Hi :)

Some problem about powerful data structure and algorithm SQRT decomposition.

If you want to learn this algorithm click here.

And a big thank to mr_agha_seyed for helping.

220B - Маленький Слоник и массив

86D - Мощный массив

13E - Лунки

455D - Серега и веселье

375D - Дерево и запросы

446C - DZY любит числа Фибоначчи

487D - Ленты конвейера

506D - Цветной граф мистера Китаюта

348C - Суммы подмножеств

617E - XOR и любимое число

444C - DZY любит цвета

398D - Мгновенные сообщения

342E - Ксюша и дерево

Maybe some of them can solve by other data structures like segment tree.

cheers! :) :D

Would be nice to have SQRT decomposition tag for those problems. Now, I guess, all of them in data structures

http://codeforces.com/problemset/tags/data%20structures

timus 1846 also nice sqrt-decomp problem.

Can you, please, elaborate a bit?

I'm thinking of splitting the queries in chunks of sqrt(N) and processing them similar to the

disjoint-set-union splitas described on e-maxx.First of all, we will call a set a DS which can handle the insert and erase operations in O(1).

Let active set and temp. set be 2 empty sets

For every chunk of sqrt(N) queries:

Go through all the remove operations (query type

'-') and, if possible, remove those numbers from the active set of numbers, and add them in a temp. set. This loop will take O(sqrt(N)).Let currGcd be the gcd of all the keys in our active set. There are at most O(N) of them.

Process the chunk again and take 2 cases:

The answer for every query will be the gcd of all the keys in the temp. set and our currGcd. There are at most O(sqrt(N)) items in the temp. set, so this loop will take O(N).

At the end of a chunk, move all the items from the temp set to the active set (and clear the temp set).

The overall complexity is O(N * sqrt(N))

можно хранить наши элементы по блокам (gcd всех элементов в нем) + хранить мапу, где запоминаем, в каком блоке лежит число, для ответа пройдемся по блокам и пересчитаем gcd, для добавления/удаления пересчитаем gcd только в одном блоке код

It easily solves with segment tree, each leaf node stores x, non-leaf nodes gcd of its children.

Are Mo Algorithm and SQRT decomposition considered the same?

In SQRT decomposition we divide the array in buckets, solve the task in these buckets and answer each query in O() time (worst case). However, using Mo Algorithm the queries are sorted according to the bucket the left end of the queries falls into ...

I think both methods have the same time complexity, but are they considered the same?

SQRT decomposition combines several approaches and algorithms. Mo Algorithm is one of them.

SQRT Descomposition is a data structure, while Mo's Algorithm is more a technique.

Not really much of a proof. SQRT-decomposition on queries isn't so much of a data structure, but is still usually meant to be called SQRT-decomp

I got stuck with the problem 446C — DZY Loves Fibonacci Numbers and here's my submissions

could someone help ?

thanks in advance

Can 13E - Лунки solved using MO's algorithm? Or There are other kind of Sqrt-Decomposition? I have solved the first two in the list. But can't find an idea about this one.

You know what, there is this thing called editorial for (almost) every round which explains how to solve the problems.

Thank you. I read the editorial before the comment. But their solution doesn't feel like the MO I learnt. And this problem is listed here. So I asked here if the solution is general, there might be some name or insights available that I want to know before solving it.

It is explained there 23:05

Thank you. I will take a look.

242E - XOR на отрезке can also be solved with SQRT-decomposition. Although it's slower than the intended solution, it can still AC.

One more very nice SQRT-decomposition problem I encountered at the Innopolis Open Elimination round (2016-2017): http://codeforces.com/gym/101182/problem/E

Is it better to use const value for the sqrt (i.e 350) or to use sqrt function on n ?

Why i am getting TLE at 220B - Маленький Слоник и массив? My Submission 29417078 .Could anyone help me!

Edited: I have changed my solution from map to array.But this also gives me a TLE! 29417554

Maybe you have to create a struct for the query, add and remove method you can improve it because you have a lot process and you can put this in you cmp.

https://www.codechef.com/AUG17/problems/HILLJUMP Another good problem on this topic.

It's great to see guys like you guide beginners like us ! Thank you so much !

446C DZY Loves Fibonacci Numbers gives TLE with sqrt decomposition. My code gives TLE although its complexity is O(N*sqrt(N))?? Any help would be appreciated.

I don't find your mistake, but i know easier way to solve it.

See my code.

Main idea : divide queries in sqrt(m) blocks.

I saw your code. Your Idea is cool. But your code and mine have literally the same complexity.

Another good problem on this topic: Chef and Graph Queries

Another one: Chef And Easy Xor Queries

I solved Timus 1390 using SQRT optimization