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Vladithur's blog

By Vladithur, history, 23 months ago, In English

Hope you liked the problems!

(from thanhchauns2) Before the round starts

1768A - Greatest Convex

Author: thanhchauns2

Hints
Tutorial
Solution
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1768B - Quick Sort

Author: Vladithur Preparation: Vladithur and Alexdat2000

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Tutorial
Solution
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1768C - Elemental Decompress

Author: thanhchauns2

Hints
Tutorial
Solution
Yet another better solution
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1768D - Lucky Permutation

Author: Vladithur Preparation: Vladithur and Alexdat2000

Hints
Tutorial
Solution
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1768E - Partial Sorting

Author: thanhchauns2

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Solution
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1768F - Wonderful Jump

Author: Vladithur Preparation: Vladithur and Alexdat2000

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Tutorial
Solution
Shorter solution (tfg)
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  • Vote: I like it
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| Write comment?
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23 months ago, # |
  Vote: I like it +100 Vote: I do not like it

From SPyofgame during the contest:

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23 months ago, # |
Rev. 2   Vote: I like it +8 Vote: I do not like it

First time ranked top100 in div2. Hope for no FST!

Update: It's frustrating that I always get downvoted and don't know the reason

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    23 months ago, # ^ |
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    Why so many downvotes? This is bully!

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    8 months ago, # ^ |
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    Giving you Downvote to motivate your frustration to frustrate you more....

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23 months ago, # |
  Vote: I like it +88 Vote: I do not like it

Permutation Forces !

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23 months ago, # |
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Delivered so fast..

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23 months ago, # |
  Vote: I like it +33 Vote: I do not like it

2023 should not be a permutation

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23 months ago, # |
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love the fast editorial

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23 months ago, # |
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I got the idea for C but not able to implement it. :-)..

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23 months ago, # |
Rev. 3   Vote: I like it -21 Vote: I do not like it

Can anybody help me to figure why this code is not accepted??? https://mirror.codeforces.com/contest/1768/submission/188117185

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    23 months ago, # ^ |
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    Do not paste the code in the comment.

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    23 months ago, # ^ |
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    Write codes in spoiler or only provide the link as you have provided here, as it becomes quite difficult to read this way

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    23 months ago, # ^ |
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    Although pasting code directly is awful, I've checked your code in the link. In fact, the most part of your code is right except one point: when doing

    m1[*it1]=*it2;
    

    you need to check if (*it1>*it2). If not, there's no solution because max(p[i],q[i]) will be *it2.

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      23 months ago, # ^ |
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      ok!!!!!!!! Right I will think harder next time to not miss something like this

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23 months ago, # |
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You know what it feels like when you finish E when there're only 10 sec left but fail to submit the code before the last second?

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23 months ago, # |
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Amazing , was very curious for fast tutorial especially for Problem C.

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23 months ago, # |
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Hi guys! although the editorial they've provided is great! still if you want a video format editorial you can find it here

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23 months ago, # |
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PermutationForces?)

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23 months ago, # |
  Vote: I like it +12 Vote: I do not like it

"it took me 2 minutes to actually prove the solution"

and it took me probably a minute and a half (may be inaccurate) to find out that $$$k! + (k-1)! = (k-1)!(k+1)$$$ and the rest of the proof is just factoradic blah blah

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23 months ago, # |
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i submitted 6 unsuccessful attempts so i lost 300 points in the contest? if there is a maximum amount u can lose, how much is it?

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    23 months ago, # ^ |
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    No matter how many times you submit for a problem, you get at least 30% of points if you solved it finally.

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    23 months ago, # ^ |
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    If you have wrong submission for problem $$$X$$$ you will get 50 points less then you usually would on that problem.

    If you have few wrong submissions on a problem you didn't solve, you won't lose any points.

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23 months ago, # |
Rev. 2   Vote: I like it 0 Vote: I do not like it

Why so tight TL on E.

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    23 months ago, # ^ |
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    You can calculate the inverses of factorials more efficiently by calculating them from n to 0.

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23 months ago, # |
  Vote: I like it +13 Vote: I do not like it

Actually there's O(n) solution for C. We don't need to do any sorting. We can just count the occurence of 1-n and let occ[i]= the times i appeared in array a[]. if there's some occ[i]>2 there's no answer. Then we build two list more[] and less[]. We iterate for i from 1 to n, if occ[i]==0 we add it to less[], if occ[i]==2 we add it to more[]. since 0<=occ[i]<=2, the size of more[] and less[] will be equal. then we iterate for more[i] and less[i] reversely, if some more[i]<less[i] there's no answer. If there's no such i, we can construct p and q: for each pair of more[i] and less[i], let's call they M and L, and j = the smaller index where a[j]==M, k = the larger index where a[k]==M, we let p[j]=q[k]=M, q[j]=p[k]=L. For those j which a[j] appear only once, we just let p[j]=q[j]=a[j].

My submission:188076704

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23 months ago, # |
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It's a well know fact that n — cycles is the minimum number of swaps to get 1, 2, ..., n.

Can someone explains me this ? and where is this well know ?

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    23 months ago, # ^ |
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    each cycle of length $$$l$$$ needs $$$l-1$$$ swaps to be sorted, you can try it yourself

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23 months ago, # |
  Vote: I like it +9 Vote: I do not like it

nice E...stuck in case f=2 too longgg...

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23 months ago, # |
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codeforces!

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23 months ago, # |
  Vote: I like it +73 Vote: I do not like it

F is so fantastic! It's hard to solve, but not hard to understand the solution.

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23 months ago, # |
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Can we see pretest after the contest. This submission failed pretest 2: Link

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    23 months ago, # ^ |
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    Pretest 2 is every combination possible for $$$n \leq 5$$$, you can write a code then generate pretest 2 yourself.

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23 months ago, # |
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I'm looking for problem like today problem D and C. Specially problems on arrays that can be transformed into problems on graph.

Example 1 : You want to obtains array b from array a with some specific operation

Example 2 : You want to obtains array a and b from array c with some specific operation

Example 3 : optimizing or computing something on an array after some operation (This turns out to be somewhat related to paths on a graph ...)

In almost all the solutions we need to build some graph with specific edges. I don't know how to tackle that kind of problems.

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23 months ago, # |
  Vote: I like it +25 Vote: I do not like it

F let me feel :F

D let me feel :D

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23 months ago, # |
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I got o(n) for C lolol. 188093045

nvm its o(nlogn)

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    23 months ago, # ^ |
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    sort(putP.rbegin(), putP.rend()) It is minimum O(n logn)

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23 months ago, # |
Rev. 3   Vote: I like it +13 Vote: I do not like it

Since I didn't implement, please point out if I did anything wrong on F, or if my approach would TLE.

After the monotonic stack observation, it should be possible to use a kinetic tournament on quadratics to handle cases with $$$min(a_i,\ldots, a_j)=a_i$$$ and li-chao tree or another kinetic tournament otherwise. The time complexity would be $$$O(n2^{\alpha(n)}\log^2(n))$$$.

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23 months ago, # |
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I cannot understand the editorial of Problem C, which says there are (i — 2)*2 + 2 numbers. (there can be a repetition of numbers in p and q) also, why is this a contradiction?

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    23 months ago, # ^ |
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    What do you mean by "there can be a repetition of numbers in p and q"? $$$p$$$ and $$$q$$$ are permutations, they can't have any repeated numbers (although the same numbers that appear in $$$p$$$ also appear in $$$q$$$ since they are both permutations from $$$1$$$ to $$$n$$$).

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23 months ago, # |
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In the editorial of problem E, when calculating the intersection for f(p)<=2, the sum should be sum(i=0...n) instead of sum(i=1...n). Please fix it

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23 months ago, # |
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I had a slightly different $$$O(n)$$$ 188071468 from the one given for Problem C.

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23 months ago, # |
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No CHT solution for F? That's very interesting.

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    23 months ago, # ^ |
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    It is possible to use it to solve the second case, but you'll have to squeeze it into the tight ML.

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23 months ago, # |
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It is a well know fact that n−cycles is the minimum number of swaps needed to get the permutation 1,2,3,…,n from our initial one (in other words, to sort it).

Can anyone Please provide me the material where i can see this tutorial and learn . Thank You!!.

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    23 months ago, # ^ |
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    Someone mentioned it. Each cycle of length $$$l$$$ needs $$$l - 1$$$ swaps to sort.

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23 months ago, # |
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Can anyone explain E in a simpler way ? I am having a hard time understanding the editorial..

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    23 months ago, # ^ |
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    I modified it a little bit, maybe you'll find it easier to read.

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23 months ago, # |
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Ugh my solution to C FST'd due to TLE can someone tell me why :(( https://mirror.codeforces.com/contest/1768/submission/188118022

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23 months ago, # |
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Is it possible for you to make a report on the channels that download solutions on YouTube during the contest? Very thanks.<3

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23 months ago, # |
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Maybe I missed something, but why there is O(n*sqrt(n)) with [n, n-1, n-2, ..., 1] array? Or any similar.

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    23 months ago, # ^ |
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    In this subcase, $$$a_j < \sqrt{A}$$$.

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    23 months ago, # ^ |
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    I think this time aj is smaller than sqrtA, consider all the cases of such j, the total compexity of the j with same value will not exceed n, so the overall complexity will not exceed..nsqrtA sorry my poor english

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23 months ago, # |
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⌊n−w+k−1⌋/k
could you please eplain me why we add K-1 with n-w ? .

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    23 months ago, # ^ |
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    so as to do the ceil operation otherwise it's by default floor operation as the integer division truncates anything after the decimal point

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23 months ago, # |
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I'm having a hard time trying to understand the intersection formula for $$$f(p) \le 2$$$ from E's editorial. Can you please proofread the 'sketch and calculation' spoiler and fix some mistakes/typos?

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    23 months ago, # ^ |
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    I modified it a little bit, maybe you'll find it easier to read.

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      23 months ago, # ^ |
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      I mean I read for example this sentence:

      In the last $$$n$$$ numbers there are $$$n$$$ numbers in range $$$[n+1,2n]$$$, we have used $$$1$$$ numbers for the first $$$n$$$ numbers. There are $$$C^n_{2n-1} \cdot n!$$$ cases.

      I think you wanted to write:

      In the last $$$2n$$$ numbers there are $$$n-1$$$ numbers in range $$$[n+1,2n]$$$, we have used $$$1$$$ numbers for the first $$$n$$$ numbers.

      And if this is the case, then I don't really understand the $$$C^n_{2n-1} \cdot n!$$$ formula.

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        23 months ago, # ^ |
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        No, there are $$$n$$$ numbers, not $$$n - 1$$$. Since we used $$$1$$$ number to fill in the first $$$n$$$ numbers, there are only $$$2n-1$$$ options to choose for the last $$$n$$$ numbers, since they must be in range $$$[n + 1, 3n]$$$. I think the $$$n!$$$ part is easy to understand.

        Edit: okay I think I spotted the wrong thing, it is fixed.

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          23 months ago, # ^ |
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          Ok, I see the interval in the third case was fixed. Now I get it. Thanks!

          I still want to add something, maybe someone finds it helpful. I don't find the $$$n!$$$ parts easy to understand as they are right now in the editorial, I find them a bit unnatural if not just 'wrongly' explained. The third case actually counts the number of ways to fill the last $$$n$$$ positions. What are the other two cases counting exactly, including the $$$n!$$$ 's, explained with words?

          This is how I would split it, each part counting one third of the positions:

          • Take $$$n-i$$$ elements from $$$[1, n]$$$ and $$$i$$$ from $$$[n+1, 2n]$$$. This makes $$$n$$$ elements for first $$$n$$$ positions, and we take all the rearrangements. This is $$$C^{n-i}_n \cdot C^i_n \cdot n!$$$
          • As you explained, we need $$$n$$$ numbers in the range $$$[n+1, 3n]$$$ for the last $$$n$$$ positions, but $$$i$$$ of them were already used in the first $$$n$$$ positions, so we only have $$$2n-i$$$ left to choose from. Also, we can rearrange them. This is $$$C^n_{2n-i} \cdot n!$$$
          • The first $$$n$$$ and last $$$n$$$ positions are filled. The rest are the center $$$n$$$ positions. Rearrange them freely. This is just $$$n!$$$
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            23 months ago, # ^ |
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            This is much clearer, thanks a lot.

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            23 months ago, # ^ |
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            Kudo for lbm364dl, great explanation that help me a lot, take a long time to understand the editorial before found your comment.

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            22 months ago, # ^ |
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            Sorry for late reply, suppose we have $$$n$$$ fixed indexes for the numbers in range $$$[1, n]$$$, then there are $$$n!$$$ cases for these numbers switching places with each other, the second and third $$$n!$$$ are exactly the same.

            In conclusion:

            • The combinatorics is how we choose indexes for number in a range.

            • The factorial is the number of cases after having fixed indexes.

            The third one is $$$n!$$$ because we already chose indexes for $$$n$$$ numbers out of $$$2n$$$.

            Anyway thank you for providing a much clearer explanation for this problem!

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23 months ago, # |
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Hi guys I have made editorial videos on A,B,C,D and uploaded on the channel — https://www.youtube.com/@GrindCoding, you can have a look and let me know if you like the explanation or please provide your valuable feedbacks.

[D is currently being processed by youtube so might take a few mins to upload]

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23 months ago, # |
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There's no reason to make the mod not fixed as something like 1e9 + 7 in problem E. Any fft solution that passes that mod will pass for any other mod that you might ask for.

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23 months ago, # |
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Any idea why I got Wrong Answer instead of Runtime?

During the contest in problem C I was getting WA so I tried to modify my solutions but now that the we can see the test cases it says "wrong output format Unexpected end of file — int32 expected"

The thing is that I used an array of size $$$10^5$$$ instead of $$$2 \times 10^5$$$

WA code

AC code

So sad, with this modification I got AC with my first attempt :(

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23 months ago, # |
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In problem D,

Turns out that we can easily calculate cycles′ if we know cycles:

cycles′=cycles+1 if the vertices k and k+1 were in the same cycle in the initial graph, cycles′=cycles−1 otherwise.

Can someone explain this???

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23 months ago, # |
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thanks for the great round <3

finally become pupil after 82 contest !!

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23 months ago, # |
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Somebody please help me with my submission of problem C . https://mirror.codeforces.com/contest/1768/submission/188118465 Can't able to detect error.

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23 months ago, # |
Rev. 2   Vote: I like it +2 Vote: I do not like it

Can someone explain for problem Lucky Permutation:

Turns out that we can easily calculate cycles′ if we know cycles:

cycles′= cycles +1 if the vertices k and k+1 were in the same cycle in the initial graph, cycles′= cycles −1 otherwise.

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    23 months ago, # ^ |
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    It's not easy to explain. I noticed this by using brute force on some small cases, but I can't prove it until the end of contest.

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    23 months ago, # ^ |
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    Cycles are for sort the array, we want 1 inversion. Let's say $$$i$$$ is connected with $$$x$$$ and ($$$i$$$+1) is connected with $$$y$$$.for inversion, we break the link from $$$i$$$ to $$$x$$$ and ($$$i$$$+1) to $$$y$$$ and make a new link from $$$i$$$ to $$$y$$$ and ($$$i$$$+1) to $$$x$$$. That's it, now if we analyse breaking and making link for $$$i$$$ and $$$i$$$+1 ,

    we can see if $$$i$$$ and $$$i$$$+1 are from the same cycle they will brake the cycle and we have 2 cycles from the 1 cycle.

    If $$$i$$$ and $$$i$$$+1 in different cycle they will join together and make 1 cycle from joining 2 cycles.

    i hope it is understandable.

    graph
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23 months ago, # |
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"If we iterate from the smallest value to the top, there will be scenarios where all the remaining positions i will result in max(p[i],q[i])≥a[i] because you don't have enough smaller integers." This is written in the tutorial of problem C. Can anyone pls provide me a testcase where this scenario happens?

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    23 months ago, # ^ |
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    5 5 2 2 1

    In this case, there are no enough place for 3,4,5 to put in.

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      23 months ago, # ^ |
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      But this test case anyways has no solution, provide a test case in which iterating from the smallest value give wrong answer.

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23 months ago, # |
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Why does my submission for C give TLE although it looks nLog(n).

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    23 months ago, # ^ |
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    You are using the function upper_bound(something). Instead, use setname.upper_bound(int). The one you ar eusing can run O(n) sometimes and is bad. The one I mentioned uses binary search on sets and is much faster

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23 months ago, # |
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can anyone please help me in figuring out why is this code of mine giving runtime error on test 7? tried enough not able to figure out.188129954

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23 months ago, # |
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F is cool!

Is "1. min(ai...aj)>=A and 2. min(ai...aj)<A" (in F's Tutorial) typo ?

I think they should be sqrt(A).

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23 months ago, # |
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Got the idea for D after the contest lol

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23 months ago, # |
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Video Solutions for A-E

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23 months ago, # |
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Nlog(n) code giving Tle for problem C please help! here is the code 188134958

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    23 months ago, # ^ |
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    You are using the function upper_bound(something). Instead, use setname.upper_bound(int). The one you ar eusing can run O(n) sometimes and is bad. The one I mentioned uses binary search on sets and is much faster

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      23 months ago, # ^ |
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      In vector upper-bound is log(n) right? So why not in sets?

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        23 months ago, # ^ |
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        It is not. The normal upper_bound() function works differently and at worst cases might iterate over the entire vector/set. But there is a special upper_bound() function for sets. Use setname.upper_bound(x). This is actual logn

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23 months ago, # |
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A approach to Problem D using Group theory ,

Link To solution : 188139688

If Permutation is not sorted, then it will contain some cycles, using Cycle Decomposition, we can break the Cycle of length k into** k – 1 Transpose** (Two Length cycles). If Identity transpose ex (1 3) is multiplied to itself ( 1 3 ) => it will cancel the effect , i.e. Elements have been placed to their correct respective location . So to make the permutation sorted, if there are k transpose, we can multiple k identity transpose, thus canceling out the effect and make them sit on their place. Note : sorted permutation means zero Inversion. And at last, do multiple any transpose of adjacent elements ( 3 4 ) or (1 2 ) or ( 5 6 ) , etc. to get One Extra Inversion .

So, using DFS one can check for Cycles, find the length of cycles, cycle length – 1 is the transpose.

So answer = total no of transpose from all cycles + 1 [ General case ] (for last extra One Inversion that is been added on top of sorted permutation).

There is an edge case, what if one adjacent transpose is already present in one of the cycles, For example (1,2) is already present, and this contributes to only one Inversion, so we can take help of already present good transpose for this case note: we only need any One good transpose (adject transpose) . Let’s say good transpose is T , so first , in general case , we will multiply T with T to cancel out T and make permutation sorted, then again multiply T to add extra one inversion . So we can skip multiplication of T two(x2 ) times , because at last we want to use T as good transpose .

T x T x T = T

( extra multiplication of T two times ) so we can subtract 2 operation from the general case answer .

Ans = ( transpose + 1 ) – 2 [ when good transpose is already present in any of the cycles

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23 months ago, # |
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Fucking shit I have been associated with a psychopath

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23 months ago, # |
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Isn't a case possible in D where number of cycles will remain same?

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23 months ago, # |
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Why does my solution for C work when using stack but not unordered_map? Solution using unordered_map: Solution Solution using stack: Solution I am doing the same thing in both of them, except it works when I use stack instead of unordered_map. I see it gives wrong answer on test case 2, but I can't see the test case. Can someone give a test case that doesn't work for unordered_map? Thanks.

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    23 months ago, # ^ |
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    When you do it=extra.begin() when extra is an unordered_map, It's not guaranteed which element you will get, so probably it->second==true for both it you get for a certain i, which cause i appear 2 times in q.

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      23 months ago, # ^ |
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      But I'm taking the iterator, then erasing it before I get the next element. Shouldn't it delete the one I just used?

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        23 months ago, # ^ |
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        It's not "getting the one just used". It's "There might be multiple entries where it->second==true and you get 2 such entries for one x, then you put two x in q"

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          23 months ago, # ^ |
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          Can you give me an example of when this would happen? Thanks.

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            23 months ago, # ^ |
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            It depends on the implementation of the iterator of unordered_map, so there's no determinate example.

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          23 months ago, # ^ |
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          But why would it work when I use a stack? Couldn't this also happen with a stack???

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            23 months ago, # ^ |
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            Stack is an ordered data structure, you always get what you just put into it

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              23 months ago, # ^ |
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              So the two elements I get are guaranteed to be one in p, and one in q, right?

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23 months ago, # |
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The problemset should should have a tag for permutations, to practice for these kinds of problems.

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23 months ago, # |
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Can someone explain why there is a +k in the final result of problem B, and not just (n-w)/k??

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    23 months ago, # ^ |
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    The reason is because we want to using ceiling division. If we used (n — w) / k, we would round down.

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23 months ago, # |
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Yet another $$$O(n)$$$ solution for C, but can be implemented more easily. Without the headers, it's only 700 B long with two for loops.

solution
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23 months ago, # |
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Is $$$O(n)$$$ solution for C too hard to think? Why not hack $$$O(n \log n)$$$ solutions?

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23 months ago, # |
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Can someone help me to find the reason for TLE in Problem C for the submission 188102874

But an AC for the submission 188105380

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23 months ago, # |
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The Submission 188119572 is Successfully Hacked but the Participant got points for the problem. How is This possible?

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23 months ago, # |
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Concise solution for D:


#include <bits/stdc++.h> using namespace std; typedef long long ll; void solve() { ll n; cin >> n; vector<ll>v(n); for (int i = 0; i < n; i++) cin >> v[i]; vector<ll>col(n); ll c = 1, comp = 0, pos = 0; for (int i = 0; i < n; i++) { if (col[i]) continue; pos = i; while (col[pos] == 0) { col[pos] = c; pos = v[pos] - 1; } comp++; c++; } ll ans = n - comp; for (int i = 0; i < n - 1; i++) { if (col[i] == col[i + 1]) { ans--; break; } } if (ans == n - comp) ans++; cout << ans << endl; } int main() { ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0); int t; cin >> t; while (t--) { solve(); } return 0; }

~~~~~

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23 months ago, # |
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I'm still curious about that "the minimum number of swaps" theory in problem D, is there any prove of that theory (blog or something)?

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23 months ago, # |
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About D, How they know the way to solve this problem during the contest? I mean is this a classical question ? Or they just figure out?

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    23 months ago, # ^ |
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    i'm interesting of how could they just know whatever what is swaping in a cycle it will only minus 1,and whatever what is swaping between two cycle ,it must cost one movement to change it to the answer Do they prove it or just consider it should work

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23 months ago, # |
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Though my rating falls drastically in this contest. I love both the contest and the editorial. Keep organizing such contests Vladithur ❤️.

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23 months ago, # |
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Loved the contest, amazing problems, amazing editorial!!

By the way,
for problem C: 1768C — Elemental Decompress

"There is also another way that you can skip testing if max(p[i],q[i])=a[i]) is correct."

Another Way Here

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23 months ago, # |
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Can anyone explain or tell about resources where i can learn about counting the number of cycles in a directed graph. as a can't find it online. thanks

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23 months ago, # |
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I am just really glad this contest happened and would like to thank the authors of this round, as finally I could reach expert after this round.

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23 months ago, # |
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I love F!I think it is a quite good problem!

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23 months ago, # |
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In F tutorial,Is the "Just maintain the leftmost occurences" for the 2.1 cases a typo?Seems that it needs to maintain the rightmost occurences<j from 1 to √A

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23 months ago, # |
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Problem F is awesome. Couldn't solve it during the contest. After the contest, I looked at the "$$$a_i \le n$$$" hint from the editorial and solved it from there :) Sometimes just stressing a part of the statement can help you solve a problem :)

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23 months ago, # |
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F is a really good problem, I thought $$$O(n\sqrt n)$$$ solution for a long time during the contest but still did not know how to solve it. But later I was amazed by the tutorial of problem F :)

The facts to solve this problem are easy to understand and easy to prove, but it's really hard to find them :)

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22 months ago, # |
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Video solutions for A,B,C

https://youtu.be/erOqAwknRJU

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22 months ago, # |
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Need some help with a failed test case in problem C. 193152726

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15 months ago, # |
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return (38912738912739811 & 1) return __factorial(n * __number_of_sides_of_a_triangle) wtf lol

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7 weeks ago, # |
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Easy O(n) solution for problem C : 285672450