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(Idea and developng — gritukan)

Auto comment: topic has been updated by gritukan (previous revision, new revision, compare).Auto comment: topic has been updated by gritukan (previous revision, new revision, compare).Auto comment: topic has been updated by gritukan (previous revision, new revision, compare)."BONUS (medium): Given graph is not properly colored, but you don't have to minimize size of the set. Can you solve it?"

Yes, that's what I solved yesterday before solving actual problem xD

"BONUS (hard): Find answer minimizing number of subsequences."

Sorry if I'm missing something but isn't number of subsequences always equal to number of 0s — number of 1s, as each subsequence chosen increases number of 0s — number of 1s by 1.

Yeah, you are right, it was a joke :)

The two bonuses for "Binary cards" are the same, should they be?

Oops, my bad. It should be

n≤ 10^{5}in the second challengle. I'll fix it now.Please help in ques C, why am i getting TLE

http://codeforces.com/contest/950/submission/36191394

Thanks

"BONUS (medium): Given graph is not properly colored, but you don't have to minimize size of the set. Can you solve it?"

If a person stores his data at computers

xandyand initiallycolor_{x}=color_{y}then ifxis in the set we choose thenywon't. Similarly ifyis in the set thenxwon't. This is NAND 2-Sat clause. Additionally like in the statement we add directed edges for the cases — they are equivalent to implications.Well now for the medium problem we simply need to find a valid 2-SAT solution with at least 1 variable true.

Well we simply try fixing all possible variables to be true and then check for a solution. This way we achieve . Probably there is a faster way to do it but still this should work.

The main reason for this comment is because I think I have a solution for the hard version. Not sure it's correct tho.

So let's assign costs to the vertices. We assign a cost of

-1to all variablesxand a cost of0to . Now we search for a 2-SAT solution of the maximum cost with at least on1set to the original variables. Well this should be possible to be solved with the Maximum closure algorithm.We again try fixing every variable and then running the algorithm.

The overall complexity will be .

UPDATE:it's wrong.Your solution for medium version is correct, of course. There are several ways of optimizing it to

O(n+m) (for example by considering two cases), however it's not very interesting.I'm not completely sure about your solution for hard version, because I'm not sure if there are some correspondences between 2-SAT solutions and graph's closures as closure doesn't give any restrictions on taking both

xand !xor taking none of them.Yeah you are right. I forgot the fact that in graph closures you don't have a restriction about taking

xand !x.can some one plz tell me why my code is giving wrong answer for test 8 in Div 1 C. https://ide.geeksforgeeks.org/jwqoTyGzAy

Can anyone tell me how to maintain the list of zero's and almost zero's efficiently in the problem 949A-Zebras?

In F, what's the exact expected number of intersections we need to check, without O-notation? I solved the problem with a different random scheme, but had to const-optimise like crazy to be able to compute a sufficient number of intersection points. Since (2

N)^{2}is approximately 27 million and computing one intersection + checking if it's valid requires a lot of operations, that 5s time limit is really tight. Even worse, with a non-deterministic solution, there's a non-zero chance of any solution having to check twice as many intersections on some test and getting TLE there.I'm not surprised it has so few successful solutions to date and the only 2 solutions that passed pretests failed systests. Designing a solution that passes systests through anything but luck seems impossible (unless it's deterministic — does such a solution exist?).

It seems I have a solution for E that's linear in

Nand almost independent on (just through polylog).The extra observation is that when we decide to use cards for the first

kbits and skip the card for bitk+ 1, we can shift eachA_{i}by any number in a common fixed range [l,l+ 2^{k}) that contains 0 — the value oflcan be chosen arbitrarily by setting the cards' signs. This shift needs to make eachA_{i}divisible by 2^{k + 1}, but since we can only shift by at most 2^{k}- 1, the number we need to shift to is uniquely determined. This tells us a possible value oflfor a givenk(or that it doesn't exist).This gives an obvious recursive, possibly exponential solution: try all possible

k, shift eachA_{i}and divide by 2^{k + 1}, solve for this modified array recursively if it's possible to choose a validl(stopping when everything is 0) and addkcards; choose the option that gives the fewest cards.Now, intuition says we could take the first

kthat gives a validland set of shifts. I don't have proof this works, but I submitted it and got AC. (In fact, I got AC even with the possibly exponential solution. Idk if it can be hacked or the tests aren't strong enough?) Either way, since the recursion doesn't fork, this is clearly .plzz provide correctness proof of 'Zebras' Div1A?