could not walk on one foot, and his shadow was projected in the peace elite, turning into a daring teenager with a gun and charging.

Yi Cheng took a deep breath and hurriedly made a big move-

The derivative of the cubic function f(y) is obtained.

Rumble!

A dimensionality reduction strike.

f(y) bounces, its feet are at this end, but when it moves, you find that it has no feet.

It sees your whole life at a glance, but you have to wrestle with its shadow.

But that's not enough at all, because you get the most pitiful glances from the chicken-eating boys who look up and pray that God won't take them in.

Then do it again.

No, two more times.

Boom!

This time, Yi Cheng finally slapped it to the ground, creating a super large irregular pie.

Aha......

Yi Cheng had already foreseen his victory, so he pinched one of the dots and let it roll along the trajectory of the rankings.

What a beautiful curve.

This is the curve of the center point of the circle as a function of the ranking.

The first question is complete.

And then about the second question, although it seems simple, there is actually a small pitfall, if you really take the given parameters into the function obtained in the first question, and then get the probability by proportioning it to the whole world, then you are going far.

Keep in mind that the implicit rule here is 100 players per round.

The first question is deduced on the basis of an infinite number of 100 people.

So, we have to divide 1 equally with the set of parts and weights of 100.

Yi Cheng carefully circumvented the trap, and then carefully calculated:

P（a）=1/m（∑（m-ai）^2）

A is the ranking score.

In the interval greater than 0, the probability of shrinking the circle is inversely proportional to the increase of the ranking score, that is, the higher your ranking in the previous hand, the farther away from you in the next circle.

If you were ranked 78 in the last hand, you had 0 kills and survived for 5 minutes and 26 seconds.

Then the probability of the initial Circle of Destiny is:

0.64858

……

When it was finally done, Yi Cheng spent another ten minutes checking the papers and left the classroom.

"Isn't it?"

The rest turned their gaze to his empty seat.

"Is this guy a pervert?"

"Please, be a person, such a terrible topic can be made, how can we live?"

The rest of the people looked at Teacher Ran pitifully.

"Teacher, what you said before is not true, is it? I can't eat chickens and I'm going to die......"

"Then you should study hard and strive to eat chicken as soon as possible." Ran Bingqing said with some amusement and picked up the test paper from Yi Cheng's desktop.

Yes, this kid.

She looked at it for a while and found that Yi Cheng didn't make any mistakes, including the last question, and answered it perfectly.

Full marks.

The corners of her mouth rose slightly, worthy of her proud protégé.

……

After the devastation of the math exam in the afternoon, Bai Jingxue now looks like eating chicken.

After studying at night, Yi Cheng proposed, "Why don't we go to the mall?" ”

"Huh?"

Xiaobai looked at him in surprise.

Shopping?

She must have met a fake Yicheng.

This guy has changed sex?

"Okay, shall we go to the movies or eat?"

Bai Jingxue laughed happily, sweeping away the haze of frustration in the afternoon.

"I want to buy two clothes for the girl, you can help me with the staff."

“……”