A Union-Find data structure implementation which is able to store a priority for each item and retrieve the minimum of each class. In addition, it supports the joining and splitting the components. If you don't need this feature then you makes better to use the UnionFind class which is more efficient.
The union-find data strcuture based on a (2, 16)-tree with a tournament minimum selection on the internal nodes. The insert operation takes O(1), the find, set, decrease and increase takes O(log(n)), where n is the number of nodes in the current component. The complexity of join and split is O(log(n)*k), where n is the sum of the number of the nodes and k is the number of joined components or the number of the components after the split.
#include <lemon/unionfind.h>
Classes | |
class | ClassIt |
Class iterator. More... | |
class | ItemIt |
LEMON style iterator for the items of a class. More... | |
Public Types | |
typedef V | Value |
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typedef IM::Key | Item |
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typedef IM | ItemIntMap |
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typedef Comp | Compare |
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Public Member Functions | |
bool | alive (int cls) const |
Returns true when the given class is alive. More... | |
bool | trivial (int cls) const |
Returns true when the given class is trivial. More... | |
HeapUnionFind (ItemIntMap &_index) | |
Constructs the union-find. More... | |
void | clear () |
Clears the union-find data structure. More... | |
int | insert (const Item &item, const Value &prio) |
Insert a new node into a new component. More... | |
int | find (const Item &item) const |
The class of the item. More... | |
template<typename Iterator > | |
int | join (Iterator begin, Iterator end) |
Joins the classes. More... | |
template<typename Iterator > | |
void | split (int cls, Iterator out) |
Split the class to subclasses. More... | |
const Value & | operator[] (const Item &item) const |
Gives back the priority of the current item. More... | |
void | set (const Item &item, const Value &prio) |
Sets the priority of the current item. More... | |
void | increase (const Item &item, const Value &prio) |
Increase the priority of the current item. More... | |
void | decrease (const Item &item, const Value &prio) |
Increase the priority of the current item. More... | |
const Value & | classPrio (int cls) const |
Gives back the minimum priority of the class. More... | |
const Item & | classTop (int cls) const |
Gives back the minimum priority item of the class. More... | |
const Item & | classRep (int id) const |
Gives back a representant item of the class. More... | |
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Constructs the union-find. _index The index map of the union-find. The data structure uses internally for store references.
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Returns true when the given class is alive, ie. the class is not nested into other class.
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Returns true when the given class is trivial, ie. the class contains just one item directly.
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Erase each item from the data structure.
Insert a new node into a new component.
item | The item of the new node. |
prio | The priority of the new node. |
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The time complexity is O(log(n)).
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The current function joins the given classes. The parameter is an STL range which should be contains valid class ids. The time complexity is O(log(n)*k) where n is the overall number of the joined nodes and k is the number of classes.
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The current function splits the given class. The join, which made the current class, stored a reference to the subclasses. The splitClass()
member restores the classes and creates the heaps. The parameter is an STL output iterator which will be filled with the subclass ids. The time complexity is O(log(n)*k) where n is the overall number of nodes in the splitted classes and k is the number of the classes.
Gives back the priority of the current item.
Increase the priority of the current item.
Increase the priority of the current item.
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Gives back the minimum priority of the class.
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Gives back a representant item of the class. The representant is indpendent from the priorities of the items.