Construct
This page will contain a brief description of such topics as architecture
Introduction
The tectonics are the kind of typologies common in competitions
Formally speaking, the answer to the question is often of a regular nature, allowing for easier access at a time when the scale of the problem is growing rapidly
This requires that the problem be solved by considering the impact of the increase in the scale of the problem on the answer, and whether this impact can be replicated. For example, when designing a dynamic planning approach, consideration should be given to the implications of a shift from a state to a state of follow-up
Characteristics
One of the salient features of the tectonics is the high degree of freedom, which means that there may be many ways of tectonicizing the subject, but there will be a simpler way of tectonicizing the idea. It seems to have relaxed the requirements and made the subject simpler, but it is often this high degree of freedom that leads to a lack of clarity about the subject
Another feature of the architecture is its flexible and varied form. There is no common solution or formula to solve all the tectonics, and it is difficult to find commonality of thinking
Examples
Below are some examples that help readers to understand some of the ideas and ideas of the architecture
Case 1codeforce round #384 (div. 2) c. Vladik and actions
Construct a group, x,y,z
That's what makes a given n
, meet 1 +1 +1 =21x+1y +1z =2n
The solution
Example two shows how the subject is constructed
Apparently, +1, (+1)n, n+1, n (n+1)
For a legitimate group. Special, when = 1n = 1
, can't solve it because +1n+1
With (+1)n (n+1)
This is the same time
As for how the idea of structure was created, it's probably just to observe the sample with a little sense of numbers. It's not a hard question for people who have better instincts
Case 2 luogu p3599 koishi loves construction
Task1: try to determine if you can construct and construct a length of n
I don't know
Arrange, meet the n
A prefix and a model
It's different in meaning
Task2: try to determine if you can construct and construct a length of n
I don't know
Arrange, meet the n
Prefix in simulator n
It's different in meaning
The solution
For question 1:
When n
When odd numbers cannot be constructed for legal solvency
When n
An even number can be constructed in the form of, 1, −2, 3, ⋯n, 1, n−2, 3, ⋯
Such arrays
First, we'll find out
Must be first in the array, otherwise n
Two prefixes before and after their appearance and the inevitable equivalent of the quagmire
And then we think about how to construct the whole sequence:
Considering the acquisition of original columns by building prefixes and sequences, it is observed that the difference between prefixes and sequences is not equal in the sense of simulator, as the prefix and sequence differential sequence correspond to the original sequence
That's why we're trying to put prefixes and numbers in the equation
0,1,1,2,0,1,1,2,2,2
It's a form to construct this sequence, and it's not hard to find it perfectly meets all the limits
For question 2:
When n
Divide 44
Unable to construct a valid number when an equal number is outside break
When n
Is a prime number or 44
, which can be constructed as 1,21,32,⋯,−1−2,1,21,32,⋯,n−1n−2,n
Such arrays
Let's start with the question:
Apparently, when n
There are two smaller numbers for a single number, p,q
Make x ≡(mod)pxq≡0(modn)
E. G. (3 x 6) %9 = 0 (3 x 6) %9 = 0
So, when, p. Q
After all this, the prefix of the columns will remain at 00
, so the number is unsolved. Specially, we can find 4 = 2 x 24 = 2 x 2
Unsatisfactory, p.,q
So there's a legal solution
Let's consider how to construct this array:
The same way we found 11
It must be first in the line, otherwise 11
Two prefixes must be equal before and after the occurrence; and n
Must be the last of the array because n
All prefixes after location are modulated at 00
... The group of samples given by the subject was analysed and found that in all the samples there was a group of legally defunct pre-satisfactions that were modelled on 1,2,3,3⋯,1,2,3⋯,n
So we can construct the arrays described above to meet this condition. Then we just have to prove it
The numbers are different
We found these numbers to be 1-21-n-2
+1+1
That's why it's different
Case 3atcoder grand co{\chffffff}{\ch00ff00} ntest 032 b
Set an integer number n
Try to construct a node as n
No fig. Order no. 1.. 1... N
Is required to meet the following conditions:
Make sure the input data is solved
The solution
= 3,4,5n = 3,4,5
In the case, we can find a structure
Construct a complete k
Split, make sure this k
Part and equivalent
Equivalent, (-1) ∑1 (k-1) ∑i = 1nik
If n
For even numbers, we can pair back and forth, i. E., two pairs, two pairs, two pairs, two pairs, two pairs, two pairs, two pairs, two pairs, two pairs, two pairs
If n
For odd numbers, then we can put n
Take it out as a group, the rest -1 n-1
Two pairs, i. E., }1, −, {, −, −, }
This is the image that's built on the cylindrium 3 n3
Connectivity is clear, not to mention here
That's a question
Case, 4bzoj 4971 backpack in memory of lydsy 1708
After a hard day's work, little q went to sleep. He's got a new one in his head when he first went to college to study the 01 backpack, and then he's a new, new q
Organisation
One item of 1, 2,... V1, v2,... Vn
, calculate the selection of items (or not) from which the total volume is corresponding to w
Because the answer may be very large, you just have to output the right answer to the p
The results
Because he spent the night brushing it, he only saw the example entered w
And p
And sample output is k
I can't see how many things there are, or how much they are
And v
, please write a program to help the little q to remember a sample input
The solution
It's one of the most liberal constructions. This leads to a situation where it's hard to get started
First of all, it's not hard to find that the numbers are fake. Because we're free to construct data, we're sure we can keep the number of options up to the numbers
In a strange way, we thought we could build it
The price is 11
Small items and a few costs more than 2w2
Big stuff
As only one large item can be taken, each cost x
(-) (nw-x)
You, fi, j
Indicates i
Eleven
J
Minimum number of items
Preprocess f with dp
By calculating it, you can see that only pre-treatment is required
All the values are fine
That's a question
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