892 lines
28 KiB
C
892 lines
28 KiB
C
#include "util.h"
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#include <stdlib.h>
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#include <stdio.h>
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#include <limits.h>
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#include <math.h>
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#include "coretype.h"
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#include "inttree.h"
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#define VERIFY(condition) \
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if (!(condition)) { \
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fprintf(stderr, "Assumption \"%s\"\nFailed in file %s: at line:%i\n", \
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#condition,__FILE__,__LINE__); \
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abort();}
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/*#define DEBUG_ASSERT 1*/
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#ifdef DEBUG_ASSERT
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static void Assert(int assertion, const char *error)
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{
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if (!assertion) {
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fprintf(stderr, "Assertion Failed: %s\n", error);
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abort();
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}
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}
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#endif
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/* If the symbol CHECK_INTERVAL_TREE_ASSUMPTIONS is defined then the
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* code does a lot of extra checking to make sure certain assumptions
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* are satisfied. This only needs to be done if you suspect bugs are
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* present or if you make significant changes and want to make sure
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* your changes didn't mess anything up.
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*/
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/*#define CHECK_INTERVAL_TREE_ASSUMPTIONS 1*/
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static IntervalTreeNode *ITN_create(long low, long high, void *data);
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static void LeftRotate(IntervalTree *, IntervalTreeNode *);
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static void RightRotate(IntervalTree *, IntervalTreeNode *);
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static void TreeInsertHelp(IntervalTree *, IntervalTreeNode *);
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static void TreePrintHelper(const IntervalTree *, IntervalTreeNode *);
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static void FixUpMaxHigh(IntervalTree *, IntervalTreeNode *);
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static void DeleteFixUp(IntervalTree *, IntervalTreeNode *);
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#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
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static void CheckMaxHighFields(const IntervalTree *, IntervalTreeNode *);
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static int CheckMaxHighFieldsHelper(const IntervalTree *, IntervalTreeNode *y,
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const int currentHigh, int match);
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static void IT_CheckAssumptions(const IntervalTree *);
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#endif
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/* define a function to find the maximum of two objects. */
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#define ITMax(a, b) ( (a > b) ? a : b )
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IntervalTreeNode *
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ITN_create(long low, long high, void *data)
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{
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IntervalTreeNode *itn = yasm_xmalloc(sizeof(IntervalTreeNode));
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itn->data = data;
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if (low < high) {
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itn->low = low;
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itn->high = high;
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} else {
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itn->low = high;
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itn->high = low;
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}
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itn->maxHigh = high;
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return itn;
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}
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IntervalTree *
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IT_create(void)
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{
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IntervalTree *it = yasm_xmalloc(sizeof(IntervalTree));
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it->nil = ITN_create(LONG_MIN, LONG_MIN, NULL);
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it->nil->left = it->nil;
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it->nil->right = it->nil;
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it->nil->parent = it->nil;
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it->nil->red = 0;
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it->root = ITN_create(LONG_MAX, LONG_MAX, NULL);
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it->root->left = it->nil;
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it->root->right = it->nil;
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it->root->parent = it->nil;
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it->root->red = 0;
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/* the following are used for the Enumerate function */
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it->recursionNodeStackSize = 128;
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it->recursionNodeStack = (it_recursion_node *)
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yasm_xmalloc(it->recursionNodeStackSize*sizeof(it_recursion_node));
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it->recursionNodeStackTop = 1;
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it->recursionNodeStack[0].start_node = NULL;
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return it;
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}
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/***********************************************************************/
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/* FUNCTION: LeftRotate */
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/**/
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/* INPUTS: the node to rotate on */
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/**/
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/* OUTPUT: None */
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/**/
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/* Modifies Input: this, x */
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/**/
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/* EFFECTS: Rotates as described in _Introduction_To_Algorithms by */
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/* Cormen, Leiserson, Rivest (Chapter 14). Basically this */
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/* makes the parent of x be to the left of x, x the parent of */
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/* its parent before the rotation and fixes other pointers */
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/* accordingly. Also updates the maxHigh fields of x and y */
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/* after rotation. */
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/***********************************************************************/
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static void
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LeftRotate(IntervalTree *it, IntervalTreeNode *x)
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{
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IntervalTreeNode *y;
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/* I originally wrote this function to use the sentinel for
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* nil to avoid checking for nil. However this introduces a
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* very subtle bug because sometimes this function modifies
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* the parent pointer of nil. This can be a problem if a
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* function which calls LeftRotate also uses the nil sentinel
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* and expects the nil sentinel's parent pointer to be unchanged
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* after calling this function. For example, when DeleteFixUP
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* calls LeftRotate it expects the parent pointer of nil to be
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* unchanged.
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*/
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y=x->right;
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x->right=y->left;
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if (y->left != it->nil)
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y->left->parent=x; /* used to use sentinel here */
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/* and do an unconditional assignment instead of testing for nil */
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y->parent=x->parent;
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/* Instead of checking if x->parent is the root as in the book, we
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* count on the root sentinel to implicitly take care of this case
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*/
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if (x == x->parent->left)
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x->parent->left=y;
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else
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x->parent->right=y;
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y->left=x;
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x->parent=y;
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x->maxHigh=ITMax(x->left->maxHigh,ITMax(x->right->maxHigh,x->high));
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y->maxHigh=ITMax(x->maxHigh,ITMax(y->right->maxHigh,y->high));
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#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
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IT_CheckAssumptions(it);
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#elif defined(DEBUG_ASSERT)
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Assert(!it->nil->red,"nil not red in ITLeftRotate");
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Assert((it->nil->maxHigh=LONG_MIN),
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"nil->maxHigh != LONG_MIN in ITLeftRotate");
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#endif
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}
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/***********************************************************************/
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/* FUNCTION: RightRotate */
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/**/
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/* INPUTS: node to rotate on */
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/**/
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/* OUTPUT: None */
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/**/
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/* Modifies Input?: this, y */
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/**/
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/* EFFECTS: Rotates as described in _Introduction_To_Algorithms by */
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/* Cormen, Leiserson, Rivest (Chapter 14). Basically this */
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/* makes the parent of x be to the left of x, x the parent of */
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/* its parent before the rotation and fixes other pointers */
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/* accordingly. Also updates the maxHigh fields of x and y */
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/* after rotation. */
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/***********************************************************************/
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static void
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RightRotate(IntervalTree *it, IntervalTreeNode *y)
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{
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IntervalTreeNode *x;
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/* I originally wrote this function to use the sentinel for
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* nil to avoid checking for nil. However this introduces a
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* very subtle bug because sometimes this function modifies
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* the parent pointer of nil. This can be a problem if a
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* function which calls LeftRotate also uses the nil sentinel
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* and expects the nil sentinel's parent pointer to be unchanged
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* after calling this function. For example, when DeleteFixUP
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* calls LeftRotate it expects the parent pointer of nil to be
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* unchanged.
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*/
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x=y->left;
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y->left=x->right;
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if (it->nil != x->right)
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x->right->parent=y; /*used to use sentinel here */
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/* and do an unconditional assignment instead of testing for nil */
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/* Instead of checking if x->parent is the root as in the book, we
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* count on the root sentinel to implicitly take care of this case
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*/
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x->parent=y->parent;
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if (y == y->parent->left)
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y->parent->left=x;
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else
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y->parent->right=x;
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x->right=y;
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y->parent=x;
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y->maxHigh=ITMax(y->left->maxHigh,ITMax(y->right->maxHigh,y->high));
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x->maxHigh=ITMax(x->left->maxHigh,ITMax(y->maxHigh,x->high));
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#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
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IT_CheckAssumptions(it);
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#elif defined(DEBUG_ASSERT)
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Assert(!it->nil->red,"nil not red in ITRightRotate");
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Assert((it->nil->maxHigh=LONG_MIN),
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"nil->maxHigh != LONG_MIN in ITRightRotate");
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#endif
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}
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/***********************************************************************/
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/* FUNCTION: TreeInsertHelp */
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/**/
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/* INPUTS: z is the node to insert */
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/**/
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/* OUTPUT: none */
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/**/
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/* Modifies Input: this, z */
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/**/
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/* EFFECTS: Inserts z into the tree as if it were a regular binary tree */
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/* using the algorithm described in _Introduction_To_Algorithms_ */
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/* by Cormen et al. This funciton is only intended to be called */
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/* by the InsertTree function and not by the user */
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/***********************************************************************/
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static void
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TreeInsertHelp(IntervalTree *it, IntervalTreeNode *z)
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{
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/* This function should only be called by InsertITTree (see above) */
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IntervalTreeNode* x;
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IntervalTreeNode* y;
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z->left=z->right=it->nil;
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y=it->root;
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x=it->root->left;
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while( x != it->nil) {
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y=x;
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if (x->low > z->low)
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x=x->left;
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else /* x->low <= z->low */
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x=x->right;
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}
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z->parent=y;
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if ((y == it->root) || (y->low > z->low))
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y->left=z;
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else
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y->right=z;
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#if defined(DEBUG_ASSERT)
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Assert(!it->nil->red,"nil not red in ITTreeInsertHelp");
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Assert((it->nil->maxHigh=INT_MIN),
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"nil->maxHigh != INT_MIN in ITTreeInsertHelp");
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#endif
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}
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/***********************************************************************/
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/* FUNCTION: FixUpMaxHigh */
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/**/
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/* INPUTS: x is the node to start from*/
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/**/
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/* OUTPUT: none */
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/**/
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/* Modifies Input: this */
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/**/
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/* EFFECTS: Travels up to the root fixing the maxHigh fields after */
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/* an insertion or deletion */
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/***********************************************************************/
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static void
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FixUpMaxHigh(IntervalTree *it, IntervalTreeNode *x)
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{
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while(x != it->root) {
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x->maxHigh=ITMax(x->high,ITMax(x->left->maxHigh,x->right->maxHigh));
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x=x->parent;
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}
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#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
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IT_CheckAssumptions(it);
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#endif
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}
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/* Before calling InsertNode the node x should have its key set */
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/***********************************************************************/
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/* FUNCTION: InsertNode */
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/**/
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/* INPUTS: newInterval is the interval to insert*/
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/**/
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/* OUTPUT: This function returns a pointer to the newly inserted node */
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/* which is guarunteed to be valid until this node is deleted. */
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/* What this means is if another data structure stores this */
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/* pointer then the tree does not need to be searched when this */
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/* is to be deleted. */
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/**/
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/* Modifies Input: tree */
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/**/
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/* EFFECTS: Creates a node node which contains the appropriate key and */
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/* info pointers and inserts it into the tree. */
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/***********************************************************************/
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IntervalTreeNode *
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IT_insert(IntervalTree *it, long low, long high, void *data)
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{
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IntervalTreeNode *x, *y, *newNode;
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x = ITN_create(low, high, data);
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TreeInsertHelp(it, x);
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FixUpMaxHigh(it, x->parent);
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newNode = x;
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x->red=1;
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while(x->parent->red) { /* use sentinel instead of checking for root */
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if (x->parent == x->parent->parent->left) {
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y=x->parent->parent->right;
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if (y->red) {
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x->parent->red=0;
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y->red=0;
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x->parent->parent->red=1;
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x=x->parent->parent;
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} else {
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if (x == x->parent->right) {
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x=x->parent;
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LeftRotate(it, x);
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}
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x->parent->red=0;
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x->parent->parent->red=1;
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RightRotate(it, x->parent->parent);
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}
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} else { /* case for x->parent == x->parent->parent->right */
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/* this part is just like the section above with */
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/* left and right interchanged */
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y=x->parent->parent->left;
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if (y->red) {
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x->parent->red=0;
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y->red=0;
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x->parent->parent->red=1;
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x=x->parent->parent;
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} else {
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if (x == x->parent->left) {
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x=x->parent;
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RightRotate(it, x);
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}
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x->parent->red=0;
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x->parent->parent->red=1;
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LeftRotate(it, x->parent->parent);
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}
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}
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}
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it->root->left->red=0;
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#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
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IT_CheckAssumptions(it);
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#elif defined(DEBUG_ASSERT)
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Assert(!it->nil->red,"nil not red in ITTreeInsert");
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Assert(!it->root->red,"root not red in ITTreeInsert");
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Assert((it->nil->maxHigh=LONG_MIN),
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"nil->maxHigh != LONG_MIN in ITTreeInsert");
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#endif
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return newNode;
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}
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/***********************************************************************/
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/* FUNCTION: GetSuccessorOf */
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/**/
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/* INPUTS: x is the node we want the succesor of */
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/**/
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/* OUTPUT: This function returns the successor of x or NULL if no */
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/* successor exists. */
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/**/
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/* Modifies Input: none */
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/**/
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/* Note: uses the algorithm in _Introduction_To_Algorithms_ */
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/***********************************************************************/
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IntervalTreeNode *
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IT_get_successor(const IntervalTree *it, IntervalTreeNode *x)
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{
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IntervalTreeNode *y;
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if (it->nil != (y = x->right)) { /* assignment to y is intentional */
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while(y->left != it->nil) /* returns the minium of the right subtree of x */
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y=y->left;
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return y;
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} else {
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y=x->parent;
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while(x == y->right) { /* sentinel used instead of checking for nil */
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x=y;
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y=y->parent;
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}
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if (y == it->root)
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return(it->nil);
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return y;
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}
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}
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/***********************************************************************/
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/* FUNCTION: GetPredecessorOf */
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/**/
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/* INPUTS: x is the node to get predecessor of */
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/**/
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/* OUTPUT: This function returns the predecessor of x or NULL if no */
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/* predecessor exists. */
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/**/
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/* Modifies Input: none */
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/**/
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/* Note: uses the algorithm in _Introduction_To_Algorithms_ */
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/***********************************************************************/
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IntervalTreeNode *
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IT_get_predecessor(const IntervalTree *it, IntervalTreeNode *x)
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{
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IntervalTreeNode *y;
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if (it->nil != (y = x->left)) { /* assignment to y is intentional */
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while(y->right != it->nil) /* returns the maximum of the left subtree of x */
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y=y->right;
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return y;
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} else {
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y=x->parent;
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while(x == y->left) {
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if (y == it->root)
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return(it->nil);
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x=y;
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y=y->parent;
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}
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return y;
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}
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}
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/***********************************************************************/
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/* FUNCTION: Print */
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/**/
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/* INPUTS: none */
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/**/
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/* OUTPUT: none */
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/**/
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/* EFFECTS: This function recursively prints the nodes of the tree */
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/* inorder. */
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/**/
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/* Modifies Input: none */
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/**/
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/* Note: This function should only be called from ITTreePrint */
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/***********************************************************************/
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static void
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ITN_print(const IntervalTreeNode *itn, IntervalTreeNode *nil,
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IntervalTreeNode *root)
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{
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printf(", l=%li, h=%li, mH=%li", itn->low, itn->high, itn->maxHigh);
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printf(" l->low=");
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if (itn->left == nil)
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printf("NULL");
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else
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printf("%li", itn->left->low);
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printf(" r->low=");
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if (itn->right == nil)
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printf("NULL");
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else
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printf("%li", itn->right->low);
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printf(" p->low=");
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if (itn->parent == root)
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printf("NULL");
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else
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printf("%li", itn->parent->low);
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printf(" red=%i\n", itn->red);
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}
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static void
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TreePrintHelper(const IntervalTree *it, IntervalTreeNode *x)
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{
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if (x != it->nil) {
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TreePrintHelper(it, x->left);
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ITN_print(x, it->nil, it->root);
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TreePrintHelper(it, x->right);
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}
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}
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void
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IT_destroy(IntervalTree *it)
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{
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IntervalTreeNode *x = it->root->left;
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SLIST_HEAD(node_head, nodeent)
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stuffToFree = SLIST_HEAD_INITIALIZER(stuffToFree);
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struct nodeent {
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SLIST_ENTRY(nodeent) link;
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struct IntervalTreeNode *node;
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} *np;
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if (x != it->nil) {
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if (x->left != it->nil) {
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np = yasm_xmalloc(sizeof(struct nodeent));
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np->node = x->left;
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SLIST_INSERT_HEAD(&stuffToFree, np, link);
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}
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if (x->right != it->nil) {
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np = yasm_xmalloc(sizeof(struct nodeent));
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np->node = x->right;
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SLIST_INSERT_HEAD(&stuffToFree, np, link);
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}
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yasm_xfree(x);
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while (!SLIST_EMPTY(&stuffToFree)) {
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np = SLIST_FIRST(&stuffToFree);
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x = np->node;
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SLIST_REMOVE_HEAD(&stuffToFree, link);
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yasm_xfree(np);
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if (x->left != it->nil) {
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np = yasm_xmalloc(sizeof(struct nodeent));
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np->node = x->left;
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SLIST_INSERT_HEAD(&stuffToFree, np, link);
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}
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if (x->right != it->nil) {
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|
np = yasm_xmalloc(sizeof(struct nodeent));
|
|
np->node = x->right;
|
|
SLIST_INSERT_HEAD(&stuffToFree, np, link);
|
|
}
|
|
yasm_xfree(x);
|
|
}
|
|
}
|
|
|
|
yasm_xfree(it->nil);
|
|
yasm_xfree(it->root);
|
|
yasm_xfree(it->recursionNodeStack);
|
|
yasm_xfree(it);
|
|
}
|
|
|
|
|
|
/***********************************************************************/
|
|
/* FUNCTION: Print */
|
|
/**/
|
|
/* INPUTS: none */
|
|
/**/
|
|
/* OUTPUT: none */
|
|
/**/
|
|
/* EFFECT: This function recursively prints the nodes of the tree */
|
|
/* inorder. */
|
|
/**/
|
|
/* Modifies Input: none */
|
|
/**/
|
|
/***********************************************************************/
|
|
|
|
void
|
|
IT_print(const IntervalTree *it)
|
|
{
|
|
TreePrintHelper(it, it->root->left);
|
|
}
|
|
|
|
/***********************************************************************/
|
|
/* FUNCTION: DeleteFixUp */
|
|
/**/
|
|
/* INPUTS: x is the child of the spliced */
|
|
/* out node in DeleteNode. */
|
|
/**/
|
|
/* OUTPUT: none */
|
|
/**/
|
|
/* EFFECT: Performs rotations and changes colors to restore red-black */
|
|
/* properties after a node is deleted */
|
|
/**/
|
|
/* Modifies Input: this, x */
|
|
/**/
|
|
/* The algorithm from this function is from _Introduction_To_Algorithms_ */
|
|
/***********************************************************************/
|
|
|
|
static void
|
|
DeleteFixUp(IntervalTree *it, IntervalTreeNode *x)
|
|
{
|
|
IntervalTreeNode *w;
|
|
IntervalTreeNode *rootLeft = it->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(it, 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(it, w);
|
|
w=x->parent->right;
|
|
}
|
|
w->red=x->parent->red;
|
|
x->parent->red=0;
|
|
w->right->red=0;
|
|
LeftRotate(it, 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(it, 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(it, w);
|
|
w=x->parent->left;
|
|
}
|
|
w->red=x->parent->red;
|
|
x->parent->red=0;
|
|
w->left->red=0;
|
|
RightRotate(it, x->parent);
|
|
x=rootLeft; /* this is to exit while loop */
|
|
}
|
|
}
|
|
}
|
|
x->red=0;
|
|
|
|
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
|
|
IT_CheckAssumptions(it);
|
|
#elif defined(DEBUG_ASSERT)
|
|
Assert(!it->nil->red,"nil not black in ITDeleteFixUp");
|
|
Assert((it->nil->maxHigh=LONG_MIN),
|
|
"nil->maxHigh != LONG_MIN in ITDeleteFixUp");
|
|
#endif
|
|
}
|
|
|
|
|
|
/***********************************************************************/
|
|
/* 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 */
|
|
/* ITDeleteFixUp to restore red-black properties */
|
|
/**/
|
|
/* Modifies Input: z */
|
|
/**/
|
|
/* The algorithm from this function is from _Introduction_To_Algorithms_ */
|
|
/***********************************************************************/
|
|
|
|
void *
|
|
IT_delete_node(IntervalTree *it, IntervalTreeNode *z, long *low, long *high)
|
|
{
|
|
IntervalTreeNode *x, *y;
|
|
void *returnValue = z->data;
|
|
if (low)
|
|
*low = z->low;
|
|
if (high)
|
|
*high = z->high;
|
|
|
|
y= ((z->left == it->nil) || (z->right == it->nil)) ?
|
|
z : IT_get_successor(it, z);
|
|
x= (y->left == it->nil) ? y->right : y->left;
|
|
if (it->root == (x->parent = y->parent))
|
|
/* assignment of y->p to x->p is intentional */
|
|
it->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!=it->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(it, x->parent);
|
|
if (!(y->red)) {
|
|
y->red = z->red;
|
|
DeleteFixUp(it, x);
|
|
} else
|
|
y->red = z->red;
|
|
yasm_xfree(z);
|
|
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
|
|
IT_CheckAssumptions(it);
|
|
#elif defined(DEBUG_ASSERT)
|
|
Assert(!it->nil->red,"nil not black in ITDelete");
|
|
Assert((it->nil->maxHigh=LONG_MIN),"nil->maxHigh != LONG_MIN in ITDelete");
|
|
#endif
|
|
} else {
|
|
FixUpMaxHigh(it, x->parent);
|
|
if (!(y->red))
|
|
DeleteFixUp(it, x);
|
|
yasm_xfree(y);
|
|
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
|
|
IT_CheckAssumptions(it);
|
|
#elif defined(DEBUG_ASSERT)
|
|
Assert(!it->nil->red,"nil not black in ITDelete");
|
|
Assert((it->nil->maxHigh=LONG_MIN),"nil->maxHigh != LONG_MIN in ITDelete");
|
|
#endif
|
|
}
|
|
return returnValue;
|
|
}
|
|
|
|
|
|
/***********************************************************************/
|
|
/* FUNCTION: Overlap */
|
|
/**/
|
|
/* INPUTS: [a1,a2] and [b1,b2] are the low and high endpoints of two */
|
|
/* closed intervals. */
|
|
/**/
|
|
/* OUTPUT: stack containing pointers to the nodes between [low,high] */
|
|
/**/
|
|
/* Modifies Input: none */
|
|
/**/
|
|
/* EFFECT: returns 1 if the intervals overlap, and 0 otherwise */
|
|
/***********************************************************************/
|
|
|
|
static int
|
|
Overlap(int a1, int a2, int b1, int b2)
|
|
{
|
|
if (a1 <= b1)
|
|
return (b1 <= a2);
|
|
else
|
|
return (a1 <= b2);
|
|
}
|
|
|
|
|
|
/***********************************************************************/
|
|
/* 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] */
|
|
/**/
|
|
/* Modifies Input: none */
|
|
/**/
|
|
/* 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 interative 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.
|
|
*/
|
|
void
|
|
IT_enumerate(IntervalTree *it, long low, long high, void *cbd,
|
|
void (*callback) (IntervalTreeNode *node, void *cbd))
|
|
{
|
|
IntervalTreeNode *x=it->root->left;
|
|
int stuffToDo = (x != it->nil);
|
|
|
|
/* Possible speed up: add min field to prune right searches */
|
|
|
|
#ifdef DEBUG_ASSERT
|
|
Assert((it->recursionNodeStackTop == 1),
|
|
"recursionStack not empty when entering IntervalTree::Enumerate");
|
|
#endif
|
|
it->currentParent = 0;
|
|
|
|
while (stuffToDo) {
|
|
if (Overlap(low,high,x->low,x->high) ) {
|
|
callback(x, cbd);
|
|
it->recursionNodeStack[it->currentParent].tryRightBranch=1;
|
|
}
|
|
if(x->left->maxHigh >= low) { /* implies x != nil */
|
|
if (it->recursionNodeStackTop == it->recursionNodeStackSize) {
|
|
it->recursionNodeStackSize *= 2;
|
|
it->recursionNodeStack = (it_recursion_node *)
|
|
yasm_xrealloc(it->recursionNodeStack,
|
|
it->recursionNodeStackSize * sizeof(it_recursion_node));
|
|
}
|
|
it->recursionNodeStack[it->recursionNodeStackTop].start_node = x;
|
|
it->recursionNodeStack[it->recursionNodeStackTop].tryRightBranch = 0;
|
|
it->recursionNodeStack[it->recursionNodeStackTop].parentIndex = it->currentParent;
|
|
it->currentParent = it->recursionNodeStackTop++;
|
|
x = x->left;
|
|
} else {
|
|
x = x->right;
|
|
}
|
|
stuffToDo = (x != it->nil);
|
|
while (!stuffToDo && (it->recursionNodeStackTop > 1)) {
|
|
if (it->recursionNodeStack[--it->recursionNodeStackTop].tryRightBranch) {
|
|
x=it->recursionNodeStack[it->recursionNodeStackTop].start_node->right;
|
|
it->currentParent=it->recursionNodeStack[it->recursionNodeStackTop].parentIndex;
|
|
it->recursionNodeStack[it->currentParent].tryRightBranch=1;
|
|
stuffToDo = (x != it->nil);
|
|
}
|
|
}
|
|
}
|
|
#ifdef DEBUG_ASSERT
|
|
Assert((it->recursionNodeStackTop == 1),
|
|
"recursionStack not empty when exiting IntervalTree::Enumerate");
|
|
#endif
|
|
}
|
|
|
|
#ifdef CHECK_INTERVAL_TREE_ASSUMPTIONS
|
|
|
|
static int
|
|
CheckMaxHighFieldsHelper(const IntervalTree *it, IntervalTreeNode *y,
|
|
int currentHigh, int match)
|
|
{
|
|
if (y != it->nil) {
|
|
match = CheckMaxHighFieldsHelper(it, y->left, currentHigh, match) ?
|
|
1 : match;
|
|
VERIFY(y->high <= currentHigh);
|
|
if (y->high == currentHigh)
|
|
match = 1;
|
|
match = CheckMaxHighFieldsHelper(it, y->right, currentHigh, match) ?
|
|
1 : match;
|
|
}
|
|
return match;
|
|
}
|
|
|
|
|
|
|
|
/* Make sure the maxHigh fields for everything makes sense. *
|
|
* If something is wrong, print a warning and exit */
|
|
static void
|
|
CheckMaxHighFields(const IntervalTree *it, IntervalTreeNode *x)
|
|
{
|
|
if (x != it->nil) {
|
|
CheckMaxHighFields(it, x->left);
|
|
if(!(CheckMaxHighFieldsHelper(it, x, x->maxHigh, 0) > 0)) {
|
|
fprintf(stderr, "error found in CheckMaxHighFields.\n");
|
|
abort();
|
|
}
|
|
CheckMaxHighFields(it, x->right);
|
|
}
|
|
}
|
|
|
|
static void
|
|
IT_CheckAssumptions(const IntervalTree *it)
|
|
{
|
|
VERIFY(it->nil->low == INT_MIN);
|
|
VERIFY(it->nil->high == INT_MIN);
|
|
VERIFY(it->nil->maxHigh == INT_MIN);
|
|
VERIFY(it->root->low == INT_MAX);
|
|
VERIFY(it->root->high == INT_MAX);
|
|
VERIFY(it->root->maxHigh == INT_MAX);
|
|
VERIFY(it->nil->data == NULL);
|
|
VERIFY(it->root->data == NULL);
|
|
VERIFY(it->nil->red == 0);
|
|
VERIFY(it->root->red == 0);
|
|
CheckMaxHighFields(it, it->root->left);
|
|
}
|
|
#endif
|
|
|