### JATC's blog

By JATC, history, 17 months ago, ,

Sorry if the tutorial for F is too long.

• +87

 » 17 months ago, # | ← Rev. 7 →   +31 As for D, there is a simple O(N) solution. First of all, let's forget about a and b less than 0 We can observe that score is increased on each integer as many times, as this integer appears a divisor of some other integer. This happens floor(n / i) — 1 times for number i. Then we can see, that we have a mirror situation with a and b less than 0. And with a < 0, b > 0 and a > 0, b < 0 works the same. That's why answer is sum of i * (floor(n / i) — 1) for i from 2 to n multiplied by 4. Here is my solution 45732442
•  » » 16 months ago, # ^ |   0 Why every "i * (n / i — 1)" can be choosed?
•  » » » 16 months ago, # ^ |   0 eg: 6->2, -6->2, 6->-2, -6->-2 in all the above case 3 is the divisor of the integer 6 so suppose n=18 then 3 appears as divisor for 6,9,12,15,18 so the score becomes 3(|x|:divisor) * 5(floor(n/i)-1) * 4(for a,b +ve 0r -ve cases).
•  » » » » 16 months ago, # ^ |   0 thats what i think how it is please correct me if wrong.
•  » » » » 16 months ago, # ^ |   0 Thank you!给你花花！
•  » » 16 months ago, # ^ |   0 Thanks for suggesting this trick.Learnt something new.
 » 17 months ago, # |   +7 A can be done by an O(n) algorithm by just traversing once along the array
•  » » 16 months ago, # ^ |   0 yes i have done the same :)
 » 17 months ago, # |   0 In problem D.Could someone elaborate more on the proof that all the nodes are in the same component?
•  » » 17 months ago, # ^ | ← Rev. 6 →   0 Set of numbers that can transform into a number x is always even (if a can transform to x, -a can either), so the graph built by connections that based on two numbers which is transformable to each other or not will have vertices with even degree, so the graph is Eulerian, which means you can travel through all the vertices without coming back to previous vertices. And so all the vertices must be in a same component.I guess.
•  » » 17 months ago, # ^ | ← Rev. 3 →   +3 Suppose you transform a into b and |a| < |b| then x = b / a right? It's clear that a, b and x are in the same component. You can see that |b| ≤ n and |a| ≥ 2 so |b / a| ≤ n / 2, which means you are able to transform x into 2x as well, that makes x, 2 and 2x belong to the same component. So for every node that has at least an edge attached to it, we know that node is in the same component as 2.
•  » » 16 months ago, # ^ |   0 how to solve this problem? Can someone provide a simpler version of this problem or can explain this problem? Thanks in advance :)
 » 17 months ago, # |   +22 O(sqrt(N)) code for D: https://codeforces.com/contest/1062/submission/45742622
•  » » 17 months ago, # ^ |   +8 Cool solution, that uses the same idea as my, but faster
•  » » 17 months ago, # ^ |   0 fascinating solution :)can you please explain it? especially the line below: ans += (cnt * (cnt + 1) / 2 - 1) * (r - l + 1) 
•  » » » 16 months ago, # ^ |   0 https://codeforces.com/contest/1062/submission/45724128 It's this solution but optimized. The answer is: for each i, for each multiple of i, sum j / i as can be seen from this code. N / i is the number of multiples and you can take that sum in O(1). Now, just group the i's by the value of N / i.
 » 17 months ago, # |   +3 Can someone share their code for problem E with same solution as the editorial?
•  » » 17 months ago, # ^ |   +6 My implementation is almost the same as the editorial.One difference is that my range queries return the two smallest and two largest dfs-order labels in [l, r]. We will either delete the smallest and use the LCA of the second smallest and the largest, or we will delete the largest and use the LCA of the smallest and second largest.The editorial instead suggests to make additional queries on [l, u) and (u, r] to simulate deletion of node u.
•  » » 16 months ago, # ^ |   +8 You can find my solution here. It's the same approach as the author's, provided a quick explanation to the thought process commented above the code. If you have any questions, please let me know :)
•  » » » 16 months ago, # ^ |   +1 Thank you very much! Your clean code helped me learn and implement lca and solve this problem.
•  » » » » 16 months ago, # ^ |   +3 You're welcome! Glad i could help :)
 » 17 months ago, # |   +4 Can someone share their code for problem D with same solution as the editorial?
•  » » 17 months ago, # ^ |   0 following.
 » 17 months ago, # |   -16 Codefores is the best!!!
•  » » 16 months ago, # ^ |   0 Then why to cheat?
 » 16 months ago, # |   -7 Am i the only one who solved D in less than 10 lines?
•  » » 16 months ago, # ^ |   +1 Me too, and it was a O(n) solution.
•  » » » 16 months ago, # ^ |   0 Here is my O(n) solution.
•  » » 16 months ago, # ^ |   0 I an not able to understand how to solve that problem. Please can you help me with this. I know the theory behind Euler's path and graphs but how to think this problem can be solved using graph? Any help would be appreciated.
 » 16 months ago, # | ← Rev. 2 →   +3 There is an O(n) complexity algorithm for A. Since we need to check for the longest set of increasing difference-by-1 consecutive elements in the array, we don't need to use all pairs i,j. It can be done by for i in size of array, if a[i]==a[i-1]+1 and a[i]==a[i+1]-1 then we increase the delable_currentsize_var by 1; else (means we find the barrier of the increasing set) we update max_delable_size = max(max_delable_size, delable_current_size) and reset the delable_currentsize_var to 0.https://codeforces.com/contest/1062/submission/45727163
 » 16 months ago, # |   +83 An alternative solution to problem F:First, find any topological order of the DAG.Observation 1: A city is important if and only if all the cities before it can reach it and all the cities after it can be reached from it.Observation 2: In a DAG, vertex v can be reached from any other vertex if and only if v is the only vertex to have no outedges.From 1 and 2, we can find which cities are important(by adding the vertices in the topological order and maintain a set of the cities with an outdegree equal to zero). This is O((m + n) log n) and with some tricks it can be done in O(m + n).Now, let's focus on semi-important vertices:Observation 3: Assume that v is a vertex without outedges in a DAG. Then v can't be reached from exactly 1 city if and only if: There is only one city without outedges apart from v(let it be u); There's no vertex with exactly one outedge that points to u. So through restoring the vertices with exactly one outedge and how many times each vertex is pointed to by these vertices, we can easily deal with semi-important vertices in O(m + n).Submission: 45770465
•  » » 16 months ago, # ^ |   0 Correct me if i'm wrong. The topological ordering is not so important with two node that can't reach each other, right?So with test case 3, 5 4 1 2 3 2 2 4 4 5if i change the topo order before we apply solve(tsq, G), particularly node 3 and node 1 ( swap(tsq[3], tsq[4] ) ), your code will give answer 4, instead of 5, which is WA.
•  » » » 16 months ago, # ^ |   0 Swapping node 3 and node 1 should be swap(tsq[0], tsq[1]).
•  » » 16 months ago, # ^ |   0 Nice solution. I have found a similar one, but mine is a little bit more complex.
 » 16 months ago, # |   0 What is the intuition behind C's solution? Someone explain please.
•  » » 16 months ago, # ^ |   +6 Solve the problem by hand for some cases, and you should realize that each time the numbers keep doubling. If the whole array is ones, then a number at step i will contribute (2^(i — 1)).However that doesn't hold for zeros, so you assume everything is ones, then subtract the excess.
•  » » » 15 months ago, # ^ |   0 By doing 2^(length-1) — 2^(number of zeros), it gives wrong answer(due to some negative values in testcase number 3),but by doing 2^(number of zeros)*(2^(number of ones)-1),it gives correct answer,why?
•  » » 16 months ago, # ^ |   0 it is like when you transfer from binary to decimal and you should take attention that you should take all ones first so if the number is 101001 you can say the number is 111000 * take care that if the number is 111111 the decimal will be 2^6 — 1 and if if the number is 111000 the number is 2^6 — 2^3 so the solution is 2^(all segment) — 2^(number of zero's) hope that is clear for you
•  » » » 16 months ago, # ^ | ← Rev. 2 →   0 Can you help me? What is wrong in this code 45786145 ? I changed all things but even is getting the same result.
•  » » » » 16 months ago, # ^ |   0
•  » » » » » 16 months ago, # ^ |   0 Thank you very much!!!
•  » » » 16 months ago, # ^ | ← Rev. 3 →   -10 ahmed_nabil1297 Why are we multiplying 2^(no_of_ones)-1 and 2^(no_of_zeroes) ?
•  » » » » 16 months ago, # ^ |   -10 when you transform from binary to decimal if the one's are at the left and the zero's are at the right like 111000 you can transform it quickly by make the number equal 1000000 — 111 and 1000000 = 2^(all segment) -> 111 = 2^(no_of_zeroes)
•  » » » » » 16 months ago, # ^ |   -10 I got that part. But why are we multiplying these two values?
•  » » 16 months ago, # ^ |   0 There is a dynamic programming approach that independs of pots of 2.Let n be the number of 1's in the interval. Now you can have two processes: 1) the total deliciousness of the n pieces will be the deliciousness of the n-th piece plus the total deliciousness of n - 1 pieces. 2) the deliciousness of the n-th piece will be the total deliciousness of n - 1 pieces plus 1.Let x be the total deliciousness for the n pieces, and m be the number of 0's in the interval. Then the answer for these guys will be x *  total deliciousness of m pieces (since, instead of starting with 1, these guys are starting with x)
 » 16 months ago, # | ← Rev. 2 →   0 if anyone solved problem D by editorial approach, please provide the code.
 » 16 months ago, # |   0 is the tutorial for E has a error? it should be out[u]=max(out[v1],out[v2],...),or my understanding of in[] is wrong?
•  » » 16 months ago, # ^ |   0 "a child of u" includes all the direct and undirect childs of u. Apparently, inu = max(inv1, inv2, ..., invk) (v is a child of u, both direct and undirect) and inu = max(outv1, outv2, ..., outvk) (v is a DIRECT child of u) are basically the same.
•  » » » 16 months ago, # ^ |   0 Thanks!
 » 16 months ago, # |   0 In second sentence in E we should have the reverse implication i.e inu ≤ inv ≤ outu implies u is an ancestor of v, instead of u is an ancestor of v implies inu ≤ inv ≤ outu which is written, since this is the direction used later in the proof.
•  » » 16 months ago, # ^ |   0 You're right. It should have written as u is an ancestor of v if and only if inu ≤ inv ≤ outu
 » 16 months ago, # |   0 can anyone explain problem B again please ?
•  » » 16 months ago, # ^ |   -10 That was an easy problem bro. Check this http://codeforces.com/contest/1062/submission/45742566. I have added some comments to make things clear :)
•  » » » 16 months ago, # ^ |   0 thank you bro <3
 » 16 months ago, # |   0 Can someone explain me why in the 7 pretest of A problem answer is 2 but not 4?
•  » » 16 months ago, # ^ | ← Rev. 4 →   0 Okay, I just read the task one more time ;D
•  » » 16 months ago, # ^ |   0 The statement says "the maximum_ number of consecutive elements" not "the total number of consecutive elements".
 » 16 months ago, # |   0 Can someone explains why the complexity of the final step in tutorial F is O(N+M),please? (......After that we pop those nodes from the stack (or whatever), mark them as not visited and continue to iterate(迭代) to si−1.) (......To calculate in we reverse the directs of the edges and do the same. Because each node is visited 1 time by nodes on (P) and at most 2 times by candidate nodes ) in such a way why some nodes won't be visited more than 1 time?
•  » » 16 months ago, # ^ |   0 Assume we have: 1->2->3->4 1->5->3 2->6->4 6-> a set of nodes S1 5-> a set of nodes S2Let go backward from 4 to 1. First, at 4, because R_6 points to 4 so we start a search at 6, each node in S1 is iterated one time. After that, we reach 3, because R_5 points to 3 so we also start a search at 5 and each node in S2 is iterated one time. There maybe a chance that nodes in S1 are revisited (there is an arc from 5 to 6). Okay so let's deal with the worst case here: nodes in S1 are visited the second time. Then we reach 2, we start a search that goes from 2 to 5 and to all nodes in S1. So that's the third time we visit nodes in S1. The important thing is, this time we mark all nodes in S1 as visited and we will never visit them again. Therefore, each node is visited at most three times, one time by the nodes lie on the longest path and two times by the candidate nodes.
•  » » » 16 months ago, # ^ |   0 thank you bro ;D
 » 16 months ago, # |   0 Does anyone wrote the code for Problem D in editorial approach? please comment link.
 » 15 months ago, # |   0 In problem A, I'm getting an error on Test 7.9 1 4 5 6 7 100 101 102 103My answer is 4. However, the Jury's Answer is 2. Why is it 2? I can delete 5,6,101,102 for a total of four, right?
 » 15 months ago, # |   0 Here is my solution to problem D in less than 20 lines of code 47263480. It is a simple math problem and can be solved without any knowledge of graph. Complexity is O(N)
 » 14 months ago, # | ← Rev. 2 →   0 In A, for the test case7 :91 4 5 6 7 100 101 102 103The answer according to me should be 4 as we can remove elements 5, 6, 101 and 102 from the given array. But the jury's answer is given as 2. Please refer.
 » 14 months ago, # |   0 could someone explain problem b ?
 » 12 months ago, # |   0 Can Anybody explain why I am getting WA on Test Case 15 ?My Code
 » 2 months ago, # |   0 Great Test Cases for Problem A. Congratulations!