C++ STL: Policy based data structures

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Всем привет! После достаточно долгого затишья, я решил, что ~~мой вклад растёт слишком медленно~~ пришёл час порадовать вас ещё одной статьёй в блоге :)

2 месяца назад пользователь Perlik выложил статью, в которой описал очень интересную реализованную в STL структуру, которая позволяла очень быстро производить различные операции с подстроками. Некоторое время после этого я тестировал её на различных задачах и, к сожалению, как правило, получал негативный результат — rope оказалась слишком уж медленной, особенно когда речь шла о работе с отдельно взятыми элементами.

На некоторое время я позабыл о той статье. Однако всё чаще я сталкивался с задачами, в которых нужно было реализовать множество, да не простое, а ~~золотое~~ с возможностью узнавать порядковый номер элемента и, напротив, элемент по его порядковому номеру (т.е., порядковую статистику в множестве). Вопрос выполнения этих операций методами стандартной библиотеки достаточно тонкий и актуальный, подтверждением тому можно привести, например, этот и этот блоги. И тут я вспомнил о том, что в комментариях к той статье кто-то упомянул о загадочной структуре данных order statistics tree, которое как раз поддерживает эти две операции и которое как раз реализовано в STL (хотя и только для GNU C++). Тут и началось моё увлекательное знакомство со структурами данных, основанными на политике (policy based data structures), о которых я хочу поведать и вам :)

Итак, приступим. В данной статье я рассмотрю наиболее интересную из реализованных структур — дерево (tree). Нам потребуется подключить следующие библиотеки:

#include <ext/pb_ds/assoc_container.hpp> // Общий файл. 
#include <ext/pb_ds/tree_policy.hpp> // Содержит класс tree_order_statistics_node_update

При более внимательном рассмотрении можно обнаружить, что последние два файла содержатся в библиотеке

#include <ext/pb_ds/detail/standard_policies.hpp>

Пространство имён, с которым нам прийдётся работать в современных версиях носит название __gnu_pbds; Ранее оно называлось pb_ds;

Теперь рассмотрим конкретные структуры.

Шаблон tree имеет следующий вид:

	  template<
	  typename Key, // Тип ключа
	  typename Mapped, // Тип ассоциированных с ключём данных
	  typename Cmp_Fn = std::less<Key>, // Функтор сравнения, должен соответствовать оператору <
	  typename Tag = rb_tree_tag, // Метка, обозначающая тип дерева
	  template<
	  typename Const_Node_Iterator,
	  typename Node_Iterator,
	  typename Cmp_Fn_,
	  typename Allocator_>
	  class Node_Update = null_node_update, // Метка обновления вершин
	  typename Allocator = std::allocator<char> > // Аллокатор
	  class tree;

Опытные участники, должно быть, уже заметили, что если инициализировать в шаблоне только первые 2 типа, то мы получим практически точную копию контейнера map. Сразу оговорюсь, что из этого контейнера можно сделать set, для этого нужно просто указать вторым аргументом шаблона тип null_type (в старых версиях null_mapped_type).

А вот параметры Tag и Node_Update в обычном map'e отсутствуют. Рассмотрим их подробнее.

Tag — класс, обозначающий структуру дерева, которое мы будем использовать. В STL реализовано три класса, которые мы можем здесь использовать, это rb_tree_tag, splay_tree_tag и ov_tree_tag. На практике, однако, допустимо использование только красно-чёрного дерева, spay_tree и ov_tree же, по всей видимости, используют при обновлении линейную по времени операцию split, что и лишает их возможности к применению при решении олимпиадных задач.

Node_Update — класс, обозначающий политику обновления инвариантов вершин. По умолчанию он установлен в null_node_update, т.е., дополнительной информации в вершинах не храниться. Кроме этого, в C++ реализована политика обновления tree_order_statistics_node_update, которая, собственно, и несёт в себе необходимые операции. Рассмотрим их. Скорее всего, наилучшим способом задания дерева будет следующий:

typedef tree<
int,
null_type,
less<int>,
rb_tree_tag,
tree_order_statistics_node_update>
ordered_set;

Если мы хотим получить ассоциативный массив, а не множество, в качестве второго аргумента следует использовать тип, соответствующий значению в этом множестве. По всей видимости, дерево поддерживает все те же операции, что и set (по крайней мере, до этого у меня с ними конфликта не возникало), но кроме этого добавлены две новые функции — это find_by_order() и order_of_key(). Первая возвращает итератор на k-ый по величине элемент (отсчёт с нуля), вторая — возвращает количество элементов в множестве, строго меньших, чем наш элемент. Пример использования:


    ordered_set X;
    X.insert(1);
    X.insert(2);
    X.insert(4);
    X.insert(8);
    X.insert(16);

    cout<<*X.find_by_order(1)<<endl; // 2
    cout<<*X.find_by_order(2)<<endl; // 4
    cout<<*X.find_by_order(4)<<endl; // 16
    cout<<(end(X)==X.find_by_order(6))<<endl; // true

    cout<<X.order_of_key(-5)<<endl;  // 0
    cout<<X.order_of_key(1)<<endl;   // 0
    cout<<X.order_of_key(3)<<endl;   // 2
    cout<<X.order_of_key(4)<<endl;   // 2
    cout<<X.order_of_key(400)<<endl; // 5

Как мне кажется, наличие такой структуры в STL просто замечательно, т.к. оно позволяет ещё сильнее сузить круг задач, в которых реализация какой-нибудь общеизвестной структуры требует порой больше времени, чем придумывание решения. Напоследок хотелось бы сказать о производительности order_statistics_tree в STL. Для этого я приведу следующую таблицу задач, на которых я её тестировал и результаты по ним.

Решение\Задача	1028	1090	1521	1439
order_statistics_tree, STL	0.062	0.218	0.296	0.468
Дерево Отрезков	0.031	0.078	0.171	0.078 0.859*
Дерево Фенвика	0.031	0.062	0.062	-

* В последней задаче для реализации решения за O(mlogn) необходим прямой доступ к вершинам дерева. Без него решение работает за O(mlogn*logn).

Как можно из всего этого видеть, order_statistics_tree сравнительно немного отстаёт от рукописных структур, а порой и вовсе их обгоняет. При этом размер кода сокращается значительно. Отсюда можно сделать вывод, что order_statistics_tree — это хорошо и его можно использовать в контестах.

Кроме tree, я также хотел описать здесь trie — реализованный префиксный бор. Однако, меня смутили некоторые аспекты его реализации, сильно ограничивающие его применимость в олимпиадном программировании, в связи с чем его описание я здесь приводить не буду. Если кому-то интересно, он может самостоятельно попытаться узнать об этой структуре больше.

Полезные ссылки:
— Документация по pb_ds
— Тестирование производительности pb_ds
— Помощь с использованием pb_ds
— Демонстрация использования order_statistics_tree
— Демонстрация использования бора с поиском строк, включающих данную строку в качестве префикса
— Операции с интервалами с помощью самописного класса обновления вершин
— Прочие примеры

typedef tree< pair<int, int>, null_type, less<pair<int, int>>, rb_tree_tag, tree_order_statistics_node_update> ordered_set; int t = 0; ordered_set me; ... me.insert({x, t++}); me.erase(me.lower_bound({x, 0})); cout << me.order_of_key({x, 0}) << "\n";

auto cmp = [](int a, int b){return a < b;}; tree<int, null_type, decltype(cmp)> x(cmp); tree<int, null_type, function<bool(int, int)>> y([](int a, int b) { return a < b;});

#include<ext/pb_ds/assoc_container.hpp> using namespace __gnu_pbds; template<class key, class value, class cmp = std::less<key>> using ordered_map = tree<key, value, cmp, rb_tree_tag, tree_order_statistics_node_update>; ordered_map<int, int> my_map;

In file included from B.cc:13: /Library/Developer/CommandLineTools/SDKs/MacOSX.sdk/usr/include/c++/v1/ext/pb_ds/assoc_container.hpp:44:10: fatal error: 'bits/c++config.h' file not found #include <bits/c++config.h>

eval "$(/opt/homebrew/bin/brew shellenv)" # g++ CPLUS_INCLUDE_PATH=/opt/homebrew/Cellar/gcc@12/12.1.0_1/include/c++/12:/opt/homebrew/Cellar/gcc@12/12.1.0_1/include/c++/12/aarch64-apple-darwin21:/Users/drswad/Desktop/CP/Setup/include export CPLUS_INCLUDE_PATH export PATH=/opt/homebrew/Cellar/gcc@12/12.1.0_1/bin:$PATH # other configs ...

Tree Order Statistics / C++ STL: Policy based Template

#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace std; // using namespace __gnu_pbds; using __gnu_pbds::tree; using __gnu_pbds::rb_tree_tag; using __gnu_pbds::tree_order_statistics_node_update; using __gnu_pbds::null_type; // _GLIBCXX_DEBUG must not be defined otherwise some internal check will fail #undef _GLIBCXX_DEBUG template <typename K, typename V, typename Comp = less<K>> using indexed_map = tree<K, V, Comp, rb_tree_tag, tree_order_statistics_node_update>; template <typename K, typename Comp = less<K>> using indexed_set = indexed_map<K, null_type, Comp>; // ¡¡IMPORTANT!! (for using less_equals<K>) // using less_equals<K> makes lower_bound works as upper_bound and vice-versa // for erase use: any.erase(any.find_by_order(any.order_of_key(val))); // don't use .find() because it will always return .end() template <typename K, typename V, typename Comp = less_equal<K>> using indexed_multimap = indexed_map<K, V, Comp>; template <typename K, typename Comp = less_equal<K>> using indexed_multiset = indexed_map<K, null_type, Comp>;

bool contains(indexed_multiset<int>& tree, int val) { int order = tree.order_of_key(val); return 0 <= order && order < tree.size() && *tree.find_by_order(order) == val; } bool contains(indexed_multimap<int, int>& tree, int val) { int order = tree.order_of_key(val); return 0 <= order && order < tree.size() && tree.find_by_order(order)->first == val; }

Комментарии (161)

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adamant

10 лет назад, # |

+12

Example of trie with search of prefix range.
Problem: 1414
Solution: http://ideone.com/6VFNZl

→ Ответить

low_kii_savage

5 лет назад, # ^ |

← Rev. 2 →

Is there a way of counting number of strings in the trie with a certain prefix without iterating through them all?

daksh_

3 года назад, # ^ |

You augment the trie node to also contain a number. Update this number everytime you insert a string into the trie. To get the number of strings which share the prefix, Just traverse the prefix and output the num in the ending node.

+17

Возможно, вам покажутся слегка нетривиальными решения деревом отрезков и деревом Фенвика, особенно, задач 1521 и 1439. Скорее всего, позже я также предоставлю статью, в которой опишу некоторые интересные способы использования этих структур, которые редко встречаются.

======================================================================================= You may be wondered about how I use segment tree and binary indexed tree in my solutions, especially for problems 1521 and 1439. Most likely, later I'll provide an entry about some interesting ways of using this structures, which are quite rare.

10 лет назад, # ^ |

Here it is :)

alex-mercer

+21

This is really useful. Thanks a lot!

amitsaharana

Very useful article! I need order-statistics on a multiset. How should I define the tree as?

As I know, there is no implemented tree multiset in STL. However you can use pair<T,int> as a key where the second element in pair is the time when item has been added.

samatbor

7 лет назад, # ^ |

Apparently, you can. Once I tried to write less_equal instead of less and it started to work as multiset, I even got AC using it in region olympiad)

komendart

+11

I can't erase elements with less_equal comparator, e.g. this code output "1"

code

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;

typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

signed main() {
    ordered_set d;
    d.insert(1);
    d.erase(1);
    for (auto i: d) {
        cout << i << endl;
    }
}

So I guess it's not very useful thing (or I do something wrong).

UPD: I can delete iterator which I got with lower_bound. But it works incorrectly. This code erase 1, not 0

Code

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>

using namespace std;
using namespace __gnu_pbds;

typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

signed main() {
    ordered_set d;
    d.insert(0);
    d.insert(1);
    d.erase(d.lower_bound(0));
    for (auto i: d) {
        cout << i << ' ';
    }
}

Wow. then it really sucks. Seems like I only used it with insert operations and strangely enough it worked)

turzo_sawroop

2 года назад, # ^ |

5 years later I can say it is useful in some problems and this helped me today in this problem

glad it helped:)

Ranjeet

21 месяц назад, # ^ |

-13

You can erase elements from the multiset.

1. find the index of the element using `order_of_key`
2. store it in `idx`
3. delete using `s.erase(s.find_by_order(idx))`

Soroush

6 лет назад, # ^ |

-8

Well, actually it works fine and exactly does what you want! The issue is that you're passing less_equal<int> as the tree comparator. Therefore it uses the same function for lower_bound(). By definition of lower_bound function (according to cplusplus.com) it finds the first element not compared true. Thus returns the first element greater than val which is 1 in your example.

In order to make sure you may even test set<int,less_equal<int> > which results the same.

saurabhyadavz

4 года назад, # ^ |

← Rev. 3 →

What if I want to calculate the index of upper_bound of a particular element? Suppose we have: 1 1 2 3 4 then how to find index(upper_bound(2))?

UPDATE: Maybe it is = order_of_key(number+1) ?

jnarutoj

So to erase an element from ordered_set with less_equal I used lower_bound on (element to be erased — 1) and then erased the iterator I got from lower_bound and it works only if the element to be erased is present in the set.

nikalla

5 years later vol2, lower_bound doesn't work but you can do it like d.erase(d.find_by_order(d.order_of_key(0)) this erases iterator correctly, but it's little slow.

YohanLibert

17 месяцев назад, # ^ |

I don't actually know how does it work, but if you use upper_bound instead of lower_bound it woulf work correctly.

roll_no_1

Another drawback of using less_equal instead of less is that lower_bound works as upper_bound and vice-versa. Code

klexis

An excellent deduction.

Yash_04k

12 месяцев назад, # ^ |

Thanks this was helpful

VinCenzo___

in today's leet c?

yes bro

https://leetcode.com/contest/weekly-contest-342/submissions/detail/938214410/

here is my solution.

lamda_cdm

typedef tree<long long, null_type, less_equal<>, rb_tree_tag, tree_order_statistics_node_update> indexed_multiset; using " less_equal<> " makes it a multiset

venkycodes

What about the comparator i.e. less<int>

__Badral

typedef tree<int, null_type, less_equal, rb_tree_tag, tree_order_statistics_node_update> indexed_multiset;

Gr8

Can we use this in this question? or we can't use it, as I am not able to implement the multiset part

just use the fucking binary search on this problem

The 3rd template argument must be less_equal<int>. But adamant, is it the correct way to do this ? Since as far as I know, most of the STL containers require a comparator that offers a strict weak ordering (Not sure of the exact reasons though). So, will there be some drawbacks of trying to construct a multiset this way?

pranav.vinchurkar

To use order-statistics on a multiset: Use:: tree<int, null_type, less_equal, rb_tree_tag, tree_order_statistics_node_update> s;

find_by_order and order_of_key work the same as for a set.

However for searching, lower_bound and upper_bound work oppositely. Also, let's say you want to erase x, use s.erase(s.upper_bound(x)) (as upper bound is considered as lower bound)

killer_god

This is actually great. Whenever I needed to handle duplicate I used take pair<val,index>. This is much simpler.

.(same comment as above)

kefaa

А начиная с каких версий плюсов tree<...> компилируется?

Затрудняюсь ответить на этот вопрос :(

Пока только могу сказать, что на некоторых совсем старых версиях необходимо писать null_mapped_type вместо null_type. Например, на 4.3.2, судя по компилятору с http://ideone.com.

ravishmahur

9 лет назад, # |

what will be the complexity of erase operation? O(logn) or O(n)

9 лет назад, # ^ |

O(logn)

ILoveDoraemon

Really??

Yes.

rajat1603

Is there any efficient function to merge 2 trees ?

ILoveBitches

You can do in log(n) if the greatest element of 1 tree is smaller than smallest of other. Otherwise, I don't you have a better option. Tell me as well if you have found something interesting.

0w1

How do you merge two non-intersected rbtrees (as in the article) in O(lg n) time? I find that the default join() function takes linear time...

kuksag

Have you found something interesting about merge ? Im trying to do .join but it throws error.

draak_krijger

8 лет назад, # |

how can i use it like multiset ?

8 лет назад, # ^ |

Main idea is to keep pairs like {elem, id}.

thanks a lot :)

shishir.hstu

like me.order_of_key({x, 0}) me.find_by_order({x,0}) dose not work.. why??

Dalgerok

*me.find_by_order({x,0})

still it does not work.

MasterMind

sure it does work, but you cannot print a pair so you have to do it like this cout << me.find_by_order(1)->first ;

wtf, find_by_order takes number

GlobalElite

how to use find_by_order if I'm using ordered_set with pairs. ~~~~~ typedef tree< pair<int, int>, null_type, less<pair<int, int>>, rb_tree_tag, tree_order_statistics_node_update> ordered_set; ~~~~~

orange_trie

nice technique. worked fine! thanks a lot.

duckladydinh

Hi, adamant, the code files in Useful Links don't seem to work. Could you fix them?

Thanks for this great post. I am looking forward to your next and next next posts.

Can you elaborate please?

For example, the code in "Demonstration of trie with prefix search" cannot run on my computer. I saw that there was some old syntax like the namespace pb_ds. I changed it, then it returned a new error in another place. The truth is I am not good enough to change things any more. I hope that you can update it. (I know that I can use the trie code in one of your comments, but this post would be even better if the cost in Useful Links were also updated)

Thank you.

I can't edit the original files — they're not mine. But here is the correct version: http://ideone.com/BpZlYO

TheeLooser

7 лет назад, # |

What is the complexity of these function : find_by_order() and order_of_key() ?

Logarithmic, I suppose

https://www.e-olymp.com/ru/problems/2961 Is it possible to solve this problem using this algorithm?

[del]

coderbond007

Can anybody share a Java equivalent class for this type of set or a code which acts according to above data structure?

dalex

It does not exist.

You may use instead:

self-written tree
treap
numbers compression + fenwick tree

I thought of number compression + fenwick tree, but this solution will work for only offline queries. I want to handle online queries. The best I can think of now is Treap + Segment Tree or Treap + Fenwick Tree. But here again is the problem of implementation of mixed data structure, I am unable to think how to implement that. Can you please help me?

oversolver

6 лет назад, # |

у этой штуки правда нету count?

(понятно, что можно *s.find_by_order(s.order_of_key(x)) == x, но не красиво же)

Можно s.order_of_key(x + 1) — s.order_of_key(x)

Да, если это инты

prudent

Можете ли вы пожалуйста объяснить почему это равносильно функции count ?

Это равносильно bool(count())

спасибо, то есть он лишь проверяет есть ли этот элемент в set-e или нет?

Ну вообще обычно lower_bound с иксом сравнивают

с проверкой на end? тоже не красиво

lnzva

Any idea on how to use this pre C++11?

Tanmoy_Datta

How can I use a custom compare function in the "Key comparison functor" section for custom data types?

Just like for regular set..

I can use custom compare function for a set by using operator overloading. I want to know is there any other way to do this for both set and ordered set using lambda expression or just using a compare bool function?

Thank adamant you very much for your nice post.

I suppose you can overload operator and still use less<T>. Also you can use functors and lambdas in the way similar as for sets:

PyAlpha

Why does it only work with lambdas and not functions? On doing

tree<pair<int, int>, null_type, decltype(&comp), rb_tree_tag, tree_order_statistics_node_update> ordered_set(&comp);

Where comp is a comparator function, I get an error.

sangramsinh

It does not work for me. I tried using custom comparator but getting error. Please resolve my issue. Code Link: https://leetcode.com/submissions/detail/693650301/

I have written cmp struct but when i pass in tree argument it is giving me error.

Sorry, what doesn't work?

struct cmp{
    bool operator() (const int &a,const int &b){
        return a <= b;
    }
};

typedef tree<int,null_type,cmp,rb_tree_tag,tree_order_statistics_node_update> ordered_set;

works just fine on my side.

P.S. I would really recommend against using <= as a comparator, because it's supposed to be anti-reflexive.

haleyk100198

Is it possible to search for the order of a non-key value by passing a comparator/function ? I sometimes find myself have to use my own tree templates instead because of having to write a search function that can cope with this task.

Jubair_2147483647

What is the constant factor of order_statistics_tree though it executes in logarithmic complexity ? I think it's constant factor is very high.

ram_24

could anyone write the exact thing to use this data structure as map..pls.I'm not able do so.

And what exactly do you want from it? You can use something like that.

as it was mentioned in the article that we can use it as map by defining mapped type .So I tried to do that by couldn't. that's all;)

des1997

is this thing a order statistics tree

amankumarkeshu

Can you write the multiset implementation of ordered_set. When I use less_equal then I'm not able to erase from the ordered_set. And when I use the pair for including duplicates I'm not able to use find_by_order({x,0}).

What's wrong with find_by_order({x, 0})?

It gives an error. It says no known conversion. error: no matching function for call to '__gnu_pbds::tree<std::pair<int, int>, __gnu_pbds::null_type, std::less<std::pair<int, int> >, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>::find_by_order()

Wait, find_by_order takes number $$$k$$$ and returns $$$k$$$-th element. What exactly do you expect it to return?..

A number .

I think you should use order_of_key then

Thanks adamant I did that.

Actually find_by_order( x) takes in an integer input because it tells us the element present in the position x. Whereas find_by_order({x, 0}) is a syntax error and it wont work.

can we use it as multiset?

aasom143

u can use pair<int,int> for manage the duplicate values..

CodeKracker

It is:

typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> indexed_multiset;

_Chaitanya1999

thank you bro :) it worked for duplicate elements too..

PritamDas

what to do if i want to merge two ordered multisets?

Mouaz_Alkhodari

is it legal to use it in ICPC or any region contest ??

Vladikus004

5 лет назад, # |

How can I erase element from order_set by it's value?

oToToT

just do ordered_set<T> st; st.erase(key);

This doesn't work .

prateekrai

ordered_set :: iterator it; it=st.upper_bound(key); st.erase(it); it works;

Thanks bro

prabhav_

You can try this to erase by value from ordered multiset(or wwhatever it's called in technical terms)

How to use Ordered Multiset

typedef tree<int, null_type, less_equal<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;

To erase by value from Ordered Multiset: os.erase(os.find_by_order(os.order_of_key(val)));

andaanda

(Sorry for necroposting) Does anyone know how to compile with the pbds header files on Mac OS X ? I think the g++ command is configured to use clang by default, and so it is not directly available. I've tried adding ext/pb_ds into the include folder (the same way you would enable bits/stdc++.h) but instead new dependencies come up.

Pa.Nic

For me, I installed the latest version of gcc (gcc 9.3.0_1) and compiled with gcc-9. It works on Mojave and Catalina and it should work on High Sierra (but I haven't tested it).

To install gcc-9, I used brew and the command brew install gcc@9

DrSwad

(Again, sorry for necroposting) There is an important step that I've so-far seen all the mac g++ setup instructions ignore/skip. I also installed gcc through brew, but neither bits/stdc++.h header nor pbds data structures seemed to work. Putting the bits/stdc++.h file manually in the /usr/local/include folder allowed me to at least solve the header problem, but trying the same method for pbds spawned a lot of dependency issues.

The problem was that brew sets up the g++ command as g++-10 so that it doesn't clash with the default g++ command mac provides. So, alias-ing g++ to g++-10 in the .bashrc/.zshrc file would be enough for solving the issue if you compile using the terminal. But if you compile using an editor and the editor directly uses the /usr/bin/g++ binary for compilation, then alias-ing g++ wouldn't work anymore. For example, most of the popular VSCode extensions for CP I've seen use /usr/bin/g++ to compile. I wasn't aware that this was the root of the issue and had been missing pbds structures for a long time. The way to solve it is to simlink g++ to g++-10 and prepend it to the PATH variable so that the simlink is prioritized before the default g++.

Instructions for the simlink way

I might even find it useful myself if I ever need to setup a mac again in future.

Nanda

15 месяцев назад, # ^ |

(Sorry for Necroposting). But I have to update the details as from M1 onwards (possibly Big Sur) configurations have been changed. The Cellar directory is not available at /usr/local anymore. You can do the following instead.

cd /opt/homebrew/Cellar/gcc/12.2.0/bin

ln -s ./c++-12 ./c++

ln -s ./g++-12 ./g++

export PATH=“/opt/homebrew/Cellar/gcc/12.2.0/bin:$PATH”

Did you manage to solve PBDS issue on your mac ? Doing all above doesn't solve the PBDS issue.

Thanks for the updates.

Yes, PBDS seems to work for me. I'm running macOS Ventura on M1 (Btw I had to reinstall the command-line tools when updating from Big Sur to Ventura). Can you elaborate on the exact issue you're facing, or possibly provide some error logs?

Also, did you try compiling a source code that uses PBDS from the terminal? Because I've fixed similar issues for others who were compiling/running from an editor/IDE, but the main culprit was actually the editor. The editor might fail if you didn't properly point it toward the Homebrew g++.

I am also using ventura 13.2 on M1. I tried both on sublime build and manually on terminal to run a sample code. It shows the following error.

The .zshrc profile looks like as mentioned in the above command. I tried to add the missing file, then got reported for another missing file and so on. In fact the ext/pb_ds directory I put there myself.

I think it might have to do with the configs in .zshrc. I checked my .zshrc file and there seem to be some additional env variables I defined but I forgot why. I have these at the very top of the .zshrc file:

Check if you have similar paths and modify them accordingly before putting them in .zshrc. Also, the last path there (/Users/drswad/Desktop/CP/Setup/include) is just for any custom header files. I put my debugging template and testlib.h in there, so that they always get included in every program on my PC and the editor linter doesn't complain with red squiggly lines.

Also, try reinstalling command-line tools with xcode-select --install.

Let me know if they resolve your issue.

a61742

Note on using less_equal as comparison function to use it as a multiset:

_GLIBCXX_DEBUG must not be defined, otherwise some internal check will fail.
find will always return end.
lower_bound works like upper_bound in normal set (to return the first element > it)
upper_bound works like lower_bound in normal set (to return the first element >= it)
find_by_order and order_of_key works properly (unlike the 2 functions above).

Some code to verify the points above: Try it online!

harshraj22

adamant, while discussion, someone suggested that the time complexity of using it as a set is amortized log(n), and this post says that it means that in some cases that can be O(n). I wonder if that is true ?? If yes, is there an alternative to policy based data structures ?? Here is one solution

It shouldn't be. And even if so, what's the deal? It will always be O(n log n +q log n) if you use set of numbers of size n and run q queries.

but this link line 4 says :

> while having an amortized complexity of O(lgn) means that some (very few) operator calls can take O(n) time.

and if that's the case, won't the complexity be q*n instead of qlog(n) ?? which I suspect might be the reason of my solution getting TLE using policy based data structure while the editorial using treap and getting accepted (having same time complexity ).

Please guide me through it as I use this data structure very frequently.

It can't be. By definition amortized complexity means that algorithm is guaranteed to have such executing time if it's divided By the numbers of queries. When they say "few" they mean it

So, I should treat it as the worst time complexity of this data structure ?

If you don't revert operations and don't need it persistent then basically yes. In your case it is likely to be too large constant factor. But I'll look into it later.

AngryBaymax

Can i merge two ordered_set ? if it can be what will be its complexity?

Vosatorp

4 года назад, # |

-10

Как реализовать ordered set для произвольных самописных структур, если для структуры прописан оператор < ?

UPD: Уже ответил на свой вопрос.

yogi

Thanks,it just got me an AC.

mub.ch

If someone is having trouble to use these in windows with mingw compiler, try to find hash_standard_resize_policy_imp.hpp0000644 in MinGW\lib\gcc\mingw32\6.3.0\include\c++\ext\pb_ds\detail\resize_policy and rename it to hash_standard_resize_policy_imp.hpp. I dont know why it is named like this.

mohitsamant

thanks bro ...do you know why it name like this ... why wrong extension is given to it..

saarang

I have defined a bool cmp(pair<int,int> a, pair<int, int> b) for comparing pairs. Is it possible to use that as the comparator for the ordered_set?

Flower08

Thank you this really helped me.

ben_dover

Is this actually STL? I only see files with gcc's implementation of the c++ standard library. Actual STL is quite old (the linked post references SGI's docs, and SGI doesn't even exist any more)

jef

Nope, this has nothing to do with the C++ standard library.

This is a GNU extension, so it has nothing to do with the STL which (incorrectly) refers to the C++ standard library.

STL doesn't even refer to the C++ standard library. STL is the Standard Template Library from long ago which heavily influenced the C++ standard library but is not the same thing. https://stackoverflow.com/a/5205571

I know, but here and in many other places "STL" is incorrectly used to refer to the C++ standard library.

hieplpvip

The first returns an iterator to the k-th largest element (counting from zero)

Shouldn't it be the k-th smallest element? adamant

How to merge two ordered sets?

adderall

Iterate through every element in the smaller set and append it to the bigger one

thanks brother

nqs_1

A very Useful article helped me in a lot of places. Thank you for your contribution.

Zuciso

When to use BIT over PBDS .. if they perform same thing instead of memory constrain

When to use BIT over PBDS other then memory limit

https://codeforces.com/contest/459/problem/D can we solve this question using pbds ? Its giving me runtime error — https://codeforces.com/contest/459/submission/81689503

iabhishek15

can we use pair in place of int ??

Sure, why not. We may use any type with operator < defined.

participant123

Is insert not too slow? I tried 10^7 insertions and it took over a minute.

anshjain18

3 года назад, # |

Doesn't find_by_order(k) returns the kth smallest element in the set? In the article the values given seems like the kth smallest ones not the largest ones

yh11

Shouldn't this line

"The first returns an iterator to the k-th largest element (counting from zero),"

"The first returns an iterator to the k-th **smallest** element (counting from zero),"

because X.find_by_order(1) clearly returns 2nd smallest number.

boleyn.su

2 года назад, # |

Just saw this post and I am wondering can https://codeforces.com/contest/237/submission/2804338 be the first submission using pbds? (I did not actually used pbds in this submission just included it as part of my template.) IIRC, Gerald used to see my usage of this trick in Dec, 2013 and asked about its usage.

Sameh.Sayed14

21 месяц назад, # |

Can I make the ordered set get the first element greater than x or even greater than or equal?

*find_by_order(order_of_key(x)) -- this will be first greater or equal element than x if u wanna only greater *find_by_order(order_of_key(x+1)) <-- write this

LuchoBazz

20 месяцев назад, # |

hilbertmf

3 месяца назад, # ^ |

This comment about not using find is only when we're using indexed multimap and multiset? What if we want to check if the tree contains a given value? How can we do that if the find doesn't work?

Edit: Nvm, i've found a way, posting here if its useful for anyone:

jyoti851999

14 месяцев назад, # |

Please note erase(key) does not work if you are using ordered_map typedef tree< int, map_value_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> ordered_map;

BitSlayer

8 месяцев назад, # |

Thanks a lot bro

JAINISHx

What do we need to do to erase the specific element from the ordered_set ?

gunjjoshi

4 месяца назад, # ^ |

Just do s.erase(5), considering the name of your ordered_set is s and the element that you intend to remove is 5.

Muhammad_Aneeq

4 месяца назад, # |

can we use this in IOI

How to remove an element from an ordered_set ?

ijo

4 недели назад, # |

Regarding the trie implementation, is there an easy way to iterate over it? I'd like to be able to give a word one letter at a time, and get back the node I'm currently on, without redoing any work.

Блог пользователя adamant

Tree Order Statistics / C++ STL: Policy based Template