This is a very straight forward problem. Just add 1 to a year number while it still has equal digits.

Precalculate the next prime for every integer from 1 to 10^{5}. You can do that in any way. The main thing is to test all the divisors up to square root when you are checking if a number is prime.

Now for each *a*_{ij} (element of the given matrix) we can easily calculate *add*_{ij} — how many do we have to add in order to make *a*_{ij} prime. After that all we need to do is to find row or column with minimal sum in this new matrix.

If 3*k* > *n* there is no solution (because each of the *k* sets must have at least 3 elements). Otherwise we can divide first 3*k* words in the following way:

`1 1 2 2 3 3 ... k k 1 2 3 ... k`

For each of the *k* sets, the difference between the first and the second elements will be 1. And the difference between the second and the third elements is definitely not 1 (more precisely, it is 2*k* - *i* - 1 for the *i*-th set). So each set doesn't form an arithmetic progression for sure.

For this solution it doesn't matter how we divide the rest *n* - 3*k* words.

At first, build a trie containing all suffixes of given string (this structure is also called explicit suffix tree). Let's iterate over all substrings in order of indexes' increasing, i. e. first [1...1], then [1...2], [1...3], ..., [1...*n*], [2...2], [2...3], ..., [2...*n*], ... Note, that moving from a substring to the next one is just adding a single character to the end. So we can easily maintain the number of bad characters, and also the "current" node in the trie. If the number of bad characters doesn't exceed *k*, then the substring is good. And we need to mark the corresponding node of trie, if we never did this before. The answer will be the number of marked nodes in the trie.

There is also an easier solution, where instead of trie we use Rabin-Karp rolling hash to count substrings that differ by content. Just sort the hashes of all good substrings and find the number of unique hashes (equal hashes will be on adjacent positions after sort). But these hashes are unreliable in general, so it's always better to use precise algorithm.

It could be proved, that a card (*x*, *y*) (*x* < *y*) can be transformed to any card (1, 1 + *k*·*d*), where *d* is the maximal odd divisor of *y* - *x*, and *k* is just any positive integer. So every (*a*_{i} - 1) must be divisible by *d*, i. e. *d* is a divisor of *gcd*(*a*_{1} - 1, ..., *a*_{n} - 1), and we can just iterate over all possible divisors. Let's take a look at all the initial cards (*x*, *y*), which have have *d* as their maximal odd divisor: these are cards with *y* - *x* equal to *d*, or 2*d*, or 4*d*, 8*d*, 16*d*, ... Don't forget that the numbers *x* and *y* must not exceed *m*. It means that the total number of cards with some fixed difference *t* = *y* - *x* is exactly *m* - *t*.

The resulting solution: sum up (*m* - 2^{l}*d*), where *d* is any odd divisor of *gcd*(*a*_{1} - 1, ..., *a*_{n} - 1), and *l* is such, that 2^{l}*d* ≤ *m*.

Is there any background in problem E?

In 4rth q after so many TLE's I have drawn an inference that generally map is slower than set though both being dynamic memory allocation....

I'm quiet new in Java,I keep getting TLE and use trie data structure,any advises?(Though the same code written in C++ got AC) code

It's not because you use Java, it's because you make a lot of substring() calls.

Thanks,so is there a faster way to remove the first character from string?Or i should use array of chars instead of strings or something like that

Just remember where the string really begins.

Yup thanks got it

i m not getting the problem E' editorial can any one explain ?

Here is the proof for the solution given in the editorial.

For problem 4, suffix array with lcp can also be used. We can first pre-compute the bad character count for all the substrings and store it in a table. Then, iterating through the suffix array and avoiding duplicate substrings using the lcp table, we can find the answer.

Hello. I am having trouble with the problem D (getting TLE). I am using the trie to solve the problem. When I build it, I already keep track of the current number of bad characters. If it is bigger than

k, I leave the recursion. The final answer is the number of nodes of the tree.Could anyone help me please? What am I doing wrong? Code

Why do you have these 2 nested loops in main() function? You are not really using

`i`

anywhere.OMG, thanks RAD. It was something I was trying and forgot to remove.

Problem C: in each set Ui, its elements ui, 1, ui, 2, ..., ui, |Ui| do not form an arithmetic progression (in particular, |Ui| ≥ 3 should hold). What's the meaning of it ? Does it means when Ui < 3 there is no necessary to hold this condition ?

Can you tell me what's wrong of my code ? Problem D: 3145554

Complexity

I don't think so, I learned from this AC submission? Why his is ok ? 3105181

Try to find out what is the complexity of string comparisons

so you're saying that insertion in set is taking time??

You can implement it using sets but I think you have to iterate for len =1 to len=n and index 0 to n-len; after every len you have to clear your set to prevent it from exceeding memory limit

Problem D 271D - Good Substrings : This is my code. I've used the concept of Rolling hash/Rabin Karp algorithm. But I guess there are some collisions happening and it's failing on test case number 8. Any help is greatly appreciated. Been trying this for a long time.

Code: 27820412

Update: Solved! I tried many different ways. Initially, I used two hash moduli instead of one, but this exceeded the Time Limit on test #8 (Which is weird!). I ended up using a really large prime (About the size of 2^50) which just passed the time limit for Testcase #8 and passed the cases as well. :)

ya i was also getting wrong answer due to collisions so just used two different numbers 31 and 67 with modulo 1e9+7 and it got accepted

D can be solved using 2 pointer and little bit of a lcp array.This is my solution. https://mirror.codeforces.com/contest/271/submission/44768791

Problem D is like using 2 hashes of 10^9 size-TLE Using 1hash of 10^9 size -WA and using a very big hash and multiplying recursive -TLE

Beautiful Yearhttps://github.com/arsalanhub/CodeForces/blob/master/Beautiful%20YearHey. Please stop spamming on every tutorial blog with your solutions of Div2 A problems. There are already many solutions available in the submissions section. You're not helping anyone at all. You're just spamming and also unnecessarily bringing old posts in the

Recent Actionssection.271D using Z algorithm: https://mirror.codeforces.com/contest/271/submission/68098565

prereq: distinct substring using Z ( read it from CP algo ).

Implementation: Now I am assuming you know distinct substr using Z, then: we start counting the answer for a prefix after the zmax of that prefix. ( because we'll have distinct substring only after zmax)

can enyone help me with D problem? I am tring to sove it with hash but it has wrong answer on testcase 8;

https://mirror.codeforces.com/contest/271/submission/243292259

Yeah, you will get WA because there are more than 1e6 sub-strings that you will compare using hashes, which gives a very high chance of collision. So you should use two hashes instead of a single one, I used two by just changing the modulo.

Here is my AC submission : https://mirror.codeforces.com/contest/271/submission/245638497

thanks

In D, in sample test case 1 explanation, bab is given as a good substring but not aba. As b is a bad letter, bab should be a bad substring and aba should be a good substring. In sample test case 2 also, the solution is limiting only to two characters but there is no such constraint in the problem statement. please help me understand the question.

If you will read the question carefully, it is given that

If the i-th character of this string equals "1", then the i-th English letter is good, otherwise it's bad.In the first testcase, the value of k is 1 , i.e., we can have at most 1 bad letter, in this case which is 'a'. So, "aba" is a bad substring because it contains two 'a', whereas "bab" is a good as it contains only 1 'a'.i have facing problem with D (good substring) i am facing time limit exceed but i have implemented trie and still it is slow here is my solution 272082061 any help is appreciated

thank you!!