By adamant, 9 years ago, translation,

Hi everyone! After a relatively long lull, I decided that my contribution growing too slowly the hour has come to please you with another article in the blog :)

2 months ago user Perlik wrote an article, in which he described a very interesting STL implemented data structure that allows you to quickly perform various operations with substrings. Some time after I tested it on various tasks and, unfortunately, tend to get a negative result — rope was too slow, especially when it came to working with individual elements.

For some time, I forgot about that article. Increasingly, however, I was faced with problems in which it was necessary to implement set with the ability to know ordinal number of item and also to get item by its ordinal number (ie, order statistic in the set). And then I remembered that in the comments to that article, someone mentioned about the mysterious data structure order statistics tree, which supports these two operations and which is implemented in STL (unfortunately only for the GNU C++). And here begins my fascinating acquaintance with policy based data structures, and I want to tell you about them :)

Let's get started. In this article I will talk about IMO the most interesting of the implemented structures — tree. We need to include the following headers:

#include <ext/pb_ds/assoc_container.hpp> // Common file
#include <ext/pb_ds/tree_policy.hpp> // Including tree_order_statistics_node_update


After closer inspection you may find that the last two files contained in the library

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


Namespace, which we will have to work in newer versions of C++ is called __gnu_pbds;, earlier it was called pb_ds;

Now let's look at the concrete structure.

The tree-based container has the following declaration:

	  template<
typename Key, // Key type
typename Mapped, // Mapped-policy
typename Cmp_Fn = std::less<Key>, // Key comparison functor
typename Tag = rb_tree_tag, // Specifies which underlying data structure to use
template<
typename Const_Node_Iterator,
typename Node_Iterator,
typename Cmp_Fn_,
typename Allocator_>
class Node_Update = null_node_update, // A policy for updating node invariants
typename Allocator = std::allocator<char> > // An allocator type
class tree;



Experienced participants may have already noticed that if initialize the template only the first two types, we obtain almost exact copy of the container map. Just say, that this container can be set, for this you just need to specify the second argument template type as null_type ( in older versions it is null_mapped_type).

By the way Tag and Node_Update are missing in map. Let us examine them in more detail.

Tag — class denoting a tree structure, which we will use. There are three base-classes provided in STL for this, it is rb_tree_tag (red-black tree), splay_tree_tag (splay tree) and ov_tree_tag (ordered-vector tree). Sadly, at competitions we can use only red-black trees for this because splay tree and OV-tree using linear-timed split operation that prevents us to use them.

Node_Update — class denoting policy for updating node invariants. By default it is set to null_node_update, ie, additional information not stored in the vertices. In addition, C++ implemented an update policy tree_order_statistics_node_update, which, in fact, carries the necessary operations. Consider them. Most likely, the best way to set the tree is as follows:

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


If we want to get map but not the set, as the second argument type must be used mapped type. Apparently, the tree supports the same operations as the set (at least I haven't any problems with them before), but also there are two new features — it is find_by_order() and order_of_key(). The first returns an iterator to the k-th largest element (counting from zero), the second — the number of items in a set that are strictly smaller than our item. Example of use:

    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


Finally I would like to say about the performance of order_statistics_tree in STL. For this, I provide the following table.

 Solution\Problem 1028 1090 1521 1439 order_statistics_tree, STL 0.062 0.218 0.296 0.468 Segment tree 0.031 0.078 0.171 0.078 0.859* Binary Indexed Tree 0.031 0.062 0.062 -

* The final task requires direct access to the nodes of the tree for the implementation of solutions for O (mlogn). Without it, the solution works in O (mlogn*logn).

As you can see from all this , order_statistics_tree relatively little behind handwritten structures, and at times ahead of them in execution time. At the same time the code size is reduced considerably. Hence we can conclude is that order_statistics_tree — it is good and it can be used in contests.

Besides tree, I also wanted to describe here trie. However , I was confused by some aspects of its implementation, greatly limiting its usefulness in programming olympiads, so I decided not to talk about it. If anyone want he is encouraged to try to learn more about this structure by himself.

P.S. Sorry for my poor English :)

• +120

| Write comment?
 » 9 years ago, # |   +12 Example of trie with search of prefix range. Problem: 1414 Solution: http://ideone.com/6VFNZl
•  » » 4 years ago, # ^ | ← Rev. 2 →   0 Is there a way of counting number of strings in the trie with a certain prefix without iterating through them all?
•  » » » 2 years ago, # ^ |   0 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.
 » 9 years ago, # |   +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.
•  » » 9 years ago, # ^ |   0 Here it is :)
 » 8 years ago, # |   +21 This is really useful. Thanks a lot!
 » 8 years ago, # |   0 Very useful article! I need order-statistics on a multiset. How should I define the tree as?
•  » » 8 years ago, # ^ |   +8 As I know, there is no implemented tree multiset in STL. However you can use pair as a key where the second element in pair is the time when item has been added.
•  » » » 6 years ago, # ^ |   +8 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)
•  » » » » 6 years ago, # ^ | ← Rev. 2 →   +11 I can't erase elements with less_equal comparator, e.g. this code output "1" code#include #include using namespace std; using namespace __gnu_pbds; typedef tree, 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 #include using namespace std; using namespace __gnu_pbds; typedef tree, 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 << ' '; } } 
•  » » » » » 6 years ago, # ^ |   0 Wow. then it really sucks. Seems like I only used it with insert operations and strangely enough it worked)
•  » » » » » » 11 months ago, # ^ |   0 5 years later I can say it is useful in some problems and this helped me today in this problem
•  » » » » » » » 11 months ago, # ^ |   0 glad it helped:)
•  » » » » » » 6 months ago, # ^ |   -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)) 
•  » » » » » 5 years ago, # ^ | ← Rev. 2 →   -8 Well, actually it works fine and exactly does what you want! The issue is that you're passing less_equal 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 > which results the same.
•  » » » » » 3 years ago, # ^ | ← Rev. 3 →   0 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) ?
•  » » » » » 2 years ago, # ^ |   0 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.
•  » » » » » 6 months ago, # ^ |   0 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.
•  » » » » » 2 months ago, # ^ |   0 I don't actually know how does it work, but if you use upper_bound instead of lower_bound it woulf work correctly.
•  » » » » 3 years ago, # ^ |   +3 Another drawback of using less_equal instead of less is that lower_bound works as upper_bound and vice-versa. Code
•  » » » » » 2 years ago, # ^ |   0 An excellent deduction.
•  » » » » 20 months ago, # ^ |   0 typedef tree, rb_tree_tag, tree_order_statistics_node_update> indexed_multiset; using " less_equal<> " makes it a multiset
•  » » » 3 years ago, # ^ | ← Rev. 2 →   0 What about the comparator i.e. less
•  » » 4 years ago, # ^ |   0 typedef tree indexed_multiset;
•  » » » 4 years ago, # ^ |   0 Can we use this in this question? or we can't use it, as I am not able to implement the multiset part
•  » » » » 4 years ago, # ^ |   +8 just use the fucking binary search on this problem
•  » » » 4 years ago, # ^ | ← Rev. 2 →   0 The 3rd template argument must be less_equal. 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?
• »
»
2 years ago, # ^ |
Rev. 2   0

#### Here's a quick way using Policy-Based Data Structures in C++:

There exists something called as an Ordered Set, which lets you insert/remove elements in O(log n) time (and pretty much all other functions that std::set has to offer). It also gives 2 more features: find the Kth element and find the rank of the Xth element. The problem is that this doesn't allow duplicates :(

No Worries though! We will map duplicates with a separate index/priority, and define a new structure (call it Ordered Multiset)! I've attached my implementation below for reference.

Finally, every time you want to find the no of elements greater than say x, call the function upper_bound (No of elements less than or equal to x) and subtract this number from the size of your Ordered Multiset!

Note: PBDS use a lot of memory, so that is a constraint, I'd suggest using a Binary Search Tree or a Fenwick Tree.

Code
Usage:
##### Time Complexity : O(log n) per insert/query
•  » » » 9 months ago, # ^ |   0 I tried this problem: https://codeforces.com/problemset/problem/1354/D the following way: https://pastebin.ubuntu.com/p/Q7fq7xMY9F/ But the only inserted I am getting is an invalid one (-1000000119) Please help me out.
•  » » 21 month(s) ago, # ^ |   0 To use order-statistics on a multiset: Use:: tree 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)
•  » » » 12 months ago, # ^ |   0 This is actually great. Whenever I needed to handle duplicate I used take pair. This is much simpler.
•  » » » 4 months ago, # ^ |   0 This really helps. I was just scrolling down in hope of someone would have hinted on how to handle duplicates, and if we want to use ordered_set on them. Thanks for the ordered multiset.
 » 8 years ago, # | ← Rev. 2 →   0 .(same comment as above)
 » 8 years ago, # |   0 what will be the complexity of erase operation? O(logn) or O(n)
•  » » 8 years ago, # ^ |   0 O(logn)
•  » » » 5 years ago, # ^ |   0 Really??
•  » » » » 5 years ago, # ^ |   0 Yes.
 » 8 years ago, # |   0 Is there any efficient function to merge 2 trees ?
•  » » 5 years ago, # ^ |   +1 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.
•  » » » 4 years ago, # ^ |   0 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...
•  » » » » 4 years ago, # ^ |   0 Have you found something interesting about merge ? Im trying to do .join but it throws error.
 » 7 years ago, # |   0 how can i use it like multiset ?
•  » » 7 years ago, # ^ |   0 Main idea is to keep pairs like {elem, id}. typedef tree< pair, null_type, less>, 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"; 
•  » » » 7 years ago, # ^ |   0 thanks a lot :)
•  » » » 5 years ago, # ^ |   0 like me.order_of_key({x, 0}) me.find_by_order({x,0}) dose not work.. why??
•  » » » » 5 years ago, # ^ |   0 *me.find_by_order({x,0})
•  » » » » » 5 years ago, # ^ |   0 still it does not work.
•  » » » » » » 3 years ago, # ^ |   0 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 ;
•  » » » » » 5 years ago, # ^ |   0 wtf, find_by_order takes number
•  » » » » » » 4 years ago, # ^ |   0 how to use find_by_order if I'm using ordered_set with pairs. ~~~~~ typedef tree< pair, null_type, less>, rb_tree_tag, tree_order_statistics_node_update> ordered_set; ~~~~~
•  » » » 3 years ago, # ^ |   0 nice technique. worked fine! thanks a lot.
•  » » 4 years ago, # ^ |   0 typedef tree indexed_multiset;
 » 7 years ago, # |   0 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.
•  » » 7 years ago, # ^ |   0 Can you elaborate please?
•  » » » 7 years ago, # ^ | ← Rev. 2 →   0 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.
•  » » » » 7 years ago, # ^ |   +1 I can't edit the original files — they're not mine. But here is the correct version: http://ideone.com/BpZlYO
•  » » » » » 7 years ago, # ^ |   0 Thank you.
 » 6 years ago, # |   0 https://www.e-olymp.com/ru/problems/2961 Is it possible to solve this problem using this algorithm?
 » 5 years ago, # |   +1 Can anybody share a Java equivalent class for this type of set or a code which acts according to above data structure?
•  » » 5 years ago, # ^ | ← Rev. 2 →   0 It does not exist.You may use instead: self-written tree treap numbers compression + fenwick tree
•  » » » 5 years ago, # ^ |   0 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?
 » 5 years ago, # |   0 Any idea on how to use this pre C++11?
 » 5 years ago, # |   0 How can I use a custom compare function in the "Key comparison functor" section for custom data types?
•  » » 5 years ago, # ^ |   0 Just like for regular set..
•  » » » 5 years ago, # ^ |   0 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.
•  » » » » 5 years ago, # ^ | ← Rev. 2 →   +3 I suppose you can overload operator and still use less. Also you can use functors and lambdas in the way similar as for sets: auto cmp = [](int a, int b){return a < b;}; tree x(cmp); tree> y([](int a, int b) { return a < b;}); 
•  » » » » » 3 years ago, # ^ |   0 Why does it only work with lambdas and not functions? On doing tree, 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.
•  » » » » » 9 months ago, # ^ |   0 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.
•  » » » » » » 9 months ago, # ^ | ← Rev. 2 →   0 Sorry, what doesn't work? struct cmp{ bool operator() (const int &a,const int &b){ return a <= b; } }; typedef tree 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.
•  » » » » » » » 9 months ago, # ^ | ← Rev. 2 →   0 Hey adamant, I got correct result after putting const keyword in the end of the argument.My cmp function looks line. Code:**class cmp { public: bool operator()(const int& a,const int& b) const { return a<=b; }}; typedef tree ordered_set;**Can you please tell me why we write const after argument passing?? Thanks for help
 » 5 years ago, # |   0 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.
 » 5 years ago, # |   +6 What is the constant factor of order_statistics_tree though it executes in logarithmic complexity ? I think it's constant factor is very high.
 » 5 years ago, # |   0 could anyone write the exact thing to use this data structure as map..pls.I'm not able do so.
•  » » 5 years ago, # ^ |   0 And what exactly do you want from it? You can use something like that. #include using namespace __gnu_pbds; template> using ordered_map = tree; ordered_map my_map; 
•  » » » 5 years ago, # ^ |   0 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;)
•  » » » 5 years ago, # ^ |   0 is this thing a order statistics tree
•  » » » 3 years ago, # ^ |   0 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}).
•  » » » » 3 years ago, # ^ |   0 What's wrong with find_by_order({x, 0})?
•  » » » » » 3 years ago, # ^ |   0 It gives an error. It says no known conversion. error: no matching function for call to '__gnu_pbds::tree, __gnu_pbds::null_type, std::less >, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>::find_by_order()
•  » » » » » » 3 years ago, # ^ |   0 Wait, find_by_order takes number $k$ and returns $k$-th element. What exactly do you expect it to return?..
•  » » » » » » » 3 years ago, # ^ |   0 A number .
•  » » » » » » » » 3 years ago, # ^ |   0 I think you should use order_of_key then
•  » » » » » » » » » 3 years ago, # ^ |   0 Thanks adamant I did that.
•  » » » » » 3 years ago, # ^ | ← Rev. 2 →   0 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.
 » 5 years ago, # |   0 can we use it as multiset?
•  » » 4 years ago, # ^ |   0 u can use pair for manage the duplicate values..
•  » » 4 years ago, # ^ |   0 typedef tree indexed_multiset;
•  » » » 4 years ago, # ^ | ← Rev. 2 →   0 It is:typedef tree, rb_tree_tag, tree_order_statistics_node_update> indexed_multiset;
•  » » » » 3 years ago, # ^ |   0 thank you bro :) it worked for duplicate elements too..
•  » » » » 3 years ago, # ^ |   0 what to do if i want to merge two ordered multisets?
 » 4 years ago, # |   0 How can I erase element from order_set by it's value?
•  » » 4 years ago, # ^ |   +1 just do ordered_set st; st.erase(key);
•  » » » 3 years ago, # ^ |   0 This doesn't work .
•  » » » » 3 years ago, # ^ |   0 ordered_set :: iterator it; it=st.upper_bound(key); st.erase(it); it works;
•  » » » » » 3 years ago, # ^ |   0 Thanks bro
•  » » 17 months ago, # ^ |   +3 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, 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)));
 » 4 years ago, # |   0 (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.
•  » » 3 years ago, # ^ |   0 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
•  » » » 23 months ago, # ^ |   0 (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(Replace the version names with your g++ versions) cd /usr/local/Cellar/gcc/10.2.0_4/bin ln -s ./c++-10 ./c++ ln -s ./g++-10 ./g++ Finally, put in your .bashrc/.zshrc file: export PATH=/usr/local/Cellar/gcc/10.2.0_4/bin:$PATHI might even find it useful myself if I ever need to setup a mac again in future. •  » » » » 12 days ago, # ^ | 0 (Sorry for Necroposting). But I have to update the details as from M1 onwards (possibly Big Sur) configurations have been changed. The Cellar directory is not available at /usr/local anymore. You can do the following instead.cd /opt/homebrew/Cellar/gcc/12.2.0/binln -s ./c++-12 ./c++ln -s ./g++-12 ./g++export PATH=“/opt/homebrew/Cellar/gcc/12.2.0/bin:$PATH”Did you manage to solve PBDS issue on your mac ? Doing all above doesn't solve the PBDS issue.
•  » » » » » 12 days ago, # ^ |   0 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++.
•  » » » » » » 12 days ago, # ^ |   0 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. 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 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.
•  » » » » » » » 12 days ago, # ^ |   0 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: 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 ... 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.
•  » » » » » » » » 11 days ago, # ^ |   0 It didn't. Because the files still are not available. But I quit now.
 » 4 years ago, # | ← Rev. 2 →   +6 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!
 » 4 years ago, # | ← Rev. 2 →   0 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
•  » » 4 years ago, # ^ |   0 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.
•  » » » 4 years ago, # ^ |   0 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.
•  » » » » 4 years ago, # ^ |   0 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
•  » » » » » 4 years ago, # ^ |   0 So, I should treat it as the worst time complexity of this data structure ?
•  » » » » » » 4 years ago, # ^ |   +1 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.
 » 3 years ago, # |   0 Thanks,it just got me an AC.
 » 3 years ago, # |   0 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.
•  » » 3 years ago, # ^ |   0 thanks bro ...do you know why it name like this ... why wrong extension is given to it..
 » 3 years ago, # |   0 I have defined a bool cmp(pair a, pair b) for comparing pairs. Is it possible to use that as the comparator for the ordered_set?
 » 3 years ago, # |   0 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)
•  » » 3 years ago, # ^ |   +1 Nope, this has nothing to do with the C++ standard library.
 » 3 years ago, # | ← Rev. 2 →   +1 This is a GNU extension, so it has nothing to do with the STL which (incorrectly) refers to the C++ standard library.
•  » » 3 years ago, # ^ |   0 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
•  » » » 3 years ago, # ^ | ← Rev. 3 →   0 I know, but here and in many other places "STL" is incorrectly used to refer to the C++ standard library.
 » 3 years ago, # |   +3 The first returns an iterator to the k-th largest element (counting from zero)Shouldn't it be the k-th smallest element? adamant
 » 3 years ago, # |   0 How to merge two ordered sets?
•  » » 3 years ago, # ^ |   0 Iterate through every element in the smaller set and append it to the bigger one
•  » » » 3 years ago, # ^ |   0 thanks brother
 » 3 years ago, # |   0 When to use BIT over PBDS other then memory limit
•  » » 3 years ago, # ^ |   0 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
 » 3 years ago, # |   0 can we use pair in place of int ??
•  » » 3 years ago, # ^ |   0 Sure, why not. We may use any type with operator < defined.
 » 3 years ago, # |   0 Is insert not too slow? I tried 10^7 insertions and it took over a minute.
 » 21 month(s) ago, # |   0 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
 » 13 months ago, # | ← Rev. 2 →   0 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.
 » 6 months ago, # |   0 Can I make the ordered set get the first element greater than x or even greater than or equal?
•  » » 6 months ago, # ^ |   0 *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
»
5 months ago, # |
0

## 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>;