Why does the C++ STL not provide any "tree" containers?

Why does the C++ STL not provide any "tree" containers, and what's the best thing to use instead?

I want to store a hierarchy of objects as a tree, rather than use a tree as a performance enhancement...

There are two reasons you could want to use a tree:

You want to mirror the problem using a tree-like structure:
For this we have boost graph library

Or you want a container that has tree like access characteristics For this we have

• std::map (and std::multimap)
• std::set (and std::multiset)

Basically the characteristics of these two containers is such that they practically have to be implemented using trees (though this is not actually a requirement).

See also this question: C tree Implementation

Probably for the same reason that there is no tree container in boost. There are many ways to implement such a container, and there is no good way to satisfy everyone who would use it.

Some issues to consider:

• Are the number of children for a node fixed or variable?
• How much overhead per node? - ie, do you need parent pointers, sibling pointers, etc.
• What algorithms to provide? - different iterators, search algorithms, etc.

In the end, the problem ends up being that a tree container that would be useful enough to everyone, would be too heavyweight to satisfy most of the people using it. If you are looking for something powerful, Boost Graph Library is essentially a superset of what a tree library could be used for.

Here are some other generic tree implementations:

• Kasper Peeters' tree.hh

• Adobe's forest

• core::tree

The STL's philosophy is that you choose a container based on guarantees and not based on how the container is implemented. For example, your choice of container may be based on a need for fast lookups. For all you care, the container may be implemented as a unidirectional list -- as long as searching is very fast you'd be happy. That's because you're not touching the internals anyhow, you're using iterators or member functions for the access. Your code is not bound to how the container is implemented but to how fast it is, or whether it has a fixed and defined ordering, or whether it is efficient on space, and so on.

> "I want to store a hierarchy of objects as a tree"

C++11 has come and gone and they still didn't see a need to provide a std::tree, although the idea did come up (see here). Maybe the reason they haven't added this is that it is trivially easy to build your own on top of the existing containers. For example...

template< typename T >
struct tree_node
   {
   T t;
   std::vector<tree_node> children;
   };

A simple traversal would use recursion...

template< typename T >
void tree_node<T>::walk_depth_first() const
   {
   cout<<t;
   for ( auto & n: children ) n.walk_depth_first();
   }

If you want to maintain a hierarchy and you want it to work with STL algorithms, then things may get complicated. You could build your own iterators and achieve some compatibility, however many of the algorithms simply don't make any sense for a hierarchy (anything that changes the order of a range, for example). Even defining a range within a hierarchy could be a messy business.

If you are looking for a RB-tree implementation, then stl_tree.h might be appropriate for you too.

the std::map is based on a red black tree. You can also use other containers to help you implement your own types of trees.

In a way, std::map is a tree (it is required to have the same performance characteristics as a balanced binary tree) but it doesn't expose other tree functionality. The likely reasoning behind not including a real tree data structure was probably just a matter of not including everything in the stl. The stl can be looked as a framework to use in implementing your own algorithms and data structures.

In general, if there's a basic library functionality that you want, that's not in the stl, the fix is to look at BOOST.

Otherwise, there's a bunch of libraries out there, depending on the needs of your tree.

All STL container are externally represented as "sequences" with one iteration mechanism. Trees don't follow this idiom.

I think there are several reasons why there are no STL trees. Primarily Trees are a form of recursive data structure which, like a container (list, vector, set), has very different fine structure which makes the correct choices tricky. They are also very easy to construct in basic form using the STL.

A finite rooted tree can be thought of as a container which has a value or payload, say an instance of a class A and, a possibly empty collection of rooted (sub) trees; trees with empty collection of subtrees are thought of as leaves.

template<class A>
struct unordered_tree : std::set<unordered_tree>, A
{};

template<class A>
struct b_tree : std::vector<b_tree>, A
{};

template<class A>
struct planar_tree : std::list<planar_tree>, A
{};

One has to think a little about iterator design etc. and which product and co-product operations one allows to define and be efficient between trees - and the original STL has to be well written - so that the empty set, vector or list container is really empty of any payload in the default case.

Trees play an essential role in many mathematical structures (see the classical papers of Butcher, Grossman and Larsen; also the papers of Connes and Kriemer for examples of they can be joined, and how they are used to enumerate). It is not correct to think their role is simply to facilitate certain other operations. Rather they facilitate those tasks because of their fundamental role as a data structure.

However, in addition to trees there are also "co-trees"; the trees above all have the property that if you delete the root you delete everything.

Consider iterators on the tree, probably they would be realised as a simple stack of iterators, to a node, and to its parent, ... up to the root.

template<class TREE>
struct node_iterator : std::stack<TREE::iterator>{
operator*() {return *back();}
...};

However, you can have as many as you like; collectively they form a "tree" but where all the arrows flow in the direction toward the root, this co-tree can be iterated through iterators towards the trivial iterator and root; however it cannot be navigated across or down (the other iterators are not known to it) nor can the ensemble of iterators be deleted except by keeping track of all the instances.

Trees are incredibly useful, they have a lot of structure, this makes it a serious challenge to get the definitively correct approach. In my view this is why they are not implemented in the STL. Moreover, in the past, I have seen people get religious and find the idea of a type of container containing instances of its own type challenging - but they have to face it - that is what a tree type represents - it is a node containing a possibly empty collection of (smaller) trees. The current language permits it without challenge providing the default constructor for container<B> does not allocate space on the heap (or anywhere else) for an B, etc.

I for one would be pleased if this did, in a good form, find its way into the standard.

The problem is that there is no one-size-fits-all solution. Moreover, there is not even a one-size-fits-all interface for a tree. That is, it is not even clear which methods such a tree data structure should provide and it is not even clear what a tree is.

This explains why there is no STL support on this: The STL is for data structures that most people need, where basically everyone agrees on what a sensible interface and an efficient implementation is. For trees, such a thing just doesn't exist.

The gory details

If want to understand further what the problem is, read on. Otherwise, the paragraph above already should be sufficent to answer your question.

I said that there is not even a common interface. You might disagree, since you have one application in mind, but if you think further about it, you will see that there are countless possible operations on trees. You can either have a data structure that enables most of them efficiently, but therefore is more complex overall and has overhead for that complexity, or you have more simple data structure that only allows basic operations but these as quick as possible.

If you want the complete story, check out my paper on the topic. There you will find possible interface, asymptotic complexities on different implementations, and a general description of the problem and also related work with more possible implementations.

What is a tree?

It already starts with what you consider to be a tree:

• Rooted or unrooted: most programmers want rooted, most mathematicians want unrooted. (If you wonder what unrooted is: A - B - C is a tree where either A, B, or C could be the root. A rooted tree defines which one is. An unrooted doesn't)
• Single root/connected or multi root/disconnected (tree or forest)
• Is sibling order relevant? If no, then can the tree structure internally reorder children on updates? If so, iteration order among siblings is no longer defined. But for most trees, sibiling order is actually not meaningful, and allowing the data structure to reorder children on update is very beneficial for some updates.
• Really just a tree, or also allow DAG edges (sounds weird, but many people who initially want a tree eventually want a DAG)
• Labeled or unlabled? Do you need to store any data per node, or is it only the tree structure you're interested in (the latter can be stored very succinctly)

Query operations

After we have figured out what we define to be a tree, we should define query operations: Basic operations might be "navigate to children, navigate to parent", but there are way more possible operations, e.g.:

• Navigate to next/prev sibling: Even most people would consider this a pretty basic operation, it is actually almost impossible if you only have a parent pointer or a children array. So this already shows you that you might need a totally different implementation based on what operations you need.
• Navigate in pre/post order
• Subtree size: the number of (transitive) descendants of the current node (possibly in O(1) or O(log n), i.e., don't just enumerate them all to count)
• the height of the tree in the current node. That is, the longest path from this node to any leave node. Again, in less than O(n).
• Given two nodes, find the least common ancestor of the node (with O(1) memory consumption)
• How many nodes are between node A and node B in a pre-/post-order traversal? (less than O(n) runtime)

I emphasized that the interesting thing here is whether these methods can be performed better than O(n), because just enumerating the whole tree is always an option. Depending on your application, it might be absolutely crucial that some operations are faster than O(n), or you might not care at all. Again, you will need vastely different data structures depending on your needs here.

Update operations

Until now, I only talked about query opertions. But now to updates. Again, there are various ways in which a tree could be updated. Depending on which you need, you need a more or less sophisticated data structure:

• leaf updates (easy): Delete or add a leaf node
• inner node updates (harder): Move or delete move an inner node, making its children the children of its parent
• subtree updates (harder): Move or delete a subtree rooted in a node

To just give you some intuition: If you store a child array and your sibling order is important, even deleting a leaf can be O(n) as all siblings behind it have to be shifted in the child array of its parent. If you instead only have a parent pointer, leaf deletion is trivially O(1). If you don't care about sibiling order, it is also O(1) for the child array, as you can simply replace the gap with the last sibling in the array. This is just one example where different data structures will give you quite different update capabilities.

Moving a whole subtree is again trivially O(1) in case of a parent pointer, but can be O(n) if you have a data structure storing all nodes e.g., in pre-order.

Then, there are orthogonal considerations like which iterators stay valid if you perform updates. Some data structures need to invalidate all iterators in the whole tree, even if you insert a new leaf. Others only invalidate iterators in the part of the tree that is altered. Others keep all iterators (except the ones for deleted nodes) valid.

Space considerations

Tree structures can be very succinct. Roughly two bits per node are enough if you need to save on space (e.g., DFUDS or LOUDS, see this explanation to get the gist). But of course, naively, even a parent pointer is already 64 bits. Once you opt for a nicely-navigable structure, you might rather require 20 bytes per node.

With a lot of sophisication, one can also build a data structure that only takes some bits per entry, can be updated efficiently, and still enables all query operations asymptotically fast, but this is a beast of a structure that is highly complex. I once gave a practical course where I had grad students implement this paper. Some of them were able to implement it in 6 weeks (!), others failed. And while the structure has great asymptotics, its complexity makes it have quite some overhead for very simple operations.

Again, no one-size-fits-all.

Conclusion

I worked 5 years on finding the best data structure to represent a tree, and even though I came up with some and there is quite some related work, my conclusion was that there is not one. Depending on the use case, a highly sophsticated data struture will be outperformed by a simple parent pointer. Even defining the interface for a tree is hard. I tried defining one in my paper, but I have to acknowledge that there are various use cases where the interface I defined is too narrow or too large. So I doubt that this will ever end up in STL, as there are just too many tuning knobs.

Because the STL is not an "everything" library. It contains, essentially, the minimum structures needed to build things.

This one looks promising and seems to be what you're looking for: http://tree.phi-sci.com/

IMO, an omission. But I think there is good reason not to include a Tree structure in the STL. There is a lot of logic in maintaining a tree, which is best written as member functions into the base TreeNode object. When TreeNode is wrapped up in an STL header, it just gets messier.

For example:

template <typename T>
struct TreeNode
{
  T* DATA ; // data of type T to be stored at this TreeNode

  vector< TreeNode<T>* > children ;

  // insertion logic for if an insert is asked of me.
  // may append to children, or may pass off to one of the child nodes
  void insert( T* newData ) ;
  
} ;

template <typename T>
struct Tree
{
  TreeNode<T>* root;
  
  // TREE LEVEL functions
  void clear() { delete root ; root=0; }
  
  void insert( T* data ) { if(root)root->insert(data); } 
} ;

Reading through the answers here the common named reasons are that one cannot iterate through the tree or that the tree does not assume the similar interface to other STL containers and one could not use STL algorithms with such tree structure.

Having that in mind I tried to design my own tree data structure which will provide STL-like interface and will be usable with existing STL algorthims as much as possible.

My idea was that the tree must be based on the existing STL containers and that it must not hide the container, so that it will be accessible to use with STL algorithms.

The other important feature the tree must provide is the traversing iterators.

Here is what I was able to come up with: https://github.com/cppfw/utki/blob/master/src/utki/tree.hpp

And here are the tests: https://github.com/cppfw/utki/blob/master/tests/unit/src/tree.cpp

All STL containers can be used with iterators. You can't have an iterator an a tree, because you don't have ''one right'' way do go through the tree.