"Test" combination of mathematics "ball and box"

Topic

A
Given n different balls, put in m different boxes, the box is allowed to be empty, how many kinds of schemes are there?

B

　　Given n different balls, put in m different boxes, boxes are not allowed to be empty, how many kinds of programs?

C
Given n different balls, put in M the same box, the box is allowed to be empty, how many kinds of programs?
D
Given n different balls, put in M the same box, the box is not allowed to be empty, how many kinds of programs?
E
Given n the same ball, put in m a different box, the box is allowed to be empty, how many kinds of solutions?
F
Given n the same ball, put in m a different box, the box is not allowed to empty, how many options?
G
Given n the same ball, put in M the same box, the box is allowed to be empty, how many kinds of solutions?
H
Given n the same ball, put in M the same box, the box is not allowed to empty, how many kinds of solutions?

Nonsense

Because last night to one or two points, the head will be blown up, open examination seems to sleep half an hour, and then dizzy for half an hour

A problem of silly questions

BCD at first glance is not very good to engage directly

EF Partition method directly to

An unordered division of GH integers

Then hit A; beat GH, found that the problem can be repeated, anger re-dozen sets of the prefix and optimization; hit EF, and there's nothing to say

Because the head is very very dizzy, it took two hours to finish the above, more than half of the time

But there's nothing wrong with BCD in two hours.

Found b before the test, then my hair will not be the Mongolian equation, and then blindfolded out

The brain's still in a coma, so I decided to abandon the mask equation.

So I once again, and soon I was blindfolded.

Make a miracle 233

Find D is b divided by m!, but MoD is not prime ... So I changed the equation, removed a multiplication sign, hand play a few small data no problem, and then blindfolded ...

Then push C, this time I finally choose rational thinking, launched to find and D is the same ... Only the statistical answer is different.

found that C and D are exactly the same, which means that my BD is right ...

And then one hours later.

Then I'm going to start on the shoot, but I don't want to move ... And then I gave it up, bored to check something ...

The evaluation of the time is very virtual, because there is no cross-pat ... But it's not a good shot to push.

When I saw the AK.

It feels like flying! Shuangshuang Cool!

Although the topic of water is nothing to be happy!

But it's still cool!

300 points for the wrath of Rank2! (People don't seem to be playing with BCD)

Process is not so cool =v=

　　

Exercises

A
One Eye m^n

B

D's Answer *m!

C
D to find out, enumerate the boxes used to find a and
D

Consider each ball in turn, either open a new box or drop it in the box you've already used.

So the equation F (i,k) =f (i-1.k-1) +k*f (i-1,k)
E
With F just insert the ball manually
F
Bulkhead method C (n-1,m-1)
G
With H just insert the ball manually
H
Recursive thinking with "recursive" bzoj3612[heoi2014) Balance

Just because the number of partitions can be the same so set a prefix and

Summarize

In fact, this test should be "half an hour to push the end, half an hour to finish"?

What have I done? But because I'm insane today, it's still a lie. Before the exam or to go to bed early ... But I never seem to pay attention to the school exams.

The result is still not bad ... Feel the joy of AK again ...

In fact, all the tests are recursive ... I haven't done it in years. >.<

Long time no use of "vigorous miracle", but sometimes it is really useful ...

Unfortunately this time there is no rational analysis of the problem, but it is true that the state is not porcelain

Go to bed early in the exam, get the problem back to analysis, that is the case

"It's a great opportunity to be in front of me, and this time I'm not missing it."

"Test" combination of mathematics "ball and box"