BGQRS - Unofficial Editorial

Hi,

I want to share my detailed editorial to BGQRS problem from October Long. I used approach which barely fits time limit, but it illustrates a nice useful method that can be used to deal with these kind of query problems.

I posted the editorial on my blog (there is a better math syntax available there):

Unofficial Editorial: Big Queries from Codechef October Long 2016

I hope you like it :slight_smile:

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Nice editorial or I would say article.

I have added my editorial/explanation to the same problem.
The Update and Query range complexity for my solution is O(ln(N)).
It runs in .77 seconds in java.
You can see the same in my solution.

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Nice. Though Sqrt Decomposition is viable here, I have an alternative solution using Lazy Propogation on Segment Tree.

The only “hard” query here is the second one. However, if you store :

  1. The largest power of 2 and 5 that divides the product of the segment
  2. A boolean denoting whether a lazy update is needed
  3. The type of update that has to be applied (either a range multiplication or reset)
  4. The ends of the segment [l, r]
  5. ex2, ex5 denoting that we should multiply the range by 2^{ex2} and 5^{ex5}
  6. The endpoints of the current type 2 query that needs to be propogated
  7. laz2, laz5 denoting the largest power of 2 and 5 of y in a type 2 query.

AC Solution

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The Intended solution was i think uses Segment tree or similar binary data structure.

The takeaway from the problem was to learn how two lazy fields propagate down the tree during queries.
One lazy term was for the Multiplying a number to a node and then marking its children lazy(if they exist) and one lazy term was for resetting the node to a new sequence which was nothing but a factorial multiplied by a number and mark the children lazy for reset.

While propagating a reset update you can ignore the child’s previous lazy terms(both), convince yourself here. For propagating “multiplication” update if you encounter a node having reset lazy field then first reset the node from its reset lazy field, mark its child lazy for reset and then do a update query on this node.

For double-lazy propagation to work, in my opinion, there should be at least one reset update of some kind, because reset update tells us that we can ignore the child previous lazy terms and set them according to the new update, irrespective of the child node history, as it is a reset update. If you don’t have a reset update, then after some queries you will notice that some nodes contain both the lazy terms and you would not be able to distinguish which one to apply first and usually the order in which they are applied would matter and would yield different result, unless you suggest me some two different good operation whose order of application yields the same result(then that would make a good codechef long challenge problem :P)

REFERENCE SOLUTION

[EDIT]
A similar question that you can try is SEGSQRSS, although the test cases are very weak and you can get AC without lazy propagation, but then its just a waste of time. Do try that.

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My solution is \mathcal O(n \lg n) and passed in 0.47 seconds with some preprocessing. Idea is same as @zscoder described.

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You should see my solution if you are not very good in segment tree . good and easy solution to understand . i used basic concept (as zscoder described power of 2 and 5) . you can easily understand hows lazy working
Solution

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I have tried to implement the Lazy Propagation on a Segment Tree to fetch the queries and update the values in O(logN). But my solution wasn’t accepted. Can someone help me out with where am I going wrong? PS: My code gives the correct output for the given test case and some random test cases. Here is my code.

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Here is comparatively short and clean implementation of **O (n lg n) ** solution based on segment-tree approach passed in 0.52 seconds. solution

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can anyone suggest mistakes in my link text solution please??

And Why do we need to store the ex2,ex5,lz2,lz5?? can anyone please explain??

codechef is very slow in updating editorials

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little complex… :slight_smile:

Here is my solution which uses single segment tree. It uses oops to further simplify the problem.Solution link

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You can also see my solution too link :slight_smile:

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My [solution][1]
[1]: https://www.codechef.com/viewsolution/11833672

is O(N log N) too with Segment Tree and Lazy Propagation, pass in 0.71 s.

Sure, also noticing that the second query can be transformed to first assigning sequence 1,2,… and then multiply it by Y can help a lot while handing that query. Lazy Propagation is something closer to the intended solution. Using sqrt blocks was too tempting for me, so I went for it - I see that we have similar run times, did you need to optimize your solution?

you sure the largest ?

Sqrt Decomposition is a nice trick and can help to solve many problems. Thanks for sharing!!
Can you suggest some good problems to start mastering this trick?

@pkacprzak My solution passed without fastio too, but fastio is slightly faster.

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@ankurverma1994 I added one bonus problem at the bottom of the editorial. It is perhaps the most classical one you can get.

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I tried to solve using same approach. I am getting WA. Please help. :slight_smile:

https://www.codechef.com/viewsolution/11867542