Hello, Codeforces!

We, DK318 and unreal.eugene, are students of ITMO University. And we have recently joined the developers team of Codeforces and Polygon. We have prepared this round for more careful acquaintance with Polygon. Very soon you will be able to see the first results of our work as developers.

Except us, in round development participated MikeMirzayanov, geranazavr555 and doreshnikov. We hope that you will enjoy the competition!

Codeforces Round 731 (Div. 3) will start at Jul/10/2021 17:35 (Moscow time). You will be offered 7 problems with expected difficulties to compose an interesting competition for participants with ratings up to 1600. However, all of you who wish to take part and have a rating 1600 or higher, can register for the round unofficially.

The round will be hosted by rules of educational rounds (extended ACM-ICPC). Thus, during the round, solutions will be judged on preliminary tests, and after the round, it will be a 12-hour phase of open hacks. I tried to make strong tests — just like you will be upset if many solutions fail after the contest is over.

You will be given 7 problems and 2 hours 15 minutes to solve them.

Note that **the penalty** for the wrong submission in this round (and the following Div. 3 rounds) is **10 minutes**.

Remember that only the trusted participants of the third division will be included in the official standings table. As it is written by link, this is a compulsory measure for combating unsporting behavior. To qualify as trusted participants of the third division, you must:

- take part in at least two rated rounds (and solve at least one problem in each of them),
- do not have a point of 1900 or higher in the rating.

**Regardless of whether you are a trusted participant of the third division or not, if your rating is less than 1600, then the round will be rated for you.**

Thanks to ashmelev, Monogon, CtrlAlt, Tzak, FelixArg, antontrygubO_o, bugdone and brian for testing the round and improving tasks.

Good luck!

**UPD 1**

I hope i could never give div 3 rounds officially after this :)

Good luck! Actually, there will be many little guys of my school participate this round tomorrow. Hope everyone can learn and enjoy from this round! :)

hope you achieve your goal, bro.

The feeling is mutual.

So a participant new to codeforces is not a trusted participant right!

Hoping to get positive delta on my birthday!

Positive delta in terms of rating, not the covid variation xD

Happy Birthday!!

I hope i solve A faster and not quit from contest.

Hope to get the cyan color again on my profile :) after this round .

Hope to be expert for the first time in my life. (UPD: WOW, DREAM COME TRUE)

Yeah,wish you and me good luck. I hope to be expert for the first time in my life too!

I have been expert once: it is fantastic. You should absolutely try this life experience too, good luck!

Dream come true for me too!!

Hopeforces

Hope I finally leave this drab, lifeless colour behind

Hope I can enjoy the contest and get my first in-round-full-solve :)

I was just wondering why Mike Mirzayanov never give any contest!!

While best coders are grinding to get one black letter, Mike is casually sitting with full black nickname

the user has to be an IGM to have one black letter?

Not International but Legendary Grandmaster

Mike is most likely occasionally participating in some contests hosted on the other platforms. At least that's how I interpreted his blog post posted two months ago.

Coaches don't play!

Hope to get my nickname colored

Hope to become blue this time :)

Hope I will continue hoping after this hopeful contest.

![ ]()

FamilyForces

I was wondering who can create contests and how do you do it?

This blog should answer your questions.

Hopefully I hope to hope

Hope i will learn some important thing from hopeful contest

Nice joke

Hope

SpoilerCome on, you hesitate between codeforces and leetcode?

2 contests back to back! Hoping to have a good weekend...

Hope that I will gain confidence after this.

orz

Hope to gain some confidence after a string of disastrous rounds.

I hope to become an LGM after this round.

-_-

Well, I can at least hope

My first unrated contest ><. Feels awkward tbh, after giving every contest to gain rating.

Much waited for this but Clashing with Leetcode :( ,anyways preferred cf over all others :)

O, new authors, cool. This Div 3 promises to be interesting.

I got one wrong answer in the last div3 round because of just one

`#define int long long`

,hope not to repeat the same mistake again.How can using

`long long`

instead of`int`

cause WA?Probably it was TL cuz LL consumes more time.

Div3 is always High HopesSpoilerMy kind of High Hopes

Oh no.. I have to read for tomorrow's exam. But today is my long awaited Div 3 contest. Confused which to choose!

It's obvious, isn't it?

Good Luck EveryoneWishing best to the new authors ! Hope they wont let me miss vovuh div3s

Hope to be specialist in this round

after contest : i hope not to become newbie

I really like these problems. Thank you for this round!

guess it's time to finally learn bit operations lol

you didnt need bit operations for D

Bring back King vovuh

vovuh orz

voted mistakenly

This is the first time I pass all problem's pretest in one round. Thanks for this round!

I used SCC compression in problem G. I wonder if this is an overkill.

i dont know what youre talking about so i think it is. You can just do dfs and not pass through a vertex twice if it has infinite paths

Could you elaborate on that? Do you mean just calculate the SCCs and then bfs out or something like that only counting the first two visits? Or do you mean avoiding SCCs altogether.

Ok so my idea is that you do a dfs and mantain which vertices were in the path of the current path of the dfs. If you can go from that vertice v to a vertice p on the dfs path from 1 to v, then p has infinite paths to it.

Then, you can call a dfs to p like it would normally do and for each vertice it goes through you mark that vertice as also having infinite paths. This doesn't explode into insanity because as mentioned in the other comment you can choose not to go on vertices marked as having infinite paths (you will pass at most twice for each vertice).

You can also mark the other types of values like having 1, more than 1 or no paths pretty easily as well

Yeah I also modified some scc compression code to solve this problem but it does feel overkill for a Div3.

xD I used that same reference code when writing my solution. Definitely felt overkill, I've only seen SCC actually required on like GM+ level problems.

Can you comment what is wrong in this solution?

I was trying to make topological order of this graph, the nodes that do not appear in this are in some cycle. Then I found the number of paths of nodes in topological order and the nodes that are in cycle and get -1 ,if they are connected to 1, else 0. WA submission

I also used SCC compression to get the dag. Then using bfs to count 2 visits at max. Then using if any node in a single SCC containing multiple nodes is reachable then all nodes present in that SCC are -1. Then every node which are reachable from those -1 nodes are also -1. This can be found using multisource bfs with the -1 nodes. Don't know if it is overkill.

Gud contest, the problems were amazing. I wasn't able to solve full of it but that's okay though.

Couldn't solve E. But the contest was amazing. Liked the problems... Any hints for E?

You can see that after each move each array in A will contain one more element of it in the initial array. SO after n move => every element in A will contain the gcd of n + 1 element in the initial array (that's the worst case). If after k moves and we have an array which all of its elements are equals then that will also true for k + 1 and so on. So the main ideal here is to do a binary search on k and use sparse table to calculate the gcd from l to r in O(1) to make sure the complexity is O(nlogn). (sorry for my bad en)

This is for prob F, anyway Thanks :) I waited for this

Can use multisource shortest path kinda thing for E..

Actually, after a lot of thinking, I realized that the solution of E is pretty straightforward.

We need to scroll from left to right, maintain the answer, and scroll from right to left and maintain the answer. It doesn't matter which way we scroll first.

My solution LINK

I have solved Problem F using Segment Tree + Binary Search. Anyone who has solved this with the same approach? Just want to know.

I thought the same but was really solving slow this contest!

You can use a sparse table since the array is static. Mine passed in 155 ms. 121971699

Probably worth noting that $$$O(1)$$$ sparse table queries work here because gcd is idempotent.

Yes, I should have to use Sparse Table for that. Although, Segment Tree worked.

I used Sparse table + Binary search but I think segment tree should be sufficient. Because the time complexity of your algorithm should be O(nlog^3(n)) and n = 2e5, so you need 1.16*10^9 *C operations in total which should fit in the time constraints (4s).

Upd:Forgot to include the gcd

Mine didn't work. I tried Segment tree + binary search, but ended up with TLE. Had to change it to sparse table to get accepted.

Hm I guess the constant for the segment tree and other operations is too big

Correct me if I'm wrong, but how will segtree + binary search be $$$O(n log^2(n))$$$ here?

We will have $$$O(log(n))$$$ steps of binary search. For each step, we will need to process the answer for $$$n$$$ positions. For each position, the segtree will make at most $$$O(log(n))$$$ "combinations" of answers of child nodes. Each of these combinations will require an $$$O(log (n))$$$ gcd operation. So won't the total be $$$O(n log^3(n))$$$? While this could still pass (needs around $$$10^9$$$ ops and 4s TL), it feels risky. Or are you using a different approach that only needs $$$O(n)$$$ queries of the segtree?

Whoops, totally forgot about the gcd operations which costs O(logn) my bad

doesn't exist a way to do binary search inside a seg tree? I think errichto mentioned something like that sometime. When you are in a node if gcd so far is small enough you try left at first, secondly right else you say the node is too big and you go up in the tree

https://codeforces.com/blog/entry/63771

apparently lots of gcds chained are fast I also did segtree + binarysearch, passed with 1300ms

Segment tree without Binary Search https://codeforces.com/contest/1547/submission/121982647

i solved using segment tree + two pointer.

I think I might be the only one with a non-binary search and non-segtree approach for F. Could not get AC so I'm not even sure if it's the right approach.

I couldn't get AC in time, but does the approach sound correct?

I asked anandOza it is too slow there is many primes 70000n is too slow. but you can improve it not many primes appears a lot so you must remember at which index a prime appears and compute the longer interval on that (not confirmed solution though) but give it a try

For any prime p at appears in a[i] (ie, a[i]%p = 0) ,if p appears in a[i+1] too, then continousLen[p]++. Else contiuousLen[p] = 1.

This way you don't have to look at all the primes, but only those that are appearing in the number a[i]. We also update the maxLen over such primes only. Consider this similar to lazy updates.

So this should effectively pass in the the TL. This would be O(N * |max number of primes in one number|) Does this make sense?

it definitely make sense to me, that's beautiful

Thanks. Unfortunately thought of at the last minute so no AC. But i'm glad you liked the solution.

was F binary search with segment trees

that is how I solved it, yes

There is a solution with Sparse Table.

Simulate the process, but take adjacent equal values together as a pair of $$$(value, count)$$$

Good contest

Choked so hard on F, had every single idea except for the right one until 15 minutes for the contest to end

Can someone explain what is wrong in my solution for problem E?

Code

you need to check suffix too , I guess only prefix is checked by your solution!

See this same idea

can someone tell me why I am getting this error on C and what does it mean - wrong answer Cannot merge "a" and "b" to get given output (test case 1)

Since we need to merge the actions of both programmers, we need to take actions (numbers) from already given sets i.e. 'a' and 'b' and merge them. So, every element from 'a' and 'b' must be present in your output, not more not less. Your output may have one or more of the following problems: - There maybe an extra element in your output or - Maybe some element is missing or - Maybe relative order of elements in 'a' or 'b' or both is being changed.

For me, problem statement in C was very big and boring, totally -> nice contest

This was a great contest. What was the idea on problem F? I only got to the point that the final array will have all elements = gcd(x1,x2,x3...xn). Can you tell me the thought process?

After k processes, the element x_i will be: gcd(x_i ~ x_{i+k}). To calculate this, You can use sparse table.

A and C felt somewhat bashy but otherwise contest was fine... G was a decent problem but I kept bricking on it until I realized I needed to change like two lines :| guess that's what I get for not learning SCC.

Curious on how people solved F -- I ended up using segtree but this is obviously not intended.

How did you solve F with the help of seg-tree? Can you explain, please?

After $$$k$$$ steps $$$a_i = \gcd(a_i, a_{i + 1}, \cdots, a_{i + k})$$$ (indices taken $$$\mod n$$$). Thus you can binary search on $$$k$$$ to get the answer.

Since $$$a_i$$$ is equal to a $$$\gcd$$$ range in the original range, for a given $$$k$$$ we query this value for each $$$i$$$. Solution thus takes $$$O(\log n * n \log n) = O(n \log ^ 2 n)$$$. Look at my solution if you're curious about implementation.

Wouldn't the gcd add another log factor? Or am I missing something?

SecondThread was touching upon this in his stream, he claims that it wouldn't because of the nature of $$$\gcd$$$ decreasing at most $$$\log \text{max}(a_i)$$$ times before it'll reach $$$1$$$ (or something like that). I'm not really sure how the analysis works, maybe he can shed some light on it.

Oh, I always assumed segtree gcd queries would take

O(log^{2}n)I could be totally wrong here, but this is what I was thinking. Maybe some LGM who has a bigger brain can either confirm/deny this:

So like, the GCD can only actually change log(n) times. Each time the GCD call goes one iteration deeper, that means that the answer will decrease by a factor of about 1.6, and this happens across all layers.

The more general version of my hypothesis here is that: if you are calling the GCD with the result of previous calls n times, I think your runtime is really O(n + log(maxVal)), rather than O(n*log(maxVal)). I haven't heard other people say this before, so it might be some huge holes in my logic that makes it not true, but it seems cool enough to be interesting.

The number of accepted solutions increased gradual way.

Proves that Level of question increased in a very uniform way. Loved this !!!

Even if the problems were all of the same difficulty you could see a similar pattern.

Let's assume that everyone approaches the problems in alphabetical order, and that different coders solve problems at different speeds. The first problems will be solved by a lot of people, and the last ones only by a few very fast participants.

The distribution of the number of accepted solutions is not a proof that the problem difficulty was increasing in a uniform way.

How to solve F ?

Few observations I made :

Answer is gcd of whole array call it g.

The steps for a element ai are-> gcd<ai,ai+1>,gcd<ai,ai+1,ai+2>,...gcd<ai,...an,a1,a2...ai-1>

The minimum step# which gives g in above sequence let that number be y.

Answer is maximum over all y for all i.

Observe that After performing a minimum number of steps each element of array will be equal to the gcd of the array.

I used a segment tree with binary search. Note that gcd never increases, So suppose if I am finding the minimum number of operations that are required to make this element equal to gcd, then I can do a binary search on range $$$[i,n]$$$. If we are unable to make the element equal to gcd then do a binary search in the range $$$[1,i-1]$$$

Our answer is equal to the maximum operations that any element needs.

Does it take time for the rating to appear on my profile? Thanks

You gotta at least wait for the hacking phase to end (for educational rounds and Div 3 rounds) and then it will take another few hours for the final system test to come, so basically you have to wait 12~24 hours. But for other rounds, it takes about 2 hours for the rating to be updated.

I solved F without using segment tree/ sparse table/ binary search, although it may fail for some strong tests :(

I cannot locate error in my submission for Problem C?

Submission: https://codeforces.com/contest/1547/submission/121993312

Please help me out!

imagine i=n, and it's possible to complete with b, your j will grow to m with the while and then make a runtime error in your else (in b[j]<=k) and the condition j<m, I think so it would work

I got it. Thanks!

Any idea for E?

Or simply go once in the array from left to right, ans[i]=min(ans[i], ans[i-1]+1)

Then do the same from right to left.

I was 1199, and cf predictor shows -5. Seems like I'm the cursed one

Which cf predictor are you using. Please share link.

for firefoxfor chrome if the links don't work or you use safari, opera, vivaldi, or anything else just google cf predictor web extension

I think you might reach pupil :).

CF predictors tend to show lower sometimes

I noticed that top-ranked guys solved the first several problems within 20 mins. I was like, how is that possible...

I'd say that I came up with the solutions once I understood what the problem was saying. And I also didn't get any WAs for those problem, which would incur delays. But it still took me about 50 mins :(.

Is there any special techniques other than reading/coding speed that makes those guys incredibly fast?

What I have observed is that there are many factors behind their incredible speed.

First of all, they are quick at thinking and realizing what needs to be done to solve the problem. That usually comes with practice and experience.

Second thing is that apart from clear thought process, they have a much simpler and smaller implementation than most others.

I am not sure about this one but I think that high speed also comes from reading and understanding problems fast, leaving out the irrelevant details and focusing on what is important to solve the problem, hence reducing the effective problem reading time.

Why rating changes from Codeforces 730 were reverted and again evaluated ? Anyone please answer..

sometimes cheater are found afterwards and their standing is decrease, sometimes the contrary happens, someone proves he's not guilty. and so it's necessary to recompute the ratings (I earned 1 point more) somebody obfuscated his code maybe he was considered a cheater

I thought that problem C is a simple dfs but I got tle. Is there a specific pruning condition?

It is more greedy like.

You simulate the process, that is, whenever one of both people want to add a line, we add a line. Else the one with the smaller index changes that line.

If there are not enough lines to change the current line then there is no solution.

hint/help for D

think greedily what is the smallest value you can append to y. you start with 0. to know what the smallest think about each bit if it's needed

Choose y[0]=0.

Then choose for all subsequent y[i] the smallest possible value to set all bits of x[i-1]^y[i-1]

Something Weird happened with my submission for problem G, today. My initial submissions gave wrong answer on test 3 on submission. After the contest I found that the 4599th output of my answer differed from original answer. I made another submission and found that this was the test case my code was printing wrong answer to:

1

4 4

1 3

1 4

4 2

3 4

(Found using — this submission (See participants output for test case-3).

But when I ran this test case (in codeforces custom invocation) with my original solution it gave correct result, whatever was expected. (Original Submission Link).

Can someone help, where did I made the mistake. I am new to this platform, so any help would be appreciated.

Thanks for the round! Here's a link to my screencast.

Deleted

So after a long wait Division 3 contest is finally back. Solved 5 problems and I feel skipping the LeetCode Biweekly Contest 56 which was running at the same time as that of this contest was finally worth it!!

I Hope I reach another color this time .. just got bored from the gray color :(

Is it really necessary to use a profile picture with a swastika?

I am the only one who feel nasty statement for Problem C :):), and ended up without solving :):)

I did get confused when I first read C, especially when my perf was so high. I went straight to the example first, then went back and read the rest to check if I missed anything. The parts that that describe Monocarp and Polycarp's sequences are identical, so you can also skip those after a quick glance.

i missed vovuh

.

Are solutions with multiset or priority queue for F getting too?

This has been a very exciting contest for me. Thank you very much!

I wish i could finally be cyan.

Was this contest supposed to be unrated?

The round is

Rated. Just Wait.Why is the round unrated for me? I am at 1399 and trusted participant as well

I don't think anyone has got their ratings for this round yet because it states that whether you're trusted or not this round is rated for everyone <1600

I can see it is unrated in my chart.

why r the ratings not yet updated??

Ratings are finally updated!

HopeForces worked sharply on my rating LOL