thanhchauns2's blog

By thanhchauns2, history, 2 years ago, In English

Hi Codeforces!

Igorfardoc, Vladithur, Alexdat2000, GlowCheese, DeMen100ns, SPyofgame and me (spelling "thanh-chau-n-s-2") are delighted to invite you to participate in Codeforces Round #842 (Div. 2). This round will be rated for all participants with a rating lower than 2100.

This contest is brought to you by

Special thanks to:

Edit: there will be $$$2$$$ packages for two participants in Vietnam, the highest score and the luckiest. You have to set your region to Vietnam to be qualified.

The score distribution is $$$500-1000-1500-1750-2250-3250$$$.

Hope to see you in the final standings!

Editorial is out.

Congratulations to the winners:

Div.1+2 Div.2
1 arvindf232 drizzlo
2 Hyperbolic jiangly_fan_fan_fan_fan
3 drizzlo BedzieMagikZa2Lata
4 jiangly BeautifulChicken
5 Um_nik AE-3803

And the first solver for each problem:

A B C D E F
Div.1+2 dapingguo8 tourist youknowiknowyouknow A_G nok0 jeroenodb
Div.2 celestialcoder 1024mb youknowiknowyouknow MIOC69 cmk666 drizzlo
  • Vote: I like it
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  • Vote: I do not like it

| Write comment?
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2 years ago, # |
Rev. 3   Vote: I like it +29 Vote: I do not like it

As a slave~ setter, wishing you all peace, joy, and unconditional love at Christmas and always. And of course, with ++rating :Đ

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    2 years ago, # ^ |
      Vote: I like it +3 Vote: I do not like it

    As a tester, love you SPyofgame

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      2 years ago, # ^ |
        Vote: I like it +9 Vote: I do not like it

      love you SPyofgame orz

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        2 years ago, # ^ |
          Vote: I like it +5 Vote: I do not like it

        As a person that likes the colour cyan, this post is just pleasing for my eyes.

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          2 years ago, # ^ |
            Vote: I like it +35 Vote: I do not like it

          As a tester, I'm only GREEN.

          But they promote me to...cyan! Thanks a lot. >_<

          Spoiler
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            2 years ago, # ^ |
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            You are a green with the power of a grandmaster, and that is something to look up to.

            Spoiler
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    2 years ago, # ^ |
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    As a tester [insert joke]. I liked the problems as I've put some effort in upsolving, hope you'll enjoy them as well.

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    2 years ago, # ^ |
      Vote: I like it +11 Vote: I do not like it

    It's hard to increase your rating by only one. ++rating

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      2 years ago, # ^ |
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      I did that. actually

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      2 years ago, # ^ |
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      prvocislo: And I took that personally.

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        2 years ago, # ^ |
          Vote: I like it +8 Vote: I do not like it

        lol and then they removed cheaters and rating++ was gone :')

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          2 years ago, # ^ |
            Vote: I like it +15 Vote: I do not like it

          Nah because it was ++rating++, the bonus score is the gift from the main route mission to LGM.

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2 years ago, # |
  Vote: I like it +2 Vote: I do not like it

I am a setter.

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2 years ago, # |
  Vote: I like it +3 Vote: I do not like it

As a do-nothing-setter, gluck everyone!

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    2 years ago, # ^ |
      Vote: I like it +16 Vote: I do not like it

    As a do-nothing-setter, I found another do-nothing-setter and that's pretty POG.

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2 years ago, # |
  Vote: I like it +19 Vote: I do not like it

As a tester, Merry (late) Christmas everyone!

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2 years ago, # |
  Vote: I like it +21 Vote: I do not like it
Hi!
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2 years ago, # |
  Vote: I like it +21 Vote: I do not like it

As a tester,this is my first time.Also,i want tell you something important

Spoiler
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2 years ago, # |
  Vote: I like it +19 Vote: I do not like it

cyanforces

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2 years ago, # |
  Vote: I like it +3 Vote: I do not like it

As a tester, I can guarantee that you'll find interesting tasks in this round! GL & HF.

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2 years ago, # |
  Vote: I like it +3 Vote: I do not like it

as a tester, nya

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2 years ago, # |
  Vote: I like it +8 Vote: I do not like it

Cyan Supremacy

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

As a tester, this contest is worth participating and learning how to brainstorm ideas efficiently. Good luck and have fun in the last days of 2022!

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2 years ago, # |
  Vote: I like it +8 Vote: I do not like it

omg cyan round

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2 years ago, # |
  Vote: I like it +85 Vote: I do not like it

Regardless of my experience testing this round, the problems are good.

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2 years ago, # |
  Vote: I like it 0 Vote: I do not like it

omg cyan round :)

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2 years ago, # |
  Vote: I like it +26 Vote: I do not like it

As a cyan tester, I recommend partipating

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2 years ago, # |
  Vote: I like it +17 Vote: I do not like it

as a tester, this round is better

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2 years ago, # |
  Vote: I like it +11 Vote: I do not like it

Hoping for a problem E solvable for me (to keep my current rating)

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2 years ago, # |
  Vote: I like it +4 Vote: I do not like it

Please downvote me

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2 years ago, # |
Rev. 4   Vote: I like it +14 Vote: I do not like it

Round of specialists! (NY's magic)

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2 years ago, # |
Rev. 4   Vote: I like it +21 Vote: I do not like it

I enjoyed the "you" trick and the hidden text (doesn't work on the dark theme).

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2 years ago, # |
  Vote: I like it +9 Vote: I do not like it

CYAN IS EVERYWHERE!

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2 years ago, # |
  Vote: I like it +11 Vote: I do not like it

cyan round, so maybe i've got a chance

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2 years ago, # |
  Vote: I like it +26 Vote: I do not like it
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2 years ago, # |
  Vote: I like it +20 Vote: I do not like it

One of the most visually pleasing announcements!!

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2 years ago, # |
  Vote: I like it +8 Vote: I do not like it

This round should be named "Specialists Round"

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2 years ago, # |
  Vote: I like it +11 Vote: I do not like it

omg cyan round

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2 years ago, # |
  Vote: I like it +7 Vote: I do not like it
great contest will arise tomorrow
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2 years ago, # |
  Vote: I like it +17 Vote: I do not like it

How about every participant changing their color to cyan for this round ?

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2 years ago, # |
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Hope I don't become green after this cyan round.

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2 years ago, # |
  Vote: I like it +52 Vote: I do not like it

1000 cyans versus a LGM, just as in the old days.

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2 years ago, # |
Rev. 3   Vote: I like it +1 Vote: I do not like it

Hocus Pocus Abrakadabra , turn me into cyan

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2 years ago, # |
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Viet Nam contest legoo

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2 years ago, # |
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Cyan_Forces ✪ω✪

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2 years ago, # |
Rev. 2   Vote: I like it +3 Vote: I do not like it

wow, Filled with cyan on all sides

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2 years ago, # |
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cyanforces

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2 years ago, # |
  Vote: I like it +3 Vote: I do not like it

Help -is-this-fft- finish off 2000 problems.

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  Vote: I like it +19 Vote: I do not like it

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The most cyan round ever. It will be interesting!

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2 years ago, # |
  Vote: I like it +8 Vote: I do not like it

so~so~so~so~so~green~ ovo!

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2 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Why is everyone cyan now?

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2 years ago, # |
  Vote: I like it +1 Vote: I do not like it

Time for VietnamForces!!

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

Specialist Forces

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2 years ago, # |
  Vote: I like it +13 Vote: I do not like it

Today I feel Vietnamese.

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2 years ago, # |
  Vote: I like it +5 Vote: I do not like it

Cool fact that div made by Russians and Vietnamese while im Vietnamese but born in Russia... Great job guys!

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2 years ago, # |
Rev. 2   Vote: I like it +1 Vote: I do not like it

Nice editing for last point.

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2 years ago, # |
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Div2 finally, its my time to shine!!

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2 years ago, # |
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Hope to get Master again!

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2 years ago, # |
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I love you!

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2 years ago, # |
  Vote: I like it +27 Vote: I do not like it

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2 years ago, # |
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is the contest unrated?

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    2 years ago, # ^ |
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    Added that it's rated for everyone with rating < 2100.

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2 years ago, # |
  Vote: I like it +8 Vote: I do not like it

how to calculate the contribution?

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2 years ago, # |
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I pressed on LG "you", but it shows me grey :|

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2 years ago, # |
  Vote: I like it +1 Vote: I do not like it

THE ONE PIECE IS REAL!!!

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2 years ago, # |
  Vote: I like it +17 Vote: I do not like it

DeMen100ns, what the ..?

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2 years ago, # |
  Vote: I like it +26 Vote: I do not like it

As a tester, I became cyan.

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2 years ago, # |
Rev. 2   Vote: I like it +9 Vote: I do not like it

I hope to become cyan in the cyanforces

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2 years ago, # |
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just made it in time (i ran from the bus station), hopefully i won't turn cyan

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2 years ago, # |
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excited!

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2 years ago, # |
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All the best guys....

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2 years ago, # |
  Vote: I like it +11 Vote: I do not like it

Speedforces!

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2 years ago, # |
Rev. 2   Vote: I like it +1 Vote: I do not like it

Permutation forces

Loved it

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2 years ago, # |
  Vote: I like it +8 Vote: I do not like it

Task F is really awesome!

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2 years ago, # |
Rev. 2   Vote: I like it +5 Vote: I do not like it

As a participant I love Vietnamese Contest! (tks for free rating)

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2 years ago, # |
  Vote: I like it +16 Vote: I do not like it

Permutationforces. I love it.

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2 years ago, # |
  Vote: I like it +10 Vote: I do not like it

Any ideas for C?

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    2 years ago, # ^ |
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    I was also stuck at C , what was your approach?

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      2 years ago, # ^ |
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      Nothing special, was implementing whatever was coming to my mind

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        2 years ago, # ^ |
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        What did you guy stuck on C ? You can check for da editorial, but you can also give your question here and I will reply :v

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2 years ago, # |
  Vote: I like it -14 Vote: I do not like it

stupid speedforces

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2 years ago, # |
  Vote: I like it +13 Vote: I do not like it

Why are there so many permutation problems?

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2 years ago, # |
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From expert to pupil. I don't understand why this is happening...

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2 years ago, # |
  Vote: I like it -11 Vote: I do not like it

A<F

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    2 years ago, # ^ |
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    I am almost sure that 99% people simply saw the testcases and returned n-1 :P for A

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      2 years ago, # ^ |
        Vote: I like it +10 Vote: I do not like it

      Anyone with > 0.5 braincells can see that n! = n * (n — 1)!

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      2 years ago, # ^ |
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      is this not correct??

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        2 years ago, # ^ |
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        yes that is, but no one derived it I meant.

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          2 years ago, # ^ |
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          i have 10 min i doesn't see that it ask for max i think it ask for min i tried binary search but when loking at sunmission rate i rewrite then just a second to solve k! + (k-1)! = (k+1)(k-1)! k-1 is best choice

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    2 years ago, # ^ |
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    F>A

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2 years ago, # |
  Vote: I like it +28 Vote: I do not like it

permutationForces.

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2 years ago, # |
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Why would you do that??? So many problems on permutations! It's just ridiculously disrespectful for those who suck in this theme!

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2 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Now its time to chnage the color After very long time

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2 years ago, # |
  Vote: I like it +1 Vote: I do not like it

Hate permutations, hate sortings, hate myself. Goodbye chance to become pupil :(

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    2 years ago, # ^ |
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    +1 hate permutation problems, therefore hate this contest...

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2 years ago, # |
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I wonder how many people actually proved their solution for A.

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    2 years ago, # ^ |
      Vote: I like it +6 Vote: I do not like it

    it was kinda easy to prove .

    take the (x-1)! common from (x ! + (x-1)!) which will end up giving this equation . (x-1)! * (x+1). take a x such that x+1 = k .

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    2 years ago, # ^ |
      Vote: I like it +4 Vote: I do not like it

    It was clear to me that if there is a solution it should be k-1 to obtain the maximum number of factors from the factorial. To prove that this answer always works, I did a simple proof.
    for x = k — 1
    x! + (x — 1)! = (x — 1)! * (x + 1) = (k — 2)! * k

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2 years ago, # |
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how to solve C anybody ?

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2 years ago, # |
Rev. 3   Vote: I like it +2 Vote: I do not like it

Hi guys I have uploaded editorial solutions here — check.

have uploaded A,B,C for now and would upload D in a few mins :) let me know if you find these helpful :)

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2 years ago, # |
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Permutation Round!!!

BTW, how to solve D?

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    2 years ago, # ^ |
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    Permutation with inversion number can only be in form $$$s := {1,2, ...x-1, x+1, x, x+2, ...n}$$$.

    So the basic idea is to try each $$$x$$$, there are $$$n-1$$$ possibilities.

    When changing your permutation from $$$p$$$ to $$$s$$$, it is equal to swapping $$$x, x+1$$$ in $$$p$$$ and sorting $$$p$$$. It is well known that the minimum swap required to solve $$$p$$$ is $$$len(p) - component(p)$$$ (p after $$$x, x+1$$$ swapping). So we need to find $$$x$$$ that maximizes the number of components after $$$x, x+1$$$ swapping.

    Another conclusion is that if $$$a$$$ and $$$b$$$ are in the same component, then swap $$$a, b$$$ adds one component. Otherwise, if $$$a$$$ and $$$b$$$ are in different components, then swap $$$a, b$$$ decreases the number of components by $$$1$$$. So we need to check whether there exists an $$$x$$$ such that $$$x, x+1$$$ are in the same component~

    Besides, how to solve B???

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      2 years ago, # ^ |
        Vote: I like it +3 Vote: I do not like it

      Best possible arrangement is for any N is 1 2 .... N , in sorted order.

      You just need to find the longest best arrangement possible

      For eg : N = 5 , A[] = [ 1 , 3 , 2 , 5 , 4 ] , the best possible arrangement that is already possible is taking [1 , 2] & not perform any operation on them as they are in longest sorted order & perform the operations on the remaining elements, taking the ceil of [Remaining elements / K] as the answer.

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2 years ago, # |
  Vote: I like it +1 Vote: I do not like it

How to solve B, please??? A+C+D <= 40min. Unfortunately, I have no idea to solve B in the left time. I have to admit I am stupid.

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    2 years ago, # ^ |
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    Find 1 in the permutation. On the right of it, find 2. Continue this process until you can't find the larger number. ( n — numbers you've found )/k is the answer (round up).

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    2 years ago, # ^ |
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    check editorial here — click

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    2 years ago, # ^ |
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    Yes, scan $$$1,2,3...$$$ in LEFT->RIGHT direction. E.g. dynamic regex: /\b(??{ $s })\b(?{ $s ++ })(*F)/

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2 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Please help in problem D My idea was to find minimum moves to make the array equal to the sorted permutation in which exactly one pair of adjacent elements is interchanged This gave WA

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    2 years ago, # ^ |
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    idea is the same just you have to make component s if the adjacent is not in the same component at all first we find all then all +1

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For Problem D , I tried with finding cycles for shifting/swapping. Then was trying something based on the cycle size. Something similar to min swaps needed to sort an array. but couldn't get it. Any ideas?

One observation I had was : to have exactly 1 inversion, we need i and i + 1 to be swapped , rest entire array needs to be sorted.

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    2 years ago, # ^ |
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    You were correct in your approach and observation.

    Let x — min swaps required to sort the array. You just need to check if the cycle has a consecutive number then the answer is x-1.

    Else answer is x+1.

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    2 years ago, # ^ |
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    yes thats the main observation after that you have to grp them (components) type then just find the ans

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

    Let $$$x$$$ be the min swaps to sort the array, let if $$$i$$$ and $$$i + 1$$$ are in the same cycle, you need $$$x - 1$$$ swaps to get the array where the only inversion is $$$(i + 1, i)$$$, otherwise you need $$$x + 1$$$ swaps. (can't really prove it tho)

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2 years ago, # |
Rev. 3   Vote: I like it +2 Vote: I do not like it

Problem A is very bad for the CP contests, it is better for math competitions.

It is bad because it doesn't check any skills and knowledge because it was worth to try just $$$k-1$$$ after looking at the sample tests.

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2 years ago, # |
  Vote: I like it +1 Vote: I do not like it

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

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Any hints for D?

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    2 years ago, # ^ |
      Vote: I like it +4 Vote: I do not like it

    i think this is a hint: answer is min swaps to sort + 1 or min swaps to sort — 1

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      2 years ago, # ^ |
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      What I was able to analyze is that eventually our answer would look like 1.2.3.4...i+1.i....n So yes the answer should be the swaps to sort + 1 or -1 depending upon can we make the above state just before the last swap to sort. Now IDK whether this is correct or not but if we have some i which is at position(i-1) or (i+1){1 based positions} then we'd subtract 1 otherwise we'd add 1. Is the above correct? Please give reason as well

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        2 years ago, # ^ |
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        Incorrect.

        1
        5
        3 4 5 2 1
        

        2 in position 3. But answer is 4. Because 2 and 5 (in position 3) belongs to different cycles (1 3 5) and (2 4). So you cannot in two moves get 1 2 4 3 5.

        If you'd get cycle likee 2 5 x x 1 (two consecutive numbers in one cycle) then you can in one move get 2 1 x x 5.

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          2 years ago, # ^ |
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          the positions are 1 based but u gave 0 based.

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            2 years ago, # ^ |
            Rev. 3   Vote: I like it 0 Vote: I do not like it

            Ok, then that

            1
            8
            1 7 5 8 2 6 3 4
            

            You got cycle x 7 5 x 2 x 3 x, so you can in two moves do

            x 7 5 x 2 x 3 x
            x 3 5 x 2 x 7 x
            x 3 2 x 5 x 7 x

            So you need to substract one, but there is no such i in i-th or (i + 2)th position

            Reason: all cycles can be treated indepenedent, so in cycle with len l need do l - 1 moves to sort cycle, and if in cycle exists two consecutive numbers then you need l - 2 moves to get one inversion in that cycle.

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        2 years ago, # ^ |
        Rev. 2   Vote: I like it 0 Vote: I do not like it

        Incorrect

        1
        6
        6 5 3 4 1 2
        

        no such i but we'd subtract 1

        we cannot guarantee that the i is the inversion by just looking at this, this is actually my proposed solution in the contest :/ which i got Wrong Ans2

        Reason: idk, have some counter case

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    2 years ago, # ^ |
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    Hint1
    Hint2
    Hint3
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      2 years ago, # ^ |
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      Yo, could u check my soln once? the one i wrote above

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    2 years ago, # ^ |
    Rev. 2   Vote: I like it 0 Vote: I do not like it

    Hint 1: A permutation has one inversion if and only if the permutation is $$$(i,i+1)$$$ for some $$$i$$$.

    Hint 2: The minimum number of transpositions from a permutation $$$\pi$$$ to change it to the identity is $$$n-c$$$ where $$$c$$$ is the number of cycles in the permutation.

    hint 3: The distance between two permutations is the distance between the permutation given by the composition of first with inverse of second, and the identity permutation.

    hint 4: count number of cycles $$$c_i$$$ in $$$p$$$ composed with $$$(i,i+1)$$$ for all i in O(n) time. The answer is $$$n- max(c_i)$$$

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    2 years ago, # ^ |
    Rev. 3   Vote: I like it 0 Vote: I do not like it

    Just check out this. All Will be clearminimum-number-swaps-required-sort-array Secondly check if there is any x+1=y element in the cycle.

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2 years ago, # |
  Vote: I like it +7 Vote: I do not like it

Is problem C a little difficult to write? I wrote it twice.

Besides, the problems of this competition is very interesting.

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    2 years ago, # ^ |
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    You know, it's permutationspecialistforces. :)

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    2 years ago, # ^ |
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    I dunno, my solution was straightforward and simple :think:, maybe you can hack me I guess

    But as a setter, can you give detail for the issues you have to deal with during the contest ?

    Linear Solution for Problem C
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2 years ago, # |
Rev. 2   Vote: I like it 0 Vote: I do not like it

WA on test 2 in problem C... can anybody help (188113413)?

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2 years ago, # |
  Vote: I like it +7 Vote: I do not like it
  • Permutation of B Solved
  • Permutation of C Solved
  • Permutation of D Fucked Up Man
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2 years ago, # |
Rev. 2   Vote: I like it +19 Vote: I do not like it
Spoiler
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2 years ago, # |
  Vote: I like it +132 Vote: I do not like it

Is Um_nik stronger than 1000 cyans? Let's find out! Screencast with commentary

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2 years ago, # |
  Vote: I like it -28 Vote: I do not like it

Problems A, B, C, D, and E were all very straightforward and meaningless to solve. With all respect to the authors, it was one of the worst contests that I participated in.

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    2 years ago, # ^ |
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    I wish I could say this in some rounds.

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2 years ago, # |
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fuck this system bro i swear to god half of c submissions from youtube channels

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    2 years ago, # ^ |
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    I hope all of those skipped! If you can make a blog as you spotted those similar solutions. Go on, Do!

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2 years ago, # |
  Vote: I like it +10 Vote: I do not like it

finally cyan in the cyanforces <3

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2 years ago, # |
  Vote: I like it +24 Vote: I do not like it

Ratings updated preliminarily. We will remove cheaters and update the ratings again soon!

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2 years ago, # |
  Vote: I like it +6 Vote: I do not like it

permutation_forces

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2 years ago, # |
Rev. 2   Vote: I like it +12 Vote: I do not like it

So happy today !!! Became Specialist for the first time !!

Thanks a lot for the contest

I m shocked to observe that I somehow solved C in O(N)

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2 years ago, # |
  Vote: I like it +10 Vote: I do not like it

Became Cyan (finally) in the Cyan round!

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2 years ago, # |
Rev. 2   Vote: I like it +1 Vote: I do not like it

I would like to point out that the first to address F in Div.2 should be drizzlo. derekFeng's rating is 2746, and I think it may have been New Year's magic that led to an oversight on the part of the blog writers.


Updated:

Already fixed at light speed! Thanks again to the author for preparing such a great round and for the attention to feedback!

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2 years ago, # |
  Vote: I like it +1 Vote: I do not like it

Short Statements = Beautiful

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2 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Can anyone help me figuring out why I'm getting runtime error for problem C on test case 7.I'm trying from 3 hours still not able to figure it out.Your time will be worth a lot.Thanks in advance . Here's my code 188125909

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    2 years ago, # ^ |
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    Your code is such a mess. You can Google your exit code (-1073741819 )on test 7, it is something about memory access violation. My !guess! is x--; q[i]=*x; s.erase(x) Or x--; k.erase(x); p[i]=*x;

    But I haven't tried to fully understand what your program is doing

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2 years ago, # |
  Vote: I like it +16 Vote: I do not like it

One of my favorite rounds, all of the problems have short statements and very clean solutions. I hope you guys author more rounds in the future!

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

.

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2 years ago, # |
  Vote: I like it 0 Vote: I do not like it

I became cyan for the 7th time. Thanks for this contest, created by 7 'cyans'.

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2 years ago, # |
  Vote: I like it 0 Vote: I do not like it

Why are the top 2 in division 2 new accounts?

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2 years ago, # |
  Vote: I like it +1 Vote: I do not like it

me sitting happy with +0 delta.

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2 years ago, # |
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MikeMirzayanov Hi, I received this message: Your solution 188082997 for the problem 1768C significantly coincides with solutions csegura/188082997, Sahil9259/188104072, UnRiVaLeD__/188104217, Frieza_Comeback/188106033, ashu1509goel/188107094, atharv_soni/188109171, bs_biswa/188109314, POSEIDON_RAGNAROK/188119467, soumabha_12/188120764. Such a coincidence is a clear rules violation. Note that unintentional leakage is also a violation. For example, do not use ideone.com with the default settings (public access to your code). If you have conclusive evidence that a coincidence has occurred due to the use of a common source published before the competition, write a comment to post about the round with all the details.

I see that I was not skipped because I was the first one to submit the code; Good job in identifyng the copy. I don't use any online system, so it was leaked through the codeforces system. By the time that my code was leaked, it seems that the only person in my room that had closed the problem was coderpro2, so, if this is confirmed, in my opinion, actions against this account should also be taken.

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

Got WA, can somebody help me? I still can't figure out the testcase which my code fails on. (188511376)

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

I'm having a serious trouble solving Problem F with Java 8.I believe my code is essentially the same as the description in tutorial, but all I got is TLE in case 24/25. Is there anyone ACed this problem with Java? Or can someone tell me why my code is so slow?
Here's my code:188557390 Sorry for the trouble

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

    solved by fixing multiple mistakes. turns out I understand nothing of the solution :)