Hi!

I'm back with not one, not two, but three contests, although I have no promises about when to expect them....

The first of them, codeforces round #563, will take place on Jun/03/2019 17:05 (Moscow time). It's rated for the second division, but, as usual, first division participants can take part out of competition.

I'm the problemsetter of the round. I'd like to thank KAN for coordinating the round (and his patience .. try coordinating ~20 problems), BanRussiaAtIOI for helping with the preparation, Um_nik, _overrated_, Aleks5d, wiwitrifai, pllk, Bedge, Ivan19981305, and PrianishnikovaRina for testing the round, and MikeMirzayanov for the great codeforces and polygon platforms.

In this round, you'll be given 6 problems and 2 hours to solve them.

**UPD:** I decided to drop the 3 seconds rule. The scoring distribution is 500-1000-1500-1750-2500-2500. That means you should probably read both E and F :D

Good luck & Have fun!

**UPD:** here's the editorial.

**UPD:** congratulations to the winners!

Div.1+Div.2:-

Div.2:-

See you in the second round :D

Trying to make enough money to afford MIT. I see you. Only a few ten thousand dollars left np

Dude, application fees :3 But first things first, how dare you say her name!

I have stalked her long enough to at least be allowed to do so. Fight me.

I don't get it. Some internal joke?

alphatrance I think they're referring to this meme xD

deleted comment

`By tradition, the scoring distribution will be announced 3 seconds before the contest.`

So accurate!

But now rules should get changed

Imagine next rounds you would actually use high precision clocks to measure the interval of announcing score distributions... ;)

Maybe even high-precision randoms!

The time is good for Chinese.

Oh,No.The best time is before 8 p.m, so that they can go to bed earlier.

code with girlfriend wonderfully

i m very excited about the new contest

Yeah1.

4 contests in the next 7 days, great.

4(2)

Looking forward to more fun XOR questions

Upvoted for creating 3 contests simultaneously (Great job!).

Downvoted for not capitalize "Codeforces" and "Polygon".

How did you vote twice??

It seems that another competition season has come

So many contests these days :)

mohammedehab2002 previous rounds all problem names start with "Mahmoud"(round #396), "Ehab"(round #525) and "Mahmoud and Ehab"(round #473). Guess which start is next ??

To get all the combination, Ehab and Mahmoud is the last one to start with :)

the next start is an empty string

HaHaHa

John cena problems

or maybe concatenated version MahmoudEhab:)

up to which rating second division?

Upto 2099, but if div1 and div2 rounds are held simultaneously people who are rated greater than equal to 1900 must participate in div1

Wait, sorry guys I am new here. Do you have to start at that exact time? Or is there a contest window where we can choose to do it?

You need to register before the contest starts. Registration's usually open till 5 minutes prior to the start of a contest. Some contests support extra reg which opens 10 minutes after the contest start and continues for 20 minutes.

There's no window, the contest starts at the same time for everyone.

Let's get ready to rumblllllllleeeeeeeeeeeeeeeeeeee!!!!!!!!!!!!!!

cute !!

Hope this round not unrated and no accident

Do we have a hacking phase?

No

No u

`Scoring distribution shall be announced 3 seconds before contest`

`I decided to drop the 3 seconds rule. The scoring distribution is 500-1000-1500-1750-2500-2500.`

Rules are made to be broken here. xD

You really like GCD and prime numbers ! (WOW!)

The description of the topic is short and concise。

Apparently, it wasn't.

if only query d at beginning and query s on LCA

then will get FST

but I have no idea to solve it correctly now : /

How To solve problem D ?

Think in terms of prefix xors.

Instead of directly construct the array, just construct the prefix xor version of the array S1, S2,..., Sn. So the condition that no subseg has the xor equals to 0 or x is the same as the array S is distinct and there is no pair in S that xor of them is x.

So iterate from 1 -> 2^n-1, if x^i also belongs to the given range [1, 2^n) then just pick one, or else pick both.

To construct the answer array A from S, use : Ai = Si^S(i-1).

What is prefix xor ? And why prefix xor array changes the condition?

First observation, if there is no number x restricted. You can simply construct something like

`1 2 1 4 1 2 1 8 1 2 1 4 1 2 1...`

This pattern is optimal because at every i-th number where i is 2^x, you cannot add any new number using numbers in range [1..2^x), any new addition will cause XOR to be 0. Hence, you will need to add 2^x every time you are at the 2^x-th number (1, 2, 4, 8, 16, ...).Now, what about the restricted number? Well you can simply take the biggest 2^x that forms x. e.g. if x is 5, restricted number will be 4. Now, you can simply skip the restricted number when you want to form the sequence. (Why biggest? To minimize the largest number in the sequence) e.g. x = 5

`1 2 1 8 1 2 1 16 1 2 1 8 1 2 1`

, if at any time the number has exceed 2^n, just stop adding new sequences.Nice approach. Here is my code implementing this: https://codeforces.com/contest/1174/submission/55059114 .

What can be pretest 7?

I thought of something like

`4 5`

. Answer should be longer than`1 2 1 8, ...`

But I initially only answered`1 2 1`

which is a wrong answerI will explain the complete solution of D.

Hint 1Suppose you calculate accumulate xor sequence.

If $$$a = $$${$$$1,3,1$$$}, accumulate xor is {$$$0, 0 \ xor \ 1, 0 \ xor \ 1 \ xor \ 3, 0 \ xor \ 1 \ xor \ 3 \ xor \ 1$$$} $$$=$$$ {$$$0,1,2,3$$$}.

Suppose the problem is not "There is no subsegment which xor is $$$0$$$ or $$$x$$$", but "There is no subsegment which xor is $$$0$$$". In this problem, the only condition that the sequence should satisfy is that "All values of accumulate xor is different". For example, sequence {$$$1,3,1$$$} satisfy the condition because accumulate xor is {$$$0,1,2,3$$$} and it's all different, but sequence {$$$2,1,1$$$} does not satisfy the condition.

So, it means if $$$x$$$ is greater than or equal to $$$2^{N}$$$, you should output the sequence which is length $$$N−1$$$: {$$$0 \ xor \ 1, 1 \ xor \ 2, 2 \ xor \ 3, ..., (N−2) \ xor \ (N−1)$$$}.

Hint 2So what about the pattern of $$$x < 2^{N}$$$? Let's think about some cases.

If $$$N=3$$$ and $$$x=4$$$, one of the optimal accumulate xor sequence is {$$$0,1,2,3$$$}.

If $$$N=3$$$ and $$$x=2$$$, one of the optimal accumulate xor sequence is {$$$0,1,4,5$$$}.

If $$$N=3$$$ and $$$x=1$$$, one of the optimal accumulate xor sequence is {$$$0,2,4,6$$$}.

Seems like the maximal length of accumulate xor sequence seems to be $$$2^{N}−1$$$. That is true but why?

In this case, two condition must be satisfy to not include a subsegment of $$$0$$$ and $$$x$$$:

1. All of the values in accumulate xor sequence is different.

2. Both $$$0$$$ and $$$0 \ xor x$$$ should not be in accumulate xor sequence. Same for $$$1$$$ and $$$1 \ xor x$$$, ... $$$2^{N}−1$$$ and $$$2^{N}−1 \ xor \ x$$$.

So, you should choose the value $$$i$$$ which is $$$0 \leq i < 2^{N}$$$ and $$$i < (i \ xor \ x)$$$. For example, if $$$N=3$$$ and $$$x=7$$$, you should choose the value {$$$0,1,2,3$$$}.

Finally, you should restore the sequence from accumulate xor sequence. In the example of $$$N=3, x=7$$$, one of the possible answer = {$$$0 \ xor \ 1, 1 \ xor \ 2, 2 \ xor \ 3$$$} = {$$$1,3,1$$$}.

Source CodeMy Solution of problem D

I found B to be harder than C and D maybe because I was approaching it wrong way.

How to solve B? And why does it get TLE 55041556 ?

To be honest, B is so simple. If we have both odd and even numbers, then the sorted array is the answer, or else just print the original array. Correct me if I'm wrong

Maybe i dont understand you but what about this test: 3 2 3 2 1 (n = 5)

It is 1 2 2 3 3. Because both odd and even exist, we can easily prove that using the allowed operation could sort the array, and obviously the lexicographically smallest array.

"You can perform the following operation on it as many times as you want:". Of course i again solve another problem (( .

if the input contains both odd and even numbers the result will always be a sorted array.

You need to notice that, if there are only odd or only even numbers you can not make any swap. Otherwise you can sort the whole array.

If we have at least one odd and another even number, we will be able to reorder the whole array (swap two odd numbers or two even numbers). For example, if you wanna swap two odd numbers

`o1`

and`o2`

, with an even number`e`

, you can do:swap

`o1`

and`e`

, swap`e`

and`o2`

, swap`e`

and`o1`

.And the position of

`o1`

and`o2`

was swapped as a result.Hints for F please.

Firstly, ask the distance from 1. Now find the centroid of the current tree and check if it is an ancestor by checking if dist(root,centroid)+dist(x,centroid) == dist(root,x) , if that holds true, query the next node on the path and make it the root and now distance from root is dist(x,centroid)-1. otherwise, you can delete the subtree rooted at the centroid and everything else remains the same.

But I got WA on test 12... have you got AC like that?

Try to optimize queries if you don't have any bugs.

I don't even know.. WA because of Wrong Node or WA because of too many queries

You can count queries, and exit with some code if limit exceeded. You will see this code.

Man, if I knew that, I would have solved it!

Thank you for the tip XD

WOW,very clever

see this : https://codeforces.com/contest/1174/submission/55042488

I've seen successful hacks made. Any hints what they were about?

In my room there were submissions that checked if there is any odd numbers and sorted based on that (I found one more submission like that after the end of contest :@ ) .

One of the mistakes on problem A was dividing sum of the numbers by 2 for checking the answer, while the sum is odd.

Sorry for bad English. :)

Your English is fine :D I understood

Thanks :) I tried too much to write understandable.

How to solve F?

god damn it when I started to feel I'm halavin I failed on the fourth hack

wow 3 hacks, how did you get them? was there a corner test case or something?

Who did not solve A by sorting the array for some reason they were swapping the first different element from the first half with the other half and then print the array

nice

Isn't there an ambiguity in Problem A? In the end, it says "They must form a reordering of a. You are allowed to not change the order". What does that mean? As per my understanding, it meant that we're allowed rotate the array(so that ordering remains same) but, can't sort it completely.

you are allowed to not change the order means you can leave it as it is and they must form a reordering of a means you can swap any element as many times as you want

Hints for F? Can it be solved using LCA?

it can be solved using Centroid

what is centroid decomposition, any good blogs and tutorials on it, from where u learn.

https://threads-iiith.quora.com/Centroid-Decomposition-of-a-Tree

After solving

(A,B,C)^zzzzzzzzzzzz01:59:29Successful hacking attemptHow to think and approach problem D?

Every number has only one number that makes (A^B == X) true. The problem asks for sub segment so it's another way to tell you to think of prefix xor. The answer should be clear after that.

fml, my bug on F was that I'm doing return the answer if there is only one edge from the current node, which

shouldbe the back edge to the parent, but I forgot the root!Nice round, I really liked it :D

Any ideas for E? i see most solution use dp. can anyone explain!

For E, $$$a_1=p_1^{e_1}p_2^{e_2}$$$. then max is $$$1+e_1+e_2$$$. that's exp step down. so $$$a_1$$$ must be $$$2^k$$$ or $$$2^{k-1}3$$$ (if $$$\leq n$$$). then remain is combination count. but no time to code.. the annoying $$$3$$$.

Am I right? or is there a better solution? wait for tomorrow morning:) sleep now

Actually,

I didn't use DP. I used only multiplying.Seriously, I didn't use DP.My solution of problem E is as follows:

---

Step 1: What is the maximal possible value of $$$f(p)$$$?Actually, the maximal possible value of $$$f(p)$$$ is as follows:

But why? Think about the sequence of {$$$g_1,g_2,g_3,...,g_k$$$} if you assume $$$g_1>g_2>g_3>...>g_n$$$. For example, if $$$A=$$$ {$$$4,6,2,1,5,3$$$}, the prefix gcd will be {$$$4,2,2,1,1,1$$$}, so $$$g$$$ will be {$$$4,2,1$$$}.

Because the optimal sequence of $$$g$$$ is {$$$2^{k−1},2^{k−2},2^{k−3},...,4,2,1$$$}. Suppose $$$N=11$$$. For the sequence {$$$8,4,2,1,11,10,9,7,6,5,3$$$}, it is easy to find that $$$g$$$ is {$$$8,4,2,1$$$}.

---

Step 2: How many ways are the maximal answer?Let's think about

writingthe value of $$$a_i$$$ which changed the prefix gcd. For example, if $$$g$$$ is {$$$8,4,6,5,2,3,1,7$$$}, the values that you willwritewill be {$$$8, 4, 6, 5$$$}.So what is the possible sequence of values which you will

write? Suppose $$$N=8$$$.So the number of possible sequence of values which you will

writewill be $$$1 \times 1 \times 2 \times 4 = 8$$$.But, how about the other values? If sequence is {$$$8,4,6,5$$$}, you should insert other values: {$$$1,3,7,2$$$}.

You should think about inserting in order of $$$1, 3, 7, 2$$$. (Insert from values which is not divisible of $$$2$$$, next not divisible for $$$4$$$, next not divisible for $$$8, 16, ...$$$

So, let's move on another example. Suppose $$$N=11$$$:

Did you get it? :)

---

Step 3: Thinking about other cases, not only $$$g =$$$ {$$$2^{k−1},2^{k−2},...,4,2,1$$$}If $$$N=12$$$, not only {$$$8,4,2,1$$$} is maximal, but also {$$$12,4,2,1$$$}, {$$$12,6,2,1$$$}, {$$$12,6,3,1$$$} is maximal.

So you should brute force sequence $$$g$$$ (There are up to $$$O(\log N)$$$ ways). If you determined the sequence $$$g$$$, you can do like step 2: first calculate the number of sequence that you will write, second calculate the number of ways of insertions and finally mutiplies.

Since the complexity for each $$$g$$$ is $$$O(N)$$$, so the total complexity is $$$O(N \log N)$$$. If you precount factorial and inversions, you can also solve with $$$O(N+\log^2 N)$$$.

Sorry for my poor English.

Code (Uploaded at 2:01 JST, 56 minutes after the contest)

seems that problem B shares the same trick with problem C in Global Round 3..

what i felt and is true for most cases : if u don't know proof just input garbage and get gold.

Yeah exactly same over here too!

I like problem E.

Thanks for mathforces (no)

X is 29.

Apparently this tc was not there in PreTest of F.

Naive Solns asking only type 2 queries will take atleast 8 queries.

Extending this tc — for $$$n*(n+1)/2$$$ vertices will take $$$n$$$ queries.

In the problem A, it was mentioned in the problem that order of the array should not be changed! What did that line mean and how do we reorder it without changing the order? Please Help!

"You are allowed to not change the order", not "You must to not change the order"

Please read it carefully :

I guess u miss read it as:

$$$A, B$$$ and $$$C$$$ felt like typing test. The situation drastically changed afterward :(

Very very nice contest, 10/10. Tl63 just because of using included sort. I hate this test -_-. But in general all it was good.

Can someone explain how to solve this example in F?

You can use a method named "Heavy-Light Decomposition".

wow I got TLE on test 63 and my rating is gone

The test 63 is the hack I used during the round, so I want to clarify a couple of points:

First that seems the only test with anti Quick sort test, I can see that 150+ solutions failed this test and if it wasn't added all these solution may have been passed, I've also always see Quick sort solution pass sys test in previous rounds, so I think such test should be always added to any problem that require sorting.

Also I'm not very proud with that kind of hack, because all I did is check if a java solution that uses sort for primitive array, so I want to raise attention against this.

For those who still want to use primitives you can build your own sort function like the radixSort function that I use in my solutions, wich I copied from uwi code ( I hope he doesn't mind )

JAVA submissions have been judged on the C++ time limit for the B question. Getting a TLE for an O(nlogn) approach. However I didn't use a StringBuilder which is bad on my part but still a correct solution should pass.

Problem is not time limit. Problem is the inbuilt sort in Java have worst case complexity of n^2. Hence the time limit. There is blog somewhere on the codeforces discussing this SORTING IN JAVA.

Hope that the rankings would be revised. Otherwise rating would take a great hit.

55036867 why using StringBuildfer was wrong and a get TLE? java

UPD: 55052153 problem was oin primitive types, only in that, i am so disappointed=(

Arrays.sort() for primitive data types in java uses quick sort O(n^2) while Collections.sort() uses merge sort . Quick sort can have O(n^2) complexity in worst case

So what we are not supposed to use Arrays.sort() in future contests?

in this particular case, we can use Integer insted of int, looks like its using another, type of sort, need to check source of class Arrays

Also judgement was based on 1s time limit. For java it should be 2s i guess.

Does the TLE differ for different languages?

No I was mistaken. Checked previous contests and found that time limit is same for all languages. However many other platforms have extended limits for Java and Python.

I also used BufferedReader, Arrays.sort(), and StringBuilder but still got a TLE :(

Lmao, I was so pissed when my naive solution for

Fhad bugs and didn't get accepted, while so many people solved it.Now I see anyway my naive solution would have got verdict

`Wrong answer on test 99`

xD.https://codeforces.com/contest/1174/hacks/560684/test

Wow, such a great hack. Congrats!

Wrong answer on test 99. Such pain in F

Problem FBut I still don't get why?

Clever naive soln take $$$O(\sqrt N)$$$ queries in worst test case.

Worst Test Case

I passed F in last 5 minutes. Exciting!

Thanks for the round very much!

Sorry, does the #23 testcase from F shows "wrong answer query limit exceeded"?

I made a submission with assertion but couldn't see that I was exceeding the limit. 55048680

May be it's because you have a query in your

`main`

but you didn't count that ?https://codeforces.com/problemset/problem/1054/D a question similar to today's D

Nice Contest.

Btw a simiar (a̶n̶d̶ ̶a̶n̶ ̶e̶a̶s̶y̶ ̶v̶e̶r̶s̶i̶o̶n̶?̶) of F recently appeared in Codechef Cook Off MYS00T

Problem F, a very nice tree and interactive problem! Thanks for writers.

Well I'm stupid and haven't debugged my F during contest, but here is my solution that should works but it got AC:

First of all let's know a height of x by first type of query with vertex 1, let it be H.

Let root be the lowest vertex that we know that has X in it's subtree.

So let choose a type of query randomly!

If we chose first type then just choose some vertex with height H in root subtree randomly and then change root!

If we chose second type then just change a root!

Was a randomized solution intended to pass for F?

Instead of using any heavy-light/centroid decomposition, I just picked a leaf at random for the current subtree, and then asked similar queries as given in the editorial.

https://codeforces.com/contest/1174/submission/55047296

I dont think randomized was intended. But sometimes its difficult to break randomised. Until and unless probability of failing it is high.

I did saw some randomised solns and one of my friend also used randomised in F.

Since editorial is not linked — EDITORIAL

^

Clickhereto go up! ^what about the left of your monitor xD

how. to. calculate. the. contribution. ?why. the. contribution. for. me. is. negative. ? i. do. nothing. God

Simply, as far as I know, the contribution points are the sum of the total votes you get in your blog posts and comments/replies divided by 5. Or maybe, it uses some logarithmic calculations.

If your total votes are 100, your contribution will be (100/5) = 20. And if it's -100, your contribution will be (-100/5) = -20.

Check those out:

ok. thanks.

Very neat and clear problem descriptions. Thanks to the writer.

I think there is a time limit problem in problem 2 for java. Same logic gets accepted for C++ but TLE for java..

How to solve the

problem D??