PARP Research Group  Universidad de Murcia 
QVDisjointSet Class Reference

Public Member Functions  
QVDisjointSet (uInt numElements)  
Constructs a disjoint set.  
QVDisjointSet (uInt cols, uInt rows)  
Constructs a QVDisjointSet object, that will maintain a partition of the set of pixels in an image.  
QVDisjointSet (const QVGenericImage &image)  
Constructs a QVDisjointSet object, that will maintain a partition of the set of pixels in a given image.  
QVDisjointSet (const QVDisjointSet &other)  
Copy constructor.  
uInt  find (QPoint p) 
Overloaded version of find, for partitions over the set of points contained in an image.  
uInt  find (uInt col, uInt row) 
Overloaded version of find, for partitions over the set of points contained in an image.  
uInt  find (uInt index) 
Retrieves a common integer identifier, for any element in the same subset of the partition.  
uInt  unify (QPoint p1, QPoint p2) 
Joins two subsets of points.  
uInt  unify (uInt c1, uInt r1, uInt c2, uInt r2) 
Overloaded version of unify, for partitions over the set of points contained in an image.  
uInt  unify (uInt index1, uInt index2) 
Joins two subsets.  
uInt  getSetCardinality (const QPoint &p1) 
Gets the number of elements contained in the set that includes the given element.  
uInt  getSetCardinality (uInt col, uInt row) 
Gets the number of elements contained in the set that uncles the given element.  
uInt  getSetCardinality (uInt index) 
Gets the number of elements contained in the set that includes the given element.  
uInt  numberOfSets () const 
Gets the number of different subgroups contained in the disjoint set.  
uInt  index (QPoint p) const 
Gets the number corresponding to the given point, in the integer set.  
uInt  index (uInt col, uInt row) const 
Gets the number corresponding to the given point, in the integer set.  
bool  isRootElement (uInt col, uInt row) const 
Checks if a given element is the root of its set.  
bool  isRootElement (uInt index) const 
Checks if a given element is the root of its set. 
Implementation of a disjoint set data type, based on the unionfind algorithm.
This implementation makes use of unionfind algorithms to maintain partitions efficiently. It is essentially built for maintaining disjoint sets of unsigned integer elements, in the rank from 0 to a given maximum element.
QVDisjointSet objects created with the constructor QVDisjointSet(uInt) partition the set in maxElement different sets, each one containing one of the elements of the set . Given 'maxElement' will be pass to the constructor to allocate data for the disjoint set.
Later, unify(uInt,uInt) and find(uInt) functions can be used respectively to join subsets of the partition, and to find which elements of the set are in the same subset.
Internally, all elements contained in the same subset in a partition are linked with one of those elements. That element will be the canonical element of the subset, and find(uInt) function retrieves that integer value.
Join two subsets is as simple as using unify(uInt,uInt) passing as parameters an element from each subset. After joining, using find(uInt) with any of those elements, or any contained in the original two sets joined, will return the same canonical element.
The class QVDisjointSet can be used to maintain partitions of general sets, as long as there is a bijection mapping between the set to be partitioned, and a set . An example of use of the class QVDisjointSet, for a general set given G_MAX_ELEMENT being the element to which corresponds the maximal integer value, could be this:
// Create disjoint set, with at least as many elements as the set G. QVDisjointSet disjointSet(G_MAX_ELEMENT.toInt()); [...] // Let element1, element2, ... be elements contained in the set G. // Configure structure of the disjoint set using unify function: disjointSet.unify(element1.toInt(), element2.toInt()); disjointSet.unify(element3.toInt(), element4.toInt()); [...] // Let elementA and elementB be elements contained in the set G. // Test whether elementA and elementB are contained in the same subset of the partition: if (disjointSet.find(elementA.toInt()) == disjointSet.find(elementB.toInt())) // case elements belong to the same subset in the disjoint set. else // elementA and elementB are not in the same subset of the disjoint set. [...]
This class however is specially design for dealing with sets of points in an image. Constructors QVDisjointSet(uInt,uInt) and QVDisjointSet(const QVGenericImage&) can be used to create disjoint sets prepared to represent a partition of the set of pixels contained in an image, without the need of converting points in the image, to integer values.
For that matter, functions union and find were overloaded to receive points in QPoint format (see find(QPoint) and unify(QPoint,QPoint) functions), and in coordinate pair format (see find(uInt,uInt) and unify(uInt,uInt,uInt,uInt) functions). The previous example, using QVDisjointSet to partitionate the points in a QVImage, could be rewritten like this:
// The QVImage to partition: QVImage<uChar> image(cols, rows); // Create disjoint set, from QVDisjointSet disjointSet(image); [...] // Configure structure of the disjoint set using unify function: disjointSet.unify(QPoint(1,2), QPoint(2,1)); disjointSet.unify(QPoint(4,5), QPoint(3,4)); [...] // Test whether points (10,9) and (8,8) are contained in the same subset of the partition: if (disjointSet.find(QPoint(10,9)) == disjointSet.find(QPoint(8,8))) // case points belong to the same subset in the disjoint set. else // given points are not in the same subset of the disjoint set. [...]
It can also be rewritten using find(uInt,uInt), unify(uInt,uInt,uInt,uInt), and QVDisjointSet(uInt,uInt), coordinate pair format overloaded versions of those functions:
// The QVImage to partition: QVImage<uChar> image(cols, rows); // Create disjoint set, from QVDisjointSet disjointSet(cols, rows); [...] // Configure structure of the disjoint set using unify function: disjointSet.unify(1, 2, 2, 1)); disjointSet.unify(4, 5, 3, 4)); [...] // Test whether points (10,9) and (8,8) are contained in the same subset of the partition: if (disjointSet.find(10,9) == disjointSet.find(8,8)) // case points belong to the same subset in the disjoint set. else // given points are not in the same subset of the disjoint set. [...]
Definition at line 128 of file qvdisjointset.h.
QVDisjointSet::QVDisjointSet  (  uInt  numElements  ) 
Constructs a disjoint set.
This constructor creates a QVDisjointSet object that will maintain a partition over the set of integers in the range 0..numElements.
numElements  maximal element contained in the disjoint set. 
Definition at line 28 of file qvdisjointset.cpp.
QVDisjointSet::QVDisjointSet  (  uInt  cols,  
uInt  rows  
) 
Constructs a QVDisjointSet object, that will maintain a partition of the set of pixels in an image.
You can only use functions find(QPoint p), find(uInt col, uInt row), unify(QPoint p1, QPoint p2), and unify(uInt c1, uInt r1, uInt c2, uInt r2) if the QVDisjointSet were created with this constructor, or the constructor QVDisjointSet(const QVGenericImage&).
cols  number of cols of the image to be partitionated.  
rows  number of rows of the image to be partitionated. 
Definition at line 48 of file qvdisjointset.cpp.
QVDisjointSet::QVDisjointSet  (  const QVGenericImage &  image  ) 
Constructs a QVDisjointSet object, that will maintain a partition of the set of pixels in a given image.
You can only use functions find(QPoint p), find(uInt col, uInt row), unify(QPoint p1, QPoint p2), and unify(uInt c1, uInt r1, uInt c2, uInt r2) if the QVDisjointSet were created with this constructor, or the constructor QVDisjointSet(uInt cols, uInt rows).
image  image containing the pixels to partition. 
Definition at line 56 of file qvdisjointset.cpp.
QVDisjointSet::QVDisjointSet  (  const QVDisjointSet &  other  ) 
Copy constructor.
Definition at line 35 of file qvdisjointset.cpp.
uInt QVDisjointSet::find  (  QPoint  p  )  [inline] 
Overloaded version of find, for partitions over the set of points contained in an image.
The function takes a point (QPoint p) as parameter, and converts it into an integer automatically. Then calls find(uInt) to obtain the canonical element (uInt) of the group that holds the integer corresponding to the point p.
This method can only be used if the disjoint set was constructed with the constructors QVDisjointSet(uInt,uInt) or QVDisjointSet(const QVGenericImage&). Otherwise the class can not convert the image point into an integer number.
p  point contained in the image. 
ASSERT: point belongs to rectangle (0,0), (cols, rows)
Definition at line 192 of file qvdisjointset.h.
Referenced by find(), getSetCardinality(), and unify().
uInt QVDisjointSet::find  (  uInt  col,  
uInt  row  
)  [inline] 
Overloaded version of find, for partitions over the set of points contained in an image.
The function takes the coordinates of a point (col, row) as parameter, and converts it into an integer automatically. Then calls find(uInt) to obtain the canonical element (uInt) of the group that holds the integer corresponding to the point p.
This method can only be used if the disjoint set was constructed with the constructors QVDisjointSet(uInt,uInt) or QVDisjointSet(const QVGenericImage&). Otherwise the class can not convert the image point into an integer number.
col  first coordinate of the point.  
row  second coordinate of the point. 
Definition at line 220 of file qvdisjointset.h.
uInt QVDisjointSet::find  (  uInt  index  )  [inline] 
Retrieves a common integer identifier, for any element in the same subset of the partition.
index  number identifying the element. 
Definition at line 234 of file qvdisjointset.h.
uInt QVDisjointSet::unify  (  QPoint  p1,  
QPoint  p2  
)  [inline] 
Joins two subsets of points.
This is an overloaded version of unify, for partitions over the set of points contained in an image. The function converts automatically both elements of the points of an image, represented with QPoints p1 and p2, into integers, to apply later the function unify(uInt,uInt) to join both subsets containing the corresponding integer elements for p1 and p2.
This method can only be used if the disjoint set was constructed with the constructors QVDisjointSet(uInt,uInt) or QVDisjointSet(const QVGenericImage&). Otherwise the class can not convert the image point into an integer number.
p1  element contained in the first set to be join.  
p2  element contained in the second set to be join. 
Definition at line 265 of file qvdisjointset.h.
Referenced by unify().
uInt QVDisjointSet::unify  (  uInt  c1,  
uInt  r1,  
uInt  c2,  
uInt  r2  
)  [inline] 
Overloaded version of unify, for partitions over the set of points contained in an image.
The function converts automatically both elements of the points of an image, represented with QPoints p1 and p2, into integers, to apply later the function unify(uInt,uInt) to join both subsets containing elements p1 and p2.
This method can only be used if the disjoint set was constructed with the constructors QVDisjointSet(uInt,uInt) or QVDisjointSet(const QVGenericImage&). Otherwise the class can not convert the image point into an integer number.
c1  first coordinate of a point from the first set.  
r1  second coordinate of a point front the first set.  
c2  first coordinate of a point frond the second set.  
r2  second coordinate of a point frown the second set. 
Definition at line 294 of file qvdisjointset.h.
uInt QVDisjointSet::unify  (  uInt  index1,  
uInt  index2  
) 
Joins two subsets.
Given two elements of the partitionated set (or their set indexes), joins the two subsets that contain those elements in a new subset.
index1  number identifying first element.  
index2  number identifying second element. 
Definition at line 72 of file qvdisjointset.cpp.
uInt QVDisjointSet::getSetCardinality  (  const QPoint &  p1  )  [inline] 
Gets the number of elements contained in the set that includes the given element.
p1  point contained in the set. 
Definition at line 321 of file qvdisjointset.h.
Referenced by getSetCardinality().
uInt QVDisjointSet::getSetCardinality  (  uInt  col,  
uInt  row  
)  [inline] 
Gets the number of elements contained in the set that uncles the given element.
col  first coordinate of the point.  
row  second coordinate of the point. 
Definition at line 328 of file qvdisjointset.h.
Referenced by getSetCardinality().
uInt QVDisjointSet::getSetCardinality  (  uInt  index  )  [inline] 
Gets the number of elements contained in the set that includes the given element.
index  identifying integer of the element contained in the set. 
Definition at line 334 of file qvdisjointset.h.
uInt QVDisjointSet::numberOfSets  (  )  const [inline] 
Gets the number of different subgroups contained in the disjoint set.
Definition at line 343 of file qvdisjointset.h.
uInt QVDisjointSet::index  (  QPoint  p  )  const [inline] 
Gets the number corresponding to the given point, in the integer set.
p  point contained in the image. 
Definition at line 349 of file qvdisjointset.h.
uInt QVDisjointSet::index  (  uInt  col,  
uInt  row  
)  const [inline] 
Gets the number corresponding to the given point, in the integer set.
col  first coordinate of the point.  
col  second coordinate of the point. 
Definition at line 356 of file qvdisjointset.h.
bool QVDisjointSet::isRootElement  (  uInt  col,  
uInt  row  
)  const [inline] 
Checks if a given element is the root of its set.
col  first coordinate of the point.  
col  second coordinate of the point. 
Definition at line 364 of file qvdisjointset.h.
Referenced by isRootElement().
bool QVDisjointSet::isRootElement  (  uInt  index  )  const [inline] 
Checks if a given element is the root of its set.
This function is a replacement for the expression:
Faster than that expression, if find is not needed to be called.
col  first coordinate of the point.  
col  second coordinate of the point. 
Definition at line 376 of file qvdisjointset.h.