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GIntervalTree.hh
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#ifndef E_INTERVAL_TREE
#define E_INTERVAL_TREE
#include "GBase.h"
#include "GVec.hh"
// This is an interval tree implementation based on red-black-trees
// as described in the book _Introduction_To_Algorithms_ by Cormen, Leisserson, and Rivest.
class GIntervalTreeNode {
friend class GIntervalTree;
protected:
GSeg* storedInterval;
int key;
int high;
int maxHigh;
int red; /* if red=0 then the node is black */
GIntervalTreeNode* left;
GIntervalTreeNode* right;
GIntervalTreeNode* parent;
public:
void Print(GIntervalTreeNode* nil,
GIntervalTreeNode* root) const {
printf(", k=%i, h=%i, mH=%i",key,high,maxHigh);
printf(" l->key=");
if( left == nil) printf("NULL"); else printf("%i",left->key);
printf(" r->key=");
if( right == nil) printf("NULL"); else printf("%i",right->key);
printf(" p->key=");
if( parent == root) printf("NULL"); else printf("%i",parent->key);
printf(" red=%i\n",red);
}
GIntervalTreeNode():storedInterval(NULL), key(0), high(0),maxHigh(0),red(0),
left(NULL), right(NULL), parent(NULL) {}
GIntervalTreeNode(GSeg * newInterval): storedInterval (newInterval),
key(newInterval->start), high(newInterval->end) ,
maxHigh(high), red(0), left(NULL), right(NULL), parent(NULL) { }
~GIntervalTreeNode() {}
};
struct G_ITRecursionNode {
public:
// this structure stores the information needed when we take the
// right branch in searching for intervals but possibly come back
// and check the left branch as well.
GIntervalTreeNode * start_node;
unsigned int parentIndex;
int tryRightBranch;
} ;
class GIntervalTree {
private:
unsigned int recursionNodeStackSize;
G_ITRecursionNode * recursionNodeStack;
unsigned int currentParent;
unsigned int recursionNodeStackTop;
protected:
// A sentinel is used for root and for nil. root->left should always
// point to the node which is the root of the tree. nil points to a
// node which should always be black but has arbitrary children and
// parent and no key or info; These sentinels are used so
// that the root and nil nodes do not require special treatment in the code
GIntervalTreeNode* root;
GIntervalTreeNode* nil;
// INPUT: the node to rotate on
// Rotates as described in _Introduction_To_Algorithms by
// Cormen, Leiserson, Rivest (Chapter 14). Basically this
// makes the parent of x be to the left of x, x the parent of
// its parent before the rotation and fixes other pointers
// accordingly. Also updates the maxHigh fields of x and y
// after rotation.
void LeftRotate(GIntervalTreeNode* x) {
GIntervalTreeNode* y;
// originally wrote this function to use the sentinel for
// nil to avoid checking for nil. However this introduces a
// very subtle bug because sometimes this function modifies
// the parent pointer of nil. This can be a problem if a
// function which calls LeftRotate also uses the nil sentinel
// and expects the nil sentinel's parent pointer to be unchanged
// after calling this function. For example, when DeleteFixUP
// calls LeftRotate it expects the parent pointer of nil to be
// unchanged.
y=x->right;
x->right=y->left;
if (y->left != nil) y->left->parent=x; // used to use sentinel here
// and do an unconditional assignment instead of testing for nil
y->parent=x->parent;
// instead of checking if x->parent is the root as in the book, we
// count on the root sentinel to implicitly take care of this case
if( x == x->parent->left) {
x->parent->left=y;
} else {
x->parent->right=y;
}
y->left=x;
x->parent=y;
x->maxHigh=GMAX(x->left->maxHigh, GMAX(x->right->maxHigh,x->high));
y->maxHigh=GMAX(x->maxHigh,GMAX(y->right->maxHigh,y->high));
}
// make the parent of x be to the left of x, x the parent of
// its parent before the rotation and fixes other pointers
// accordingly. Also updates the maxHigh fields of x and y
// after rotation.
void RightRotate(GIntervalTreeNode*y) {
GIntervalTreeNode* x;
x=y->left;
y->left=x->right;
if (nil != x->right) x->right->parent=y; //used to use sentinel here
// and do an unconditional assignment instead of testing for nil
// instead of checking if x->parent is the root as in the book, we
// count on the root sentinel to implicitly take care of this case
x->parent=y->parent;
if( y == y->parent->left) {
y->parent->left=x;
} else {
y->parent->right=x;
}
x->right=y;
y->parent=x;
y->maxHigh=GMAX(y->left->maxHigh,GMAX(y->right->maxHigh,y->high));
x->maxHigh=GMAX(x->left->maxHigh,GMAX(y->maxHigh,x->high));
}
// Inserts z into the tree as if it were a regular binary tree
// using the algorithm described in _Introduction_To_Algorithms_
// by Cormen et al. This function is only intended to be called
// by the InsertTree function and not by the user
void TreeInsertHelp(GIntervalTreeNode* z) {
// this should only be called by the Insert method
GIntervalTreeNode* x;
GIntervalTreeNode* y;
z->left=z->right=nil;
y=root;
x=root->left;
while( x != nil) {
y=x;
if ( x->key > z->key) {
x=x->left;
} else { // x->key <= z->key
x=x->right;
}
}
z->parent=y;
if ( (y == root) ||
(y->key > z->key) ) {
y->left=z;
} else {
y->right=z;
}
#if defined(DEBUG_ASSERT)
Assert(!nil->red,"nil not red in ITTreeInsertHelp");
Assert((nil->maxHigh=MIN_INT),
"nil->maxHigh != MIN_INT in ITTreeInsertHelp");
#endif
}
void TreePrintHelper(GIntervalTreeNode* x) const {
if (x != nil) {
TreePrintHelper(x->left);
x->Print(nil,root);
TreePrintHelper(x->right);
}
}
// FUNCTION: FixUpMaxHigh
// INPUTS: x is the node to start from
// EFFECTS: Travels up to the root fixing the maxHigh fields after
// an insertion or deletion
void FixUpMaxHigh(GIntervalTreeNode* x) {
while(x != root) {
x->maxHigh=GMAX(x->high,GMAX(x->left->maxHigh,x->right->maxHigh));
x=x->parent;
}
}
// FUNCTION: DeleteFixUp
// INPUTS: x is the child of the spliced
// out node in DeleteNode.
// EFFECT: Performs rotations and changes colors to restore red-black
// properties after a node is deleted
void DeleteFixUp(GIntervalTreeNode* x) {
GIntervalTreeNode * w;
GIntervalTreeNode * rootLeft = root->left;
while( (!x->red) && (rootLeft != x)) {
if (x == x->parent->left) {
w=x->parent->right;
if (w->red) {
w->red=0;
x->parent->red=1;
LeftRotate(x->parent);
w=x->parent->right;
}
if ( (!w->right->red) && (!w->left->red) ) {
w->red=1;
x=x->parent;
} else {
if (!w->right->red) {
w->left->red=0;
w->red=1;
RightRotate(w);
w=x->parent->right;
}
w->red=x->parent->red;
x->parent->red=0;
w->right->red=0;
LeftRotate(x->parent);
x=rootLeft; // this is to exit while loop
}
} else { // the code below is has left and right switched from above
w=x->parent->left;
if (w->red) {
w->red=0;
x->parent->red=1;
RightRotate(x->parent);
w=x->parent->left;
}
if ( (!w->right->red) && (!w->left->red) ) {
w->red=1;
x=x->parent;
} else {
if (!w->left->red) {
w->right->red=0;
w->red=1;
LeftRotate(w);
w=x->parent->left;
}
w->red=x->parent->red;
x->parent->red=0;
w->left->red=0;
RightRotate(x->parent);
x=rootLeft; // this is to exit while loop
}
}
}
x->red=0;
}
// Make sure the maxHigh fields for everything makes sense.
void CheckMaxHighFields(GIntervalTreeNode * x) const {
if (x != nil) {
CheckMaxHighFields(x->left);
if(!(CheckMaxHighFieldsHelper(x,x->maxHigh,0) > 0)) {
GEXIT("Error found in CheckMaxHighFields.\n");
}
CheckMaxHighFields(x->right);
}
}
int CheckMaxHighFieldsHelper(GIntervalTreeNode * y,
const int currentHigh,
int match) const {
if (y != nil) {
match = CheckMaxHighFieldsHelper(y->left,currentHigh,match) ?
1 : match;
GVERIFY(y->high <= currentHigh);
if (y->high == currentHigh)
match = 1;
match = CheckMaxHighFieldsHelper(y->right,currentHigh,match) ?
1 : match;
}
return match;
}public:
GIntervalTree():recursionNodeStackSize(128),
recursionNodeStack(NULL), currentParent(0), recursionNodeStackTop(1),
root(new GIntervalTreeNode), nil(new GIntervalTreeNode) {
//nil = new IntervalTreeNode;
nil->left = nil->right = nil->parent = nil;
nil->red = 0;
nil->key = nil->high = nil->maxHigh = INT_MIN;
nil->storedInterval = NULL;
//root = new IntervalTreeNode;
root->parent = root->left = root->right = nil;
root->key = root->high = root->maxHigh = INT_MAX;
root->red=0;
root->storedInterval = NULL;
/* the following are used for the Enumerate function */
//recursionNodeStackSize = 128;
GMALLOC(recursionNodeStack, recursionNodeStackSize*sizeof(G_ITRecursionNode));
//recursionNodeStackTop = 1;
recursionNodeStack[0].start_node = NULL;
}
~GIntervalTree() {
GIntervalTreeNode * x = root->left;
GVec<GIntervalTreeNode *> stuffToFree;
if (x != nil) {
if (x->left != nil) {
stuffToFree.Push(x->left);
}
if (x->right != nil) {
stuffToFree.Push(x->right);
}
// delete x->storedInterval;
delete x;
while( stuffToFree.Count()>0 ) {
x = stuffToFree.Pop();
if (x->left != nil) {
stuffToFree.Push(x->left);
}
if (x->right != nil) {
stuffToFree.Push(x->right);
}
// delete x->storedInterval;
delete x;
}
}
delete nil;
delete root;
GFREE(recursionNodeStack);
}
void Print() const { TreePrintHelper(root->left); }
// FUNCTION: DeleteNode
//
// INPUTS: tree is the tree to delete node z from
// OUTPUT: returns the Interval stored at deleted node
// EFFECT: Deletes z from tree and but don't call destructor
// Then calls FixUpMaxHigh to fix maxHigh fields then calls
// DeleteFixUp to restore red-black properties
GSeg* DeleteNode(GIntervalTreeNode* z) {
GIntervalTreeNode* y;
GIntervalTreeNode* x;
GSeg* returnValue = z->storedInterval;
y= ((z->left == nil) || (z->right == nil)) ? z : GetSuccessorOf(z);
x= (y->left == nil) ? y->right : y->left;
if (root == (x->parent = y->parent)) { // assignment of y->p to x->p is intentional
root->left=x;
} else {
if (y == y->parent->left) {
y->parent->left=x;
} else {
y->parent->right=x;
}
}
if (y != z) { // y should not be nil in this case
#ifdef DEBUG_ASSERT
Assert( (y!=nil),"y is nil in DeleteNode \n");
#endif
// y is the node to splice out and x is its child
y->maxHigh = INT_MIN;
y->left=z->left;
y->right=z->right;
y->parent=z->parent;
z->left->parent=z->right->parent=y;
if (z == z->parent->left) {
z->parent->left=y;
} else {
z->parent->right=y;
}
FixUpMaxHigh(x->parent);
if (!(y->red)) {
y->red = z->red;
DeleteFixUp(x);
} else
y->red = z->red;
delete z;
} else {
FixUpMaxHigh(x->parent);
if (!(y->red)) DeleteFixUp(x);
delete y;
}
return returnValue;
}
// Before calling InsertNode the node x should have its key set
// FUNCTION: InsertNode
// INPUT: newInterval is the interval to insert
// OUTPUT: This function returns a pointer to the newly inserted node
// which is guaranteed to be valid until this node is deleted.
// What this means is if another data structure stores this
// pointer then the tree does not need to be searched when this
// is to be deleted.
// EFFECTS: Creates a node node which contains the appropriate key and
// info pointers and inserts it into the tree.
GIntervalTreeNode * Insert(GSeg* newInterval) {
GIntervalTreeNode* y;
GIntervalTreeNode* newNode;
GIntervalTreeNode* x = new GIntervalTreeNode(newInterval);
TreeInsertHelp(x);
FixUpMaxHigh(x->parent);
newNode = x;
x->red=1;
while(x->parent->red) { // use sentinel instead of checking for root
if (x->parent == x->parent->parent->left) {
y=x->parent->parent->right;
if (y->red) {
x->parent->red=0;
y->red=0;
x->parent->parent->red=1;
x=x->parent->parent;
} else {
if (x == x->parent->right) {
x=x->parent;
LeftRotate(x);
}
x->parent->red=0;
x->parent->parent->red=1;
RightRotate(x->parent->parent);
}
} else { // case for x->parent == x->parent->parent->right
// this part is just like the section above with
// left and right interchanged
y=x->parent->parent->left;
if (y->red) {
x->parent->red=0;
y->red=0;
x->parent->parent->red=1;
x=x->parent->parent;
} else {
if (x == x->parent->left) {
x=x->parent;
RightRotate(x);
}
x->parent->red=0;
x->parent->parent->red=1;
LeftRotate(x->parent->parent);
}
}
}
root->left->red=0;
return(newNode);
}
// FUNCTION: GetSuccessorOf
// INPUTS: x is the node we want the successor of
// OUTPUT: This function returns the successor of x or NULL if no
// successor exists.
GIntervalTreeNode * GetPredecessorOf(GIntervalTreeNode* x) const {
GIntervalTreeNode* y;
if (nil != (y = x->right)) { // assignment to y is intentional
while(y->left != nil) { // returns the minium of the right subtree of x
y=y->left;
}
return(y);
} else {
y=x->parent;
while(x == y->right) { // sentinel used instead of checking for nil
x=y;
y=y->parent;
}
if (y == root) return(nil);
return(y);
}
}
// FUNCTION: GetPredecessorOf
// INPUTS: x is the node to get predecessor of
// OUTPUT: This function returns the predecessor of x or NULL if no
// predecessor exists.
GIntervalTreeNode * GetSuccessorOf(GIntervalTreeNode* x) const {
GIntervalTreeNode* y;
if (nil != (y = x->left)) { // assignment to y is intentional
while(y->right != nil) { // returns the maximum of the left subtree of x
y=y->right;
}
return(y);
} else {
y=x->parent;
while(x == y->left) {
if (y == root) return(nil);
x=y;
y=y->parent;
}
return(y);
}
}
// FUNCTION: Enumerate
// INPUTS: tree is the tree to look for intervals overlapping the
// closed interval [low,high]
// OUTPUT: stack containing pointers to the nodes overlapping
// [low,high]
// EFFECT: Returns a stack containing pointers to nodes containing
// intervals which overlap [low,high] in O(max(N,k*log(N)))
// where N is the number of intervals in the tree and k is
// the number of overlapping intervals
// Note: This basic idea for this function comes from the
// _Introduction_To_Algorithms_ book by Cormen et al, but
// modifications were made to return all overlapping intervals
// instead of just the first overlapping interval as in the
// book. The natural way to do this would require recursive
// calls of a basic search function. I translated the
// recursive version into an iterative version with a stack
// as described below.
// The basic idea for the function below is to take the IntervalSearch
// function from the book and modify to find all overlapping intervals
// instead of just one. This means that any time we take the left
// branch down the tree we must also check the right branch if and only if
// we find an overlapping interval in that left branch. Note this is a
// recursive condition because if we go left at the root then go left
// again at the first left child and find an overlap in the left subtree
// of the left child of root we must recursively check the right subtree
// of the left child of root as well as the right child of root.
GVec<GSeg*> * Enumerate(int low, int high) {
GVec<GSeg*> * enumResultStack;
GIntervalTreeNode* x=root->left;
int stuffToDo = (x != nil);
// Possible speed up: add min field to prune right searches
#ifdef DEBUG_ASSERT
Assert((recursionNodeStackTop == 1),
"recursionStack not empty when entering IntervalTree::Enumerate");
#endif
currentParent = 0;
enumResultStack = new GVec<GSeg*>(4);
while(stuffToDo) {
//if (Overlap(low,high,x->key,x->high) ) {
if (low<=x->high && x->key<=high) {
enumResultStack->Push(x->storedInterval);
recursionNodeStack[currentParent].tryRightBranch=1;
}
if(x->left->maxHigh >= low) { // implies x != nil
if ( recursionNodeStackTop == recursionNodeStackSize ) {
recursionNodeStackSize *= 2;
recursionNodeStack = (G_ITRecursionNode *)
realloc(recursionNodeStack,
recursionNodeStackSize * sizeof(G_ITRecursionNode));
if (recursionNodeStack == NULL)
GEXIT("realloc failed in IntervalTree::Enumerate\n");
}
recursionNodeStack[recursionNodeStackTop].start_node = x;
recursionNodeStack[recursionNodeStackTop].tryRightBranch = 0;
recursionNodeStack[recursionNodeStackTop].parentIndex = currentParent;
currentParent = recursionNodeStackTop++;
x = x->left;
} else {
x = x->right;
}
stuffToDo = (x != nil);
while( (!stuffToDo) && (recursionNodeStackTop > 1) ) {
if(recursionNodeStack[--recursionNodeStackTop].tryRightBranch) {
x=recursionNodeStack[recursionNodeStackTop].start_node->right;
currentParent=recursionNodeStack[recursionNodeStackTop].parentIndex;
recursionNodeStack[currentParent].tryRightBranch=1;
stuffToDo = ( x != nil);
}
}
}
#ifdef DEBUG_ASSERT
Assert((recursionNodeStackTop == 1),
"recursionStack not empty when exiting IntervalTree::Enumerate");
#endif
return(enumResultStack);
}
};
#endif