We will hold AtCoder Beginner Contest 182.

- Contest URL: https://atcoder.jp/contests/abc182
- Start Time: http://www.timeanddate.com/worldclock/fixedtime.html?iso=20201108T2100&p1=248
- Duration: 100 minutes
- Number of Tasks: 6
- Writer: evima, Eugle_na, kyopro_friends, QCFium, yuma000
- Rated range: ~ 1999

The point values will be 100-200-300-400-500-600.

We are looking forward to your participation!

Six hours left =.=

20 minutes left =.=

yay ! I am on a binge solving At Coders problems. They are really cut-the-shit and

`ad hoc awesome`

xD !!6 minutes left. Come on guys!!

4 wa in problem C.Know why getting WA but still can't fix that.That's how every contest made my day

I used lots of if-else :v :v

You can see my solution it's easy to understand

Just tell that what is output for 55555555 for problem c? My accepted code give -1..but after getting accepted I feel.it is wrong for above test as for it ans is 2(555555).. Am I missing something?

answer is 2..May be weak test case !!

Hey.Can u explain u r solution little bit?-emli-

He is checking all possibilities of digits. For each i, he considered each bit equal to 0 as not chosen and each bit equal to 1 chosen.

For each combination, he get the sum of digits and de number of used digits (# of one on bit representation). If the sum is divisible for 3, this combination is divisible too.

Then he printed the biggest combination that sum is divisible for 3.

You can make use of dynamic programming, everytime either leave a digit or add it to your total sum, if at the end the total sum is divisible by 3, then store the total no. of digits you erased from the given string of numbers. print the minimum of it. My solution : https://atcoder.jp/contests/abc182/submissions/17971476

I used $$$2^{len(|N|)}$$$ brute force. I know there are a lot of more efficient solutions, but this is the fastest to implement.

What is the brute force solution for this problem ?

Statement says: we can erase some subset of digits. There are at most $$$18$$$ digits, so at most $$$2^18$$$ subsets which is quite small. Just run through all subsets, check if remaining number is divisible by $$$3$$$ and if so update the answer taking minimum of current answer and number of erased digits.

I did exactly same using bitmasking. code

Oh nice . This idea did not even come to my mind because i was focusing on an efficient solution. Thanx

There is another brute force, That I think is easier to implement. At the first build array

`cnt[3]`

that`cnt[i]`

is the number of digit`x`

such that`x % 3 = i`

. Now lets brute force on the number of digit 1 and the number of digit 2 we will remove. codeUPD: After I think a little bit more about it, It's unnecessary to remove digit 1 or 2 more than 2 times. This solution will be O(length of the number). codedidn't need the memoization though.

Tried to fix a runtime error on E for an hour QAQ

Does anyone know any compilation flags that will be helpful in detecting out of bounds error?

-fsanitize=address

Thanks!

How to solve F ??

How to solve F plss

hint: Transform the problem to finding the number of (y — X) instead of y.

I think find the number of (y+X) is much easier!

How? There is no (y + X) is the problem?

Y is the change. I think “add” is very convenient

Oh, I mean the same thing by (y-X). let z = y-X. find z and z + X.

I thought your

`y`

is the`y`

in the problem.First of all notice that any number $$$X$$$ has unique minimal representation. This can be proved by greedy exchange (using the fact that each successive number is a multiple of the previous number).

Now, notice the isomorphism (structure equivalence) between the number bases and the (minimal) representation of each number in the system of Yens. There are two properties which are maintained:

1) If highest bit of $$$A$$$ is greater than $$$B$$$ in our Yen-system, then $$$A>B$$$.

2) Each number has unique representation.

So we can think of an equivalent problem: given a number $$$X$$$, how many numbers $$$b$$$ there are such that $$$X+b=a$$$ and $$$a$$$ and $$$b$$$ have no bit in common?

This can be solved, after some thinking, with DP.

Array

`g[]`

represents the representation of $$$X$$$ in Yen-systemWe introduce the concept of "span".

`span[j]`

represents the number of elements after the $$$j^{th}$$$ bits of X which have maxed out values of their bit. Then if`g[j]>0`

, we can use this bit in the number $$$b$$$ such that DUE TO the process of carry-over, we don't have this bit in $$$a$$$. You can see the details of dp transition in my Beautiful AC CodeWow you are so smart! Great explanation!

Can you explain the concept of Span a bit more. I couldn't get it. By the way your approach seems better than those of others to comprehend .

the "span" array is the count of consecutive elements whose bit is "maxed out" in $$$X$$$.

For example, consider a representation where $$$A_{i}=3A_{i-1}$$$ FOR ALL $$$i$$$. This is exactly similar to base-3 representation, and every bit can have atmost $$$2$$$ as coefficient. When a bit in X has 2 as its coefficient, I say that it is "maxed out".

So lets say the yen-array in given input is

`1 3 9 27 81 243`

and $$$X=271$$$ so that it is $$$222001$$$ in our yen system. Now $$$dp[j]$$$ denotes the number of ways in which we can have $$$b$$$ (in the equation $$$X+b=a$$$) such that $$$b$$$ has no bits in common with $$$a$$$ and only bits from index $$$j$$$ to $$$n$$$ is possibly ON in $$$b$$$. That is every bit from $$$1$$$ to $$$j-1$$$ is definitely $$$0$$$.

Now ,for example, if we want to have the $$$2^{nd}$$$ bit ON in $$$b$$$, and all before that OFF, we

musthave that bit equal to $$$1$$$, because BY THE PROCESS OF CARRY OVER, that bit will be OFF in $$$a$$$. And now, notice that carry over makes $$$3^{rd}$$$ bit $$$0$$$ in $$$a$$$. So the span of the $$$2^{nd}$$$ bit is 1, since now we can't have any bit as upto after span bits after $$$j$$$ as ON in $$$b$$$, because then there can't be a carry over.After that it is simple DP transition.

Are you considering bit numbering from left to right?

Left to right, as in the example I have taken.

Nice explanation! Can you suggest some more problems like this?

I just came out this solution, not pretty sure that it is correct. However it does get me AC.

The problem is same as "Find the number of integer $$$r$$$ with length $$$N$$$ (leading 0 is allowed) in base $$$A$$$ that shares no common digit with $$$X + r$$$, i.e., $$$\forall_{0 \le i \lt N}, r_i = 0 \lor (X + r)_i = 0$$$".

Let $$$c$$$ be carry, $$$y = X + r$$$, we have ($$$N$$$ = 4):

In particular, all digits $$$i$$$ satisfy ($$$m_i = A_{i + 1}/A_i$$$ is the limit of digit $$$i$$$):

Let $$$dp[i, c]$$$ = the number of valid ways to fill digits $$$[0, i)$$$ while $$$c_i = c$$$. This dp is computed from lower digit to higher digit due to carry-over.

By iterating all possible values ($$$0 \le r_i \lt m_i)$$$ of $$$r_i$$$, we can get an correct state transition, but it will get TLE. Key observation is that we don't need to iterate all values of $$$r_i$$$. Since $$$r_i = 0 \lor y_i = 0$$$, there are only few valid conditions.

We decompose $$$r_i = 0 \lor y_i = 0$$$ into 3

disjointconditions:Let's consider when will these conditions be true?

That's all for the dp transition. Here is my submission.

Chinese version

Is there a dp solution for C?

Yes. link

Please elaborate what are you storing at dp[i][j]. I was thinking something like declaring

dp[index][sum]---->Maximum digits required till index to make sum. Is that correct? thanks.

snippetI'm storing the maximum number of digits that I can take,upto index i, such that sum%3==0.

I think your code should work if you store the same. (PS. i'm very bad at iterative dp. xD)

Solved it. here is updated DP code for T: O(9*N*N) , S: O(9*N*N)

Just try every subset with bitsets or recursion. my solution

No need for that. Just count all digits modulo 3 and use this

what do you mean by "count all digits modulo 3"? Please explain. Do you mean that if number is k digits long then for every digit calculate it's modulo 3?

this comment

ok thanks!

what is the significance of min((c1-c2)%3,(c1%3-c2%3)) can anyone explain because I tried without this and only 1 test case failed

Yeah happened to me too. Try with 2224. The ans is 1. That's how I thought of this.

Yeah that's exactly what I mean. In the above code, c[i] is count of digits with modulo 3 as i, ex c[2] is the count of digits with modulo as 2.

ok,got it! Thanks

I feel so dumb now , I somehow assumed in my head that over all complexity of brute-force will be ~10^18 and discarded this approach immediately . Thanks anyways.

You can think of finding the longest subsequence which has sum divisible by 3. Then you can do number of digits — longest subsequence

O(logn) Solution using DP. My Code : Link

Brilliant solution , thanks for sharing , but is'nt the TC O(n)? Edit: TC would be O(n) where n is the length of the string , or O(logn) in this reference.

Does we have to use dfs in E?

No, just annoying implementation.

I used prefix and suffix sums on the rows and the columns.

i think DFS will work fine.I wasted time on D.or I Don't know if dfs will work or not

Not sure if this is what you meant, but you can just iterate over each column twice, once up and once down, and then each row twice, once left and once right. If you go over a block, everything after it is dark, and if you go over a bulb, everything after it is lit. So you just copy paste the same for loop like 5 times, change the bounds and you get the answer. Not really annoying implementation

ohh now I understand,thanks bro

we can solve it simply for every row right to left + left to right observation and every column from up to down + down to up simple operation

No, just optimize the brute force solution a little bit.

The brute force solution is, for each bulb, and for each direction, start from the bulb, and go along with this direction until you meet a block, set each grid passed illuminated by the bulbs. And then, iterate all grids, count the number of grids illuminated by the bulbs. The time complexity is $$$O((H + W)N + HW)$$$.

The brute force solution might get TLE, although I think it's time complexity is good enough to pass.

While going along with one direction, you can stop not only when you meet a block, but also when you meet a bulb. If you do so, the time complexity will be $$$O(HW)$$$ cause you will pass a grid at most 4 times.

Thanks! That brute force modification helps to not get TLE.

Using this matrix struct with already clock_rotate, you only need to repeat 4 times rotating the matrix every rotation.

Submission

please anyone explain solution for D

Hope u understandCalculate prefix sums on the input. Also calculate the maximum sum you achieve on the input for every $$$0$$$ to $$$i$$$, where i is from 0 to N — 1 (0-based indexing). Then, you can find the maximum coordinate by iterating from 0 to n and adding the maximum sum in range(0, i) to your current coordinate.

CodeLet us define end[i] as coordinate after the end of ith round (let us assume 0-based index) then, end[i] = end[i-1] + prefix[i]

Now, if your answer is after round i, and before round i+1

ans = max(end[i], end[i]+prefix[0] , end[i]+prefix[1] , end[i]+prefix[2] ,..)

ans = max(end[i], end[i]+max(prefix[0],prefix[1],..,prefix[i]))

sudo code :

Thanks man, really helped!

It was an issue in translation. In Japanese version of issue description it stated that 'positive direction' = direction where it should move. So we take final position of robot after series of move and apply next line of steps. Taking a sample 2, we have robot movements: I1 (-2) [-2] I2 (-2, 1) [-4, -3] I3 (-2, 1, 3) [-5, -4, -1] I4 (-2, 1, 3, -1) [-3, -2, 1, 0] I5 (-2, 1, 3, -1, -1) [-2 ,-1, 2, 1, 0] Among all steps robot position 2 was biggest one

What's the idea for E? I spent 50 mins on it thinking it was easier than D but I couldn't get it to work on one of the sample tests; probably some implementation errors. D was easier than I thought though. Great contest, thanks!

HintThe key idea for E is that you can remember if you've already visited a square when going in one of the 4 directions, so you can reduce the number of iterations. My solution: https://atcoder.jp/contests/abc182/submissions/17982339

thanks;)

There are a lot of ways. Shortest would be: assume light doesn't pass through a square with another light bulb, which doesn't affect the answer, and then for each light bulb iterate through all squares it illuminates and mark them (with the modified rules each square will be touched at most $$$4$$$ times, so it's $$$O(HW)$$$).

Thanks rchaves and Proszek_na_ludka, understood.

am I the only one who solved it with Binary Search ?

What's your idea with binary search?

Can you provide link of your solution?

How to solve E. My

O((H+W)*N) solution gave TLE.solution with commentHow many fake account do you have?

Rudro25_ ,Rudro25. BD_King. CF.

4/5 — cause of 10 minutes comment restriction !! I attend contest by only one account.. I respect the CF rule :|

Press X for doubt Rudro25

I have this exact this approach but instead of int[][] I used vector<vector> but get TLE at big test cases. Poor me

can someone explain sample test case 2, problem D, how the answer is 2?

The positions after each step are:

SpoilerTherefore, the greatest coordinate occupied is $$$2$$$.

thank u very much. My bad, I wasn't go through all step edit:got AC now T_T

Problem C and D were easier to do than B for me. Can anyone explain how B should be done?

You can just brute force for the possible value of the answer from 2 to 1000. Whichever value gives maximum count of divisions is the answer.

My bad....that should have been pretty easy :(

I just check for all prime numbers but still got AC.

Brute force numbers from 2 to 1000 and calculate how many numbers in A are divisible by them. The one with the maximum count of numbers divisible is the answer.

How to solve problem F?

https://codeforces.com/blog/entry/84405?#comment-719394

How to solve C? People are saying it can be solved using DP. I don't know DP. Can anyone please tell me which variation of DP should actually I learn(as DP is huge) to be able to solve this problem(C)??

It's a standard knapsack problem. For every digit you either use it in the answer or you don't.

Oh! Thanks dude. I shall really look forward to learn standard knapsack asap and solve it.

Pls share your solution.

CodeJust an optimization that will help you in solving a lot more problems, when you call the solve function, you pass $$$sum + c$$$ you should take module $$$3$$$, this way the sum will never be $$$\ge 3$$$. In the return statement, check if the sum is $$$0$$$ then the number is divisible by $$$3$$$. This way you will reduce the states and your code will be much more faster.

u can use recursive, it will be O(2^digit)

By generating all possible subsets?

yes, for easier implementation, I use string for storing the input

It can also be solved by observation.

https://atcoder.jp/contests/abc182/submissions/17985247(The code is a bit messy though)

well, ok!

It can be solved using greedy approach as well. As for N to be divisible by 3, sum of its digit must be divisible by 3. And sum%3 can be either

0, 1 or 2.If its 0 than we have to do nothing.

If it's 1 then we remove one digit (which is

1 mod 3i.e. d%3=1) or 2 digits (which are2 mod 3.i.e, d%3=2).Similarity for the case where sum%3 = 2.

If we aren't able to remove the digits in such a way then answer is -1.

Thanks. i feel so dumb for not seeing this. xD

Great! How I missed this idea! :")

Same greedy done by me and i thought i had done a very similar problem on cf earlier with almost same approach.

Can you give the cf problem link?

I think the solution with bitmasks is pretty nice

My submission

Thanks! Can you suggest me any blog/resource to learn this technique?

Hi! I think a good resource for bitmask DP is this HackerEarth tutorial, I remember it helped me understand the logic behind it. After that, it's just solving problems, some problems that come to mind, from easiest to hardest, are 580D - Kefa and Dishes, this CSES task, 16E - Fish, 678E - Another Sith Tournament.

Thanks a lot dude! You're awesome :'D

You can also try this

Can someone tell me what are the 21 solutions to the last sample of problem F, I don't get how there are so many.

Can anyone please tell me what's wrong with my code for E: https://pastebin.com/1WPa7pUD ? EDIT: I finally fixed it...I am so stupid!

is it possible to see the submission of other participants after the contest at Atcoder.??

Yes, for example, see my submission in my comment here.

But I am not able to see the solution of particular participant in the standing section as we have in codeforces where we just double click on the submission to view the code.

Click the magnifying glass next to a user on the standings to see their submissions.

I recorded a video of me solving the contest: https://youtu.be/VsUvBvgeb9Y. I got 64th, solving all problems in about an hour.

Your solution for solving F is fantastic.

Thanks for sharing that.

Here is my editorial for this contest.

English editorial

中文题解

Can we use line sweep for E to solve for any H,W.

For problem C what am I missing , its WA https://atcoder.jp/contests/abc182/submissions/17965994

Please help!!

https://atcoder.jp/contests/abc182/submissions/17972323 hope this helps!

Yeah!!

Got the better approach :-)

But still dont know which case is missing in mine

Anyway thnx :-))

Spoiler985198Correct answer:1(remove 1)

Your answer:2

Thnx a lot!!

SpoilerMore tests(in which your solution fails):

Here's a screencast of being destroyed by daylight saving time, also includes solutions to all problems

Thanks. It' ll be great if you could upload some video on algorithms and important data structure for beginners that will be really helpful for all beginners.

Please tell me, what is the test case20? I just get WA in this case...QAQ

For Question E will a flood fill(dfs) approach work?

probably TLE, why don't you try it..

it wont work,thought on it as it will try searching for connected components of squares which is not what we want

Nice contest