Is there any MFC / STL class that represents Binary Tree [duplicate] - c++
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
"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.
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.
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.
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.
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.
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.
Related
Can a map be used as a tree?
eg. std::map<Item, std::vector<Item> >. Would that be able serve as a "quick-and-dirty" tree structure (with some helper functions on top and given that less is implemented for Item), given that theres none in the std/boost ? Would a std::unordered_map be better suited/more usefull/beneficial ? that requires a hash instead of compare though - which can be harder to implement. I can see one issue though, finding parent/owner have to brute force go through the entire map (although that might be best stored in seperate structure if needed). Another thing Im not so fond of is the sort of dual meaning of a map entry with an Item with an empty child list.
Can a map be used as a tree? Situation is inverse: std::map is internally implemented using a tree. So tree can (is) used as a map. Neither map nor unordered map are useful for implementing a general tree structure. Only if your intention is to use the tree as a map would it be useful to use these structures (because they are maps which was desirable in this scenario)
You can absolutely represent a tree in this manner; whether it's a good idea in a given situation depends entirely on which operations you need to be fast, which operations you're okay with being slow, and what your space requirements are. (And of course in many applications the answer to all of the above may be "I don't care," in which case any implementation is probably fine.)
How can I get the root of a binary tree (set or map)?
How can I get the root node of an std::set or std::map? It provides function for getting the begin() and end() iterators, but I haven't seen anything in the documentation about getting the root.
You can not do that. That is why you were provided with iterators - to abstract yourself away from implementation details. Moreover, I have just done Ctrl + F on "tree" keyword in C++ Standard and found only 5 occurrences none of which is related to set/map implementation details. If you need root of binary tree - create your own data structure.
I was also looking at this functionality. Looks like we can't directly get the root value of an stl map or set unless we iterate thru the map/set. Ex: from the total size of the map, get the root index (which is size/2) and then iterate till you have covered that many elements in the map. THis approach will work since the stl map is internally a balanced tree. Why I need this? For a problem, I want to get the median. The easiest way out is to return the root (or the average of root and its right child). I also have my own implementation of a binary tree which I could use here. But for this problem, I want the tree to be balanced. I have the following options - use a stl map. This is a balanced DS. however, there is no easy way of getting the root or an element by index number. Ex: I can't get the element at index 4. So, I was thinking of iterating thru the map till I get the root. Nice and quick and easy - but calculating the median will take O(n/2). Implement a balanced tree and add a function to return the root value. More work to do. However, I can retrieve the median in O(1) time. If you can think of a better way to do this, pls let me know.
There is no concept of root node in any of those Abstract Data Types (neither set nor map). The fact that they are implemented as a red–black tree is just an implementation detail. Here are the operations supported: Set: Operations Map (associative array): Operations From the wikipedia page, one of the benefits about ADT is: Encapsulation Abstraction provides a promise that any implementation of the ADT has certain properties and abilities; knowing these is all that is required to make use of an ADT object. The user does not need any technical knowledge of how the implementation works to use the ADT. In this way, the implementation may be complex but will be encapsulated in a simple interface when it is actually used. It seems you are trying to break that encapsulation trying to know too much about the implementation.
Algorithm for removing multiple elements from a Red-Black tree
Is there an algorithm that allows to delete multiple nodes in RB or the only algorithm to delete nodes from RB is to do it in a way: 1. Delete one and 2. if necessary fix tree
If more than half the nodes are being deleted, you can throw away the existing tree and build a new one in less time, since insertion and deletion have the same cost.
If there is no constraint that says the tree must remain balanced while you are doing a multiple node deletion, it seems reasonable to me that you could fix the tree after doing multiple deletes. The purpose of balancing the tree after each deletion is to make sure the delete operation is consistent in its computational cost. If you do not require deletes to be consistent in this fashion, you could write your delete algorithm differently. The fixup operation will be a more lengthy computation than after just one delete, though. It will also likely be a more complicated one, too.
You might be interested in a data structure called TeardownTree. It supports delete_range operation that works in O(k + log n) time, where n is the initial number of items in the tree and k is the number of items deleted (and returned to the caller). Full disclosure: I am the author. I have to emphasize that the data structure does not support the insert operation, but is optimized for clone and delete_range. I have written up an informal description of the algorithm. With all the optimizations the code is now significantly different from that document, but it should be enough to grasp the idea.
The way I solved this problem was to create a linked list of nodes to be deleted and to use the standard deletion method on them in succession. I would be interested to know if there is a better algorithm for mass deletion.
I would suggest using a Treap instead of a Red-Black tree, since balancing the tree in various scenarios seems easier with a Treap v/s a Red-Black tree. I'm have the same problem as you, but with Treaps. https://cstheory.stackexchange.com/questions/20495/algorithm-to-bulk-delete-nodes-from-a-treap Am unsure if the expected height bounds remain valid post bulk-deletion (algorithm mentioned in the question).
How to load/save C++ class instance (using STL containers) to disk
I have a C++ class representing a hierarchically organised data tree which is very large (~Gb, basically as large as I can get away with in memory). It uses an STL list to store information at each node plus iterators to other nodes. Each node has only one parent, but 0-10 children.
Abstracted, it looks something like:
struct node {
public:
node_list_iterator parent; // iterator to a single parent node
double node_data_array[X];
map<int,node_list_iterator> children; // iterators to child nodes
};
class strategy {
private:
list<node> tree; // hierarchically linked list of nodes
struct some_other_data;
public:
void build(); // build the tree
void save(); // save the tree from disk
void load(); // load the tree from disk
void use(); // use the tree
};
I would like to implement the load() and save() to disk, and it should be fairly fast, however the obvious problems are:
I don't know the size in advance;
The data contains iterators, which
are volatile;
My ignorance of C++ is prodigious.
Could anyone suggest a pure C++ solution please?
It seems like you could save the data in the following syntax: File = Meta-data Node Node = Node-data ChildCount NodeList NodeList = sequence (int, Node) That is to say, when serialized the root node contains all nodes, either directly (children) or indirectly (other descendants). Writing the format is fairly straightforward: just have a recursive write function starting at the root node. Reading isn't that much harder. std::list<node> iterators are stable. Once you've inserted the root node, its iterator will not change, not even when inserting its children. Hence, when you're reading each node you can already set the parent iterator. This of course leaves you with the child iterators, but those are trivial: each node is a child of its parents. So, after you've read all nodes you'll fix up the child iterators. Start with the second node, the first child (The first node one was the root) and iterate to the last child. Then, for each child C, get its parent and the child to its parent's collection. Now, this means that you have to set the int child IDs aside while reading, but you can do that in a simple std::vector parallel to the std::list<node>. Once you've patched all child IDs in the respective parents, you can discard the vector.
You can use boost.serialization library. This would save entire state of your container, even the iterators.
boost.serialization is a solution, or IMHO, you can use SQLite + Visitor pattern to load and save these nodes, but it won't be easy as it sounds.
Boost Serialization has already been suggested, and it's certainly a reasonable possibility. A great deal depends on how you're going to use the data -- the fact that you're using a multiway tree in memory doesn't mean you necessarily have to store it as a multiway tree on disk. Since you're (apparently) already pushing the limits of what you can store in memory, the obvious question is whether you're just interested in serializing the data so you can re-constitute the same tree when needed, or whether you want something like a database so you can load parts of the information into memory as needed, and update records as needed. If you want the latter, some of your choices will also depend on how static the structure is. For example, if a particular node has N children, is that number constant or is it subject to change? If it's subject to change, is there a limit on the maximum number of children? If you do want to be able to traverse the structure on disk, one obvious possibility would be as you write it out, substitute the file offset of the appropriate data in place of the iterator you're using in memory. Alternatively, since it looks like (at least most of) the data in an individual node has a fixed size, you might create a database-like structure of fixed-size records, and in each record record the record numbers of the parent/children. Knowing the overall size in advance isn't particularly important (offhand, I can't think of any way I'd use the size even if it was known in advance).
Actually, I think your best option is to move the entire data structure into database tables. That way you get the benefit of people much smarter then you (or me) having dealt with issues of serialization. It will also prevent you from having to worry about whether the structure can fit into memory.
I've answered something like this on SO before, so I will summarize: 1. Use a database. 2. Substitute file offsets for links (pointers). 3. Store the data without the tree structure, in records, as a database would. 4. Use XML to create the tree structure, using node names instead of links. 5. This would be soooo much easier if you used a database like SqLite or MySQL. When you spend too much time on the "serialization" and less on the primary purpose of your project, you need to use a database.
If you're doing it for persistence then there are several solutions you can use from the web i.e. google "persist std::list" or you can roll your own using mmap to create a file backed memory area.
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
"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.
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.
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.
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.
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.
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.