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Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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I'll try to explain my idea on F, because I couldn't get the editorial (I'm pretty sure they aren't same solution) and wanted to write mine.

My solution: http://codeforces.com/contest/946/submission/36022552

Let's get any subsequence. For every occurence of

sin that subsequence ofF(x), we'll increase the answer by 1. Instead, for every possible occurence we can increase the answer by number of subsequences that have that substring in it. Let's consider a subsequencei_{1},i_{2}....,i_{n}(indices ofF(x)) such that if we concatenate the characters at such index, we would obtains. It means that in every following subsequence we should update the answer by 1.jthat is equal to somei_{k}, it must contain it.jthat isn't equal to somei_{k}buti_{1}<j<i_{n}, it can't contain it.j<i_{1}orj>i_{n}, it can contain it, so we have 2 possibilities.So, for every set of indices (called

i) we can increase the answer by 2^{i1 - 1 + n - in}and we can obtain the answer.Let's create a function

f(l,r,x) which is equal to answer when we are search fors[l..r] inF(x). (Not exactly but we'll come to that later.)F(x) is equal toF(x- 1)F(x- 2) so, that substring could be inF(x- 1),F(x- 2) or divided in both. If it's inF(x- 1), it means that we should calculate the number of ways and get the answer. Here's the key point, ifrequals tonit means that we won't get anything from right so we should multiply it by 2^{|(F(x - 2)|}.Since 2

^{x}* 2^{y}= 2^{x + y}in the end we will get the each occurence multiplied by 2^{n - in}. When we will handle thel= 1 cases, similarly, we will get the answer.I've seen your code. There's "ret = add(ret, mul(f(l, k, x — 1), f(k + 1, r, x — 2)));". Why can they be simply multiplied? I think that f(l,k,x-1) may contain some subsequence like ...l,t... , and so to f(k+1,r,x-2). ...l,t... concatenate ...t+1,r... is ...l,t......t+1,r..., but not ...l,t,t+1,r... . How are those .... between l,t and t+1,r considered?

OK I got it. "which is equal to answer when we are search for s[l..r] in F(x)", This value depends on whether l==1 or r==n. If l==1 and r==n, it represent ...l,r... ; If l==1 and r<n , it represent ...l,r ; If l>1 and r==n, it represent l,r... ; If l>1 and r<n , it represent l,r .

Thank you!

Can you explain me better? I don't understand you.

Wow, it is so clear!

Thanks a lot, I understand the problem!

I'm most probably missing something obvious, but why would greedy not work on Problem 946D ?

Like In

O(mn) time, create ann*2 arraygreedy[day][i] where if there's still atleast one 1 in theith string, then letgreedy[i][0] denotes the number of hours that would reduce if you skip the first class in dayi, and letgreedy[i][1] denote the number of hours that would reduce if you skip the last class in dayi(these two have same values if on that day, we have only one class), and if dayihas no class, then setgreedy[i][0] =greedy[i][1] = - ∞Then initialize an heap with those

n*2 elements in time. Then at each step, I pick the largest element from the heap in time, say it'sgreedy[j][1], and I change the last 1 in dayito 0, and updategreedy[j][0] andgreedy[j][1] in the heap. I stop when I have pickedkelements.The greedy approach fails (for example) whenever there are equal options at the beggining and at the end but some side is better somehow.

Imagine: k = 3 Case 1 : 1110000111111111111 Case 2 : 1111111111110000111

Removing the first 1 reduces the time in 1 on both sides, but only one of them leads to the best solution (greedy approach won't know which). That's why you should do dp.

I am very stupid to miss such a silly counterexample. Thanks !

nice case

I have a question about 946D. The problem statement was not clear to me. 2 6 2 010010 111100 For above example, I thought answer is 3. But, Passed code's answer is 4. It means skipped lessons is based on day, not week.

So, I felt very difficult to this problem^^ Thanks

Can anyone plz explain the idea of this code http://codeforces.com/contest/946/submission/36016439 ? It's Problem F. I can't grasp the DP transition in this code clearly. As far as I studied, I guess it maybe use some math to simplify the transition. Can anyone help plz?

I appreciate this simple transition very much, so I want to make clear of it.

OK I got the idea. It's just a way by including the information of 2^length into the dp arrays. It's a very clever method, and I appreciate this very much!

Can anyone explain why on local machine I get correct answer but on server not? http://codeforces.com/contest/946/submission/36021632

got it.

Problem G can be solved with similar method as in the editorial, but without using segment tree. Let's calc dp[cnt][len] — minimum element ending sequence with cnt bad elements with length len. Calculating is similar to finding longest increasing sequence : for 1 bad element we use binary search for x-i+1, for 0 x-i.

can anyone explain me solution E?

Can someone explain in Problem B why using '%' gets AC and subtraction gets TLE?!

a = 10

^{18}, b = 1, you subtracted 10^{18}/2 timesImagine test 10^18 1, you make 5*10^17 subtractions but just one division. You can find proof of Euclid's algorithm with division complexity (it's O(log n)) and apply it here.

How to solve problem E? I am not able to get the approach through editorial.

Can you specify what part you don't understand?

the implementation part-4th paragraph in editorial

I can share my implementation with you, hope it helps.

Thanks

Thanks, this was very useful!

Does n^3 solution work where n = 500. Wont it be of order of 10^8, I left the D question for the same reason. I used to think order 10^7 is borderline for time limit of 2 seconds!!

10^7 is like the limit for python or some other slow lang. You can assume it to be about 2-4 * 10^8 for C++.

Ohh, alright thanks.

By the way thats for 2 seconds, so if time limit is one second then i should expect 10^7 operations right ?

10^8

Problem G -

I didn't use rollback. I have used only 1 segment tree with range query and point updates.

Solution

Brief Idea -

LNDS — Longest Non-decreasing Subsequence

A[i] = A[i] — ifor every'i'For every index

'i', we want the length ofLNDSending at'i-1', sayE[i-1], and the length ofLNDSfrom[i+1, n]whose 1st element is greater thanA[i-1], sayS[i+1]. We can easily calculateS[i+1]using segment tree. Calculation ofE[i-1]is trivial.Final answer would minimum of

n — 1 — E[i-1] — S[i+1].Complexity —

O(N*logN)For problem G, there's a very concise code. http://codeforces.com/contest/946/submission/36058677

Using DP to manipulate the LIS arrays, I find there IS an optimal structure for them.

Can someone explain me the solution of C written in the editorial ?

Have a char variable C which is intitially equal to 'a'.You need to check if there exists a subsequence of the English Alphabet in the given string. So iterate through the string fully, for each iteration check if the current character of string is not greater than C and increment C. So in the end, if your C value is not equal to 'z', then it means you don't have a subsequence of the English Alphabet. Hope this helps :)

For question C, I understand how this:

aacceeggiikkmmooqqssuuwwyybecomes:abcdefghijklmnopqrstuvwxyzHowever, I do not understand why the check is only if the current character is not greater than variable C.

I do not understand why this:

aadabecomes:abdcWhy does the final character become c from a? The impression I got from the question is that a character can only move to the next character in the alphabet (a -> b, f -> g etc). Given this it seems that the final character could only become b.

If that makes sense, anyone got any ideas what i've missed?

aada-> abda -> abdb -> abdc (coz can use as much moves as needed)

Does hacking in educational rounds give you points?

No , It does not

nice editorial

Can anyone explain why I (and some other people) get WA 16 in D problem? My code is here: 36048111. I coded the solution as in the editorial.

Got it.

Iam getting wa in 16 too,what was the error?

It shows tutorial not available

For problem E,i think the DFS algorithm is much easier.You can see my code. :)

For problem G, there's a very concise code. http://codeforces.com/contest/946/submission/36058677

Using DP to manipulate the LIS arrays, I find there IS an optimal structure for them.

What does 'length(cur)' mean in Problem D?

for lenghthcur in (0,k): // dp transition

OK, thank you ;)

For problem D: I tried solving it using a priority queue ( pq ). It's top is the day that if I skip a lesson in it, it will result in the maximum time saving...

Say we got these strings in the pq:

a: 100011011 --> saves 4 units of time if I skip a lesson

b: 100101111 --> saves 3 units of time if I skip a lesson

c: 010000111 --> saves 5 units of time if I skip a lesson

The pq top is c as it will result it will help to maximize time saving, hence minimizing the time spent at school..

What's wrong with this approach??

You can check my submissions..

And in case of a tie like this:

1110111 --> saves 1 unit of time if I skip a lesson

1111011 --> saves 1 unit of time if I skip a lesson

It'll choose the second string as it has a 0 nearer to 1 so in the second skipped lesson the string becomes: 1111000 but if it chooses the first string, it will become: 1110100 hence less time saving. That's how my pq works.. what's wrong ?

Got it. This will break the pq sorting criteria..

Can someone elaborate D some more? How should I calc this mn[i][j]? What should i put in mn[i][j] if I can't achieve j lessons in i-th day?

losmi247, my solution uses an array that I call opt[i][j], wich is the minimun amount of hours you have to spend in the i-th day if you kick off exactly j classes that day. That is the mn[i][j]. This can be done greedly by taking the best prefix and suffix of lessons of that day such len(prefix)+len(suffix)==j. Then you can do dp[i][j] = min(dp[i][j], dp[i-1][j-k] + opt[i][k]);

PD: if the number of lessons you going to skip the i-th day is greater or equal than the number of lessons you have to attend that day opt[i][j] should be 0

I can't thank you enough for this, thank you very much

can anyone please help me in understanding 946D timetable really i will appreciate the effort. I have no idea what is going on..

please please from scratch

Please explain me problem F. Considering test 1:- 2 4 11 Judge answer is 14. But, I thought of problem as creating fibonacci string of 4 that is F(4) which is equal to 10110, then finding cost that is number of time string s that is 11 (entered by user) contained in F(4).

So, my answer comes out to be 1(int) as 11(string) is contained only one time is F(4) i.e. 10110(string).

Please, someone explain me. This is driving me crazy for days.

You misunderstand the problem description.

"calculate the sum of costs of

all subsequences of the string F(x)"Yeah, I see . But can you explain me using 1st test case. I'll appreciate your efforts.

All subsequences of "10110" include

`2^5=32`

strings: 1, 0, 1, 1, 0, 10, 11, 11, 10...Maybe you need to check the definition of

subsequencein wikipedia.Can someone explain why my solution for problem c is getting TLE[submission:36266766]

Got selected I use C# method to convert char array to string. C# is taking more time then usual dont know why

ans += s[i].ToString() give |s|^2, use StringBuilder instead

Can someone point me to problems similar to Problem D : Timetable ? I usually get stuck at such problems which involve preprocessing before beginning DP.

So basically we'll have to do two DPs. One to create

`mn[i][j]`

which gives the minimum number of hours Ivan has to attend college on the ith day, and by skipping j lectures. (Note that the terminology for`mn`

is different in the tutorial).The other one is

`dp[i][j]`

which gives the minimum number of hours Ivan has to attend collegetillthe ith day and by skipping j lectures intotal.Pretty similar DPs aren't they.

One another thing to create is

`vector<int> dp[n]`

, in which`day[i][j]`

will store the position of the jth lecture on the ith day. Now recursions:Firstly to calculate

`mn[i][j]`

, we need to remove exactly $$$j$$$ lectures. Now removing a lecture from the midst wouldn't actually bring us any result as thetotaltime Ivan stays in college matters. So, we'll target the lectures at the front and the lectures at the end. In total we have to delete $$$j$$$ lectures, so let's say we delete $$$l$$$ lectures from the front, then obviously we'll delete $$$r = j-l$$$ lectures from the end.So we need the hours Ivan stays in college in the given scenario. We can find this by

`day[i][total-r-1]-day[i][l]+1`

(since we're using 0-indexing here). This simply means that we've deleted $$$r$$$ lectures from the right and $$$l$$$ lectures from the left, so the remaining lectures' hours are simply the difference of the first and last lectures remaining.Now to calculate

`dp[i][j]`

. Again my recursion is different than that of the tutorial. We here need to remove $$$j$$$ lectures in total, in the first $$$i$$$ days. The remaining hours make up`dp[i][j]`

. So how is`dp[i][j]`

made up from the already calculated dp[i-1]?Let's see.

We had not seen the values for the

`i`

th day yet. That is`dp[i-1]`

doesn't consider the ith day. So different values of ith day will be used with`dp[i-1]`

.So if I use delete two lectures of the ith day, I'll have

`mn[i][2]`

hours. This will go with`dp[i-1][j-2]`

which means that we deleted $$$j-2$$$ lectures for the starting $$$i-1$$$ days. We used this to remove a total of $$$j$$$ lectures and consider $$$i$$$ starting days.So we can make this a loop:

I will leave some initialisation details for you to fill, but this is mainly how this works.

Here is my submission.

Problem F:

I wonder if my solution works ? If not, please explain and give example(s). Thanks in advance :D

For each step i, I store 2 strings pre and suf that is the prefix and suffix of F[i]. Each string's length is smaller than the length of the given string s. With this, at each step I can string match to find new occurences that appears due to the concatenation of F[i] and F[i — 1]. In addition, I notice that F[i]'s pre = F[i — 1]'s pre and F[i]'s suf = F[i — 2]'s suf.

Hey awoo ,could you please elaborate the explanation of the following line of 946D

dp[i + 1][j + lengthcur] with dp[i][j] + mn[i][lengthcur]. Thanks,in advance.

Consider it the other way, say you are at day i and have skipped j lectures, this means that over the past i — 1 days you must have skipped "at max j lectures". So dp[i][j] is the min over all (k <= j) the value (dp[i -1][k] + mn[i][j — k]) (i.e. you have to skip j — k lectures on day i which can be obtd from the preprocessed array)

You can refer this for the implementation

Can E be solved using binary search, by finding the least significant position which can be reduced by 1, so that its possible to construct a maximal number which is a palindrome ?