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/* $Id: avl.c 2243 2009-01-10 02:24:02Z bird $
*
* AVL-Tree (lookalike) implementation.
*
* Copyright (c) 1999 knut st. osmundsen
*
* GPL
*
*/
/*******************************************************************************
* Defined Constants And Macros *
*******************************************************************************/
/*
* AVL helper macros.
*/
#define AVL_HEIGHTOF(pNode) ((unsigned char)((pNode) != NULL ? pNode->uchHeight : 0))
#define max(a,b) (((a) > (b)) ? (a) : (b))
#ifndef INLINE
# if defined(__IBMC__)
# define INLINE _Inline
# elif defined(__IBMCPP__)
# define INLINE inline
# elif defined(__WATCOMC__)
# define INLINE __inline
# elif defined(__WATCOM_CPLUSPLUS__)
# define INLINE inline
# else
# error message("unknown compiler - inline keyword unknown!")
# endif
#endif
/*******************************************************************************
* Internal Functions *
*******************************************************************************/
#include <os2.h>
#include "avl.h"
#if defined(RING0) || defined(RING3)
#include "dev32.h"
#else
#define SSToDS(a) (a)
#endif
#include "string.h"
#if defined(__IBMCPP__) || defined(__IBMC__)
#include <builtin.h>
#define assert(a) ((a) ? (void)0 : __interrupt(3) )
#else
#include <assert.h>
#endif
/*******************************************************************************
* Structures and Typedefs *
*******************************************************************************/
/*
* A stack used to avoid recursive calls...
*/
typedef struct _AVLStack
{
unsigned cEntries;
PPAVLNODECORE aEntries[AVL_MAX_HEIGHT];
} AVLSTACK, *PAVLSTACK;
typedef struct _AVLStack2
{
unsigned cEntries;
PAVLNODECORE aEntries[AVL_MAX_HEIGHT];
char achFlags[AVL_MAX_HEIGHT];
} AVLSTACK2, *PAVLSTACK2;
/*******************************************************************************
* Internal Functions *
*******************************************************************************/
INLINE void AVLRebalance(PAVLSTACK pStack);
/**
* Inserts a node into the AVL-tree.
* @returns TRUE if inserted.
* FALSE if node exists in tree.
* @param ppTree Pointer to the AVL-tree root node pointer.
* @param pNode Pointer to the node which is to be added.
* @sketch Find the location of the node (using binary three algorithm.):
* LOOP until NULL leaf pointer
* BEGIN
* Add node pointer pointer to the AVL-stack.
* IF new-node-key < node key THEN
* left
* ELSE
* right
* END
* Fill in leaf node and insert it.
* Rebalance the tree.
* @status completely implemented.
* @author knut st. osmundsen
*/
BOOL AVLInsert(PPAVLNODECORE ppTree, PAVLNODECORE pNode)
{
AVLSTACK AVLStack;
PPAVLNODECORE ppCurNode = ppTree;
register AVLKEY Key = pNode->Key;
register PAVLNODECORE pCurNode;
AVLStack.cEntries = 0;
while ((pCurNode = *ppCurNode) != NULL)
{
assert(AVLStack.cEntries < AVL_MAX_HEIGHT);
assert(pNode != pCurNode);
AVLStack.aEntries[AVLStack.cEntries++] = ppCurNode;
#ifdef AVL_MAY_TRY_INSERT_EQUAL
/* check if equal */
if (AVL_E(pCurNode->Key, Key))
return FALSE;
#endif
if (AVL_G(pCurNode->Key, Key))
ppCurNode = &pCurNode->pLeft;
else
ppCurNode = &pCurNode->pRight;
}
pNode->pLeft = pNode->pRight = NULL;
pNode->uchHeight = 1;
*ppCurNode = pNode;
AVLRebalance(SSToDS(&AVLStack));
return TRUE;
}
/**
* Removes a node from the AVL-tree.
* @returns Pointer to the node.
* @param ppTree Pointer to the AVL-tree root node pointer.
* @param Key Key value of the node which is to be removed.
* @sketch Find the node which is to be removed:
* LOOP until not found
* BEGIN
* Add node pointer pointer to the AVL-stack.
* IF the keys matches THEN break!
* IF remove key < node key THEN
* left
* ELSE
* right
* END
* IF found THEN
* BEGIN
* IF left node not empty THEN
* BEGIN
* Find the right most node in the left tree while adding the pointer to the pointer to it's parent to the stack:
* Start at left node.
* LOOP until right node is empty
* BEGIN
* Add to stack.
* go right.
* END
* Link out the found node.
* Replace the node which is to be removed with the found node.
* Correct the stack entry for the pointer to the left tree.
* END
* ELSE
* BEGIN
* Move up right node.
* Remove last stack entry.
* END
* Balance tree using stack.
* END
* return pointer to the removed node (if found).
* @status completely implemented.
* @author knut st. osmundsen
*/
PAVLNODECORE AVLRemove(PPAVLNODECORE ppTree, AVLKEY Key)
{
AVLSTACK AVLStack;
PPAVLNODECORE ppDeleteNode = ppTree;
register PAVLNODECORE pDeleteNode;
AVLStack.cEntries = 0;
while ((pDeleteNode = *ppDeleteNode) != NULL)
{
assert(AVLStack.cEntries < AVL_MAX_HEIGHT);
AVLStack.aEntries[AVLStack.cEntries++] = ppDeleteNode;
#ifndef AVL_CMP
if (AVL_E(pDeleteNode->Key, Key))
break;
if (AVL_G(pDeleteNode->Key, Key))
ppDeleteNode = &pDeleteNode->pLeft;
else
ppDeleteNode = &pDeleteNode->pRight;
#else
{
int register iDiff;
if ((iDiff = AVL_CMP(pDeleteNode->Key, Key)) == 0)
break;
if (iDiff > 0)
ppDeleteNode = &pDeleteNode->pLeft;
else
ppDeleteNode = &pDeleteNode->pRight;
}
#endif
}
if (pDeleteNode != NULL)
{
if (pDeleteNode->pLeft != NULL)
{
unsigned iStackEntry = AVLStack.cEntries;
PPAVLNODECORE ppLeftLeast = &pDeleteNode->pLeft;
register PAVLNODECORE pLeftLeast;
while ((pLeftLeast = *ppLeftLeast)->pRight != NULL) /* Left most node. */
{
assert(AVLStack.cEntries < AVL_MAX_HEIGHT);
AVLStack.aEntries[AVLStack.cEntries++] = ppLeftLeast;
ppLeftLeast = &pLeftLeast->pRight;
pLeftLeast = pLeftLeast->pRight;
}
/* link out pLeftLeast */
*ppLeftLeast = pLeftLeast->pLeft;
/* link in place of the delete node. */
pLeftLeast->pLeft = pDeleteNode->pLeft;
pLeftLeast->pRight = pDeleteNode->pRight;
pLeftLeast->uchHeight = pDeleteNode->uchHeight;
*ppDeleteNode = pLeftLeast;
AVLStack.aEntries[iStackEntry] = &pLeftLeast->pLeft;
}
else
{
*ppDeleteNode = pDeleteNode->pRight;
AVLStack.cEntries--;
}
AVLRebalance(SSToDS(&AVLStack));
}
return pDeleteNode;
}
/**
* Gets a node from the tree (does not remove it!)
* @returns Pointer to the node holding the given key.
* @param ppTree Pointer to the AVL-tree root node pointer.
* @param Key Key value of the node which is to be found.
* @sketch
* @status completely implemented.
* @author knut st. osmundsen
*/
PAVLNODECORE AVLGet(PPAVLNODECORE ppTree, AVLKEY Key)
{
#ifndef AVL_CMP
register PAVLNODECORE pNode = *ppTree;
while (pNode != NULL && AVL_NE(pNode->Key, Key))
{
if (AVL_G(pNode->Key, Key))
pNode = pNode->pLeft;
else
pNode = pNode->pRight;
}
#else
register int iDiff;
register PAVLNODECORE pNode = *ppTree;
while (pNode != NULL && (iDiff = AVL_CMP(pNode->Key, Key)) != 0)
{
if (iDiff > 0)
pNode = pNode->pLeft;
else
pNode = pNode->pRight;
}
#endif
return pNode;
}
/**
* Gets a node from the tree and its parent node (if any) (does not remove any nodes!)
* @returns Pointer to the node holding the given key.
* @param ppTree Pointer to the AVL-tree root node pointer.
* @param ppParent Pointer to a variable which will hold the pointer to the partent node on
* return. When no node is found, this will hold the last searched node.
* @param Key Key value of the node which is to be found.
* @sketch
* @status completely implemented.
* @author knut st. osmundsen
*/
PAVLNODECORE AVLGetWithParent(PPAVLNODECORE ppTree, PPAVLNODECORE ppParent, AVLKEY Key)
{
#ifndef AVL_CMP
register PAVLNODECORE pNode = *ppTree;
register PAVLNODECORE pParent = NULL;
while (pNode != NULL && AVL_NE(pNode->Key, Key))
{
pParent = pNode;
if (AVL_G(pNode->Key, Key))
pNode = pNode->pLeft;
else
pNode = pNode->pRight;
}
#else
register PAVLNODECORE pNode = *ppTree;
register PAVLNODECORE pParent = NULL;
register int iDiff;
while (pNode != NULL && (iDiff = AVL_CMP(pNode->Key, Key)) != 0)
{
pParent = pNode;
if (iDiff > 0)
pNode = pNode->pLeft;
else
pNode = pNode->pRight;
}
#endif
*ppParent = pParent;
return pNode;
}
/**
* Gets node from the tree (does not remove it!) and it's adjecent (by key value) nodes.
* @returns Pointer to the node holding the given key.
* @param ppTree Pointer to the AVL-tree root node pointer.
* @param Key Key value of the node which is to be found.
* @param ppLeft Pointer to left node pointer.
* @param ppRight Pointer to right node pointer.
* @sketch Find node with the given key, record search path on the stack.
* IF found THEN
* BEGIN
* Find the right-most node in the left subtree.
* Find the left-most node in the right subtree.
* Rewind the stack while searching for more adjecent nodes.
* END
* return node with adjecent nodes.
* @status completely implemented.
* @author knut st. osmundsen
*/
PAVLNODECORE AVLGetWithAdjecentNodes(PPAVLNODECORE ppTree, AVLKEY Key, PPAVLNODECORE ppLeft, PPAVLNODECORE ppRight)
{
AVLSTACK AVLStack;
PPAVLNODECORE ppNode = ppTree;
PAVLNODECORE pNode;
#ifdef AVL_CMP
int iDiff;
#endif
AVLStack.cEntries = 0;
#ifndef AVL_CMP
while ((pNode = *ppNode) != NULL && AVL_NE(pNode->Key, Key))
#else
while ((pNode = *ppNode) != NULL && (iDiff = AVL_CMP(pNode->Key, Key)) != 0)
#endif
{
assert(AVLStack.cEntries < AVL_MAX_HEIGHT);
AVLStack.aEntries[AVLStack.cEntries++] = ppNode;
#ifndef AVL_CMP
if (AVL_G(pNode->Key, Key))
#else
if (iDiff > 0)
#endif
ppNode = &pNode->pLeft;
else
ppNode = &pNode->pRight;
}
if (pNode != NULL)
{
PAVLNODECORE pCurNode;
/* find rigth-most node in left subtree. */
pCurNode = pNode->pLeft;
if (pCurNode != NULL)
while (pCurNode->pRight != NULL)
pCurNode = pCurNode->pRight;
*ppLeft = pCurNode;
/* find left-most node in right subtree. */
pCurNode = pNode->pRight;
if (pCurNode != NULL)
while (pCurNode->pLeft != NULL)
pCurNode = pCurNode->pLeft;
*ppRight = pCurNode;
/* rewind stack */
while (AVLStack.cEntries-- > 0)
{
pCurNode = *AVLStack.aEntries[AVLStack.cEntries];
#ifndef AVL_CMP
if (AVL_L(pCurNode->Key, Key) && (*ppLeft == NULL || AVL_G(pCurNode->Key, (*ppLeft)->Key)))
*ppLeft = pCurNode;
else if (AVL_G(pCurNode->Key, Key) && (*ppRight == NULL || AVL_L(pCurNode->Key, (*ppRight)->Key)))
*ppRight = pCurNode;
#else
if ((iDiff = AVL_CMP(pCurNode->Key, Key)) < 0 && (*ppLeft == NULL || AVL_G(pCurNode->Key, (*ppLeft)->Key)))
*ppLeft = pCurNode;
else if (iDiff > 0 && (*ppRight == NULL || AVL_L(pCurNode->Key, (*ppRight)->Key)))
*ppRight = pCurNode;
#endif
}
}
else
*ppLeft = *ppRight = NULL;
return pNode;
}
/**
* Iterates tru all nodes in the given tree.
* @returns 0 on success. Return from callback on failiure.
* @param ppTree Pointer to the AVL-tree root node pointer.
* @param fFromLeft TRUE: Left to right.
* FALSE: Right to left.
* @param pfnCallBack Pointer to callback function.
* @param pvParam Userparameter passed on to the callback function.
* @status completely implemented.
* @author knut st. osmundsen
*/
unsigned AVLDoWithAll(PPAVLNODECORE ppTree, int fFromLeft, PAVLCALLBACK pfnCallBack, void *pvParam)
{
AVLSTACK2 AVLStack;
PAVLNODECORE pNode;
unsigned rc;
if (*ppTree == NULL)
return 0;
AVLStack.cEntries = 1;
AVLStack.achFlags[0] = 0;
AVLStack.aEntries[0] = *ppTree;
if (fFromLeft)
{ /* from left */
while (AVLStack.cEntries > 0)
{
pNode = AVLStack.aEntries[AVLStack.cEntries - 1];
/* left */
if (!AVLStack.achFlags[AVLStack.cEntries - 1]++)
{
if (pNode->pLeft != NULL)
{
AVLStack.achFlags[AVLStack.cEntries] = 0; /* 0 first, 1 last */
AVLStack.aEntries[AVLStack.cEntries++] = pNode->pLeft;
continue;
}
}
/* center */
rc = pfnCallBack(pNode, pvParam);
if (rc != 0)
return rc;
/* right */
AVLStack.cEntries--;
if (pNode->pRight != NULL)
{
AVLStack.achFlags[AVLStack.cEntries] = 0;
AVLStack.aEntries[AVLStack.cEntries++] = pNode->pRight;
}
} /* while */
}
else
{ /* from right */
while (AVLStack.cEntries > 0)
{
pNode = AVLStack.aEntries[AVLStack.cEntries - 1];
/* right */
if (!AVLStack.achFlags[AVLStack.cEntries - 1]++)
{
if (pNode->pRight != NULL)
{
AVLStack.achFlags[AVLStack.cEntries] = 0; /* 0 first, 1 last */
AVLStack.aEntries[AVLStack.cEntries++] = pNode->pRight;
continue;
}
}
/* center */
rc = pfnCallBack(pNode, pvParam);
if (rc != 0)
return rc;
/* left */
AVLStack.cEntries--;
if (pNode->pLeft != NULL)
{
AVLStack.achFlags[AVLStack.cEntries] = 0;
AVLStack.aEntries[AVLStack.cEntries++] = pNode->pLeft;
}
} /* while */
}
return 0;
}
/**
* Starts an enumeration of all nodes in the given AVL tree.
* @returns Pointer to the first node in the tree.
* @param ppTree Pointer to the AVL-tree root node pointer.
* @param pEnumData Pointer to enumeration control data.
* @param fFromLeft TRUE: Left to right.
* FALSE: Right to left.
* @status completely implemented.
* @author knut st. osmundsen
*/
PAVLNODECORE AVLBeginEnumTree(PPAVLNODECORE ppTree, PAVLENUMDATA pEnumData, int fFromLeft)
{
if (*ppTree != NULL)
{
pEnumData->fFromLeft = (char)fFromLeft;
pEnumData->cEntries = 1;
pEnumData->aEntries[0] = *ppTree;
pEnumData->achFlags[0] = 0;
}
else
pEnumData->cEntries = 0;
return AVLGetNextNode(pEnumData);
}
/**
* Get the next node in the tree enumeration.
* @returns Pointer to the first node in the tree.
* @param pEnumData Pointer to enumeration control data.
* @status completely implemented.
* @author knut st. osmundsen
*/
PAVLNODECORE AVLGetNextNode(PAVLENUMDATA pEnumData)
{
PAVLNODECORE pNode;
if (pEnumData->fFromLeft)
{ /* from left */
while (pEnumData->cEntries > 0)
{
pNode = pEnumData->aEntries[pEnumData->cEntries - 1];
/* left */
if (pEnumData->achFlags[pEnumData->cEntries - 1] == 0)
{
pEnumData->achFlags[pEnumData->cEntries - 1]++;
if (pNode->pLeft != NULL)
{
pEnumData->achFlags[pEnumData->cEntries] = 0; /* 0 left, 1 center, 2 right */
pEnumData->aEntries[pEnumData->cEntries++] = pNode->pLeft;
continue;
}
}
/* center */
if (pEnumData->achFlags[pEnumData->cEntries - 1] == 1)
{
pEnumData->achFlags[pEnumData->cEntries - 1]++;
return pNode;
}
/* right */
pEnumData->cEntries--;
if (pNode->pRight != NULL)
{
pEnumData->achFlags[pEnumData->cEntries] = 0;
pEnumData->aEntries[pEnumData->cEntries++] = pNode->pRight;
}
} /* while */
}
else
{ /* from right */
while (pEnumData->cEntries > 0)
{
pNode = pEnumData->aEntries[pEnumData->cEntries - 1];
/* right */
if (pEnumData->achFlags[pEnumData->cEntries - 1] == 0)
{
pEnumData->achFlags[pEnumData->cEntries - 1]++;
if (pNode->pRight != NULL)
{
pEnumData->achFlags[pEnumData->cEntries] = 0; /* 0 right, 1 center, 2 left */
pEnumData->aEntries[pEnumData->cEntries++] = pNode->pRight;
continue;
}
}
/* center */
if (pEnumData->achFlags[pEnumData->cEntries - 1] == 1)
{
pEnumData->achFlags[pEnumData->cEntries - 1]++;
return pNode;
}
/* left */
pEnumData->cEntries--;
if (pNode->pLeft != NULL)
{
pEnumData->achFlags[pEnumData->cEntries] = 0;
pEnumData->aEntries[pEnumData->cEntries++] = pNode->pLeft;
}
} /* while */
}
return NULL;
}
/**
* Finds the best fitting node in the tree for the given Key value.
* @returns Pointer to the best fitting node found.
* @param ppTree Pointer to Pointer to the tree root node.
* @param Key The Key of which is to be found a best fitting match for..
* @param fAbove TRUE: Returned node is have the closest key to Key from above.
* FALSE: Returned node is have the closest key to Key from below.
* @status completely implemented.
* @sketch The best fitting node is always located in the searchpath above you.
* >= (above): The node where you last turned left.
* <= (below): the node where you last turned right.
* @author knut st. osmundsen
*/
PAVLNODECORE AVLGetBestFit(PPAVLNODECORE ppTree, AVLKEY Key, int fAbove)
{
#ifdef AVL_CMP
register int iDiff;
#endif
register PAVLNODECORE pNode = *ppTree;
PAVLNODECORE pNodeLast = NULL;
if (fAbove)
{ /* pNode->Key >= Key */
#ifndef AVL_CMP
while (pNode != NULL && AVL_NE(pNode->Key, Key))
#else
while (pNode != NULL && (iDiff = AVL_CMP(pNode->Key, Key)) != 0)
#endif
{
#ifndef AVL_CMP
if (AVL_G(pNode->Key, Key))
#else
if (iDiff > 0)
#endif
{
pNodeLast = pNode;
pNode = pNode->pLeft;
}
else
pNode = pNode->pRight;
}
}
else
{ /* pNode->Key <= Key */
#ifndef AVL_CMP
while (pNode != NULL && AVL_NE(pNode->Key, Key))
#else
while (pNode != NULL && (iDiff = AVL_CMP(pNode->Key, Key)) != 0)
#endif
{
#ifndef AVL_CMP
if (AVL_L(pNode->Key, Key))
#else
if (iDiff < 0)
#endif
{
pNodeLast = pNode;
pNode = pNode->pRight;
}
else
pNode = pNode->pLeft;
}
}
return pNode == NULL ? pNodeLast /* best fit */ : pNode /* perfect match */;
}
/**
* Rewindes a stack of pointer to pointers to nodes, rebalancing the tree.
* @param pStack Pointer to stack to rewind.
* @sketch LOOP thru all stack entries
* BEGIN
* Get pointer to pointer to node (and pointer to node) from stack.
* IF 2 higher left subtree than in right subtree THEN
* BEGIN
* IF higher (or equal) left-sub-subtree than right-sub-subtree THEN
* * n+2|n+3
* / \ / \
* n+2 n ==> n+1 n+1|n+2
* / \ / \
* n+1 n|n+1 n|n+1 n
*
* Or with keys:
*
* 4 2
* / \ / \
* 2 5 ==> 1 4
* / \ / \
* 1 3 3 5
*
* ELSE
* * n+2
* / \ / \
* n+2 n n+1 n+1
* / \ ==> / \ / \
* n n+1 n L R n
* / \
* L R
*
* Or with keys:
* 6 4
* / \ / \
* 2 7 ==> 2 6
* / \ / \ / \
* 1 4 1 3 5 7
* / \
* 3 5
* END
* ELSE IF 2 higher in right subtree than in left subtree THEN
* BEGIN
* Same as above but left <==> right. (invert the picture)
* ELSE
* IF correct height THEN break
* ELSE correct height.
* END
* @status
* @author knut st. osmundsen
* @remark
*/
INLINE void AVLRebalance(PAVLSTACK pStack)
{
while (pStack->cEntries > 0)
{
PPAVLNODECORE ppNode = pStack->aEntries[--pStack->cEntries];
PAVLNODECORE pNode = *ppNode;
PAVLNODECORE pLeftNode = pNode->pLeft;
unsigned char uchLeftHeight = AVL_HEIGHTOF(pLeftNode);
PAVLNODECORE pRightNode = pNode->pRight;
unsigned char uchRightHeight = AVL_HEIGHTOF(pRightNode);
if (uchRightHeight + 1 < uchLeftHeight)
{
PAVLNODECORE pLeftLeftNode = pLeftNode->pLeft;
PAVLNODECORE pLeftRightNode = pLeftNode->pRight;
unsigned char uchLeftRightHeight = AVL_HEIGHTOF(pLeftRightNode);
if (AVL_HEIGHTOF(pLeftLeftNode) >= uchLeftRightHeight)
{
pNode->pLeft = pLeftRightNode;
pLeftNode->pRight = pNode;
pLeftNode->uchHeight = (unsigned char)(1 + (pNode->uchHeight = (unsigned char)(1 + uchLeftRightHeight)));
*ppNode = pLeftNode;
}
else
{
pLeftNode->pRight = pLeftRightNode->pLeft;
pNode->pLeft = pLeftRightNode->pRight;
pLeftRightNode->pLeft = pLeftNode;
pLeftRightNode->pRight = pNode;
pLeftNode->uchHeight = pNode->uchHeight = uchLeftRightHeight;
pLeftRightNode->uchHeight = uchLeftHeight;
*ppNode = pLeftRightNode;
}
}
else if (uchLeftHeight + 1 < uchRightHeight)
{
PAVLNODECORE pRightLeftNode = pRightNode->pLeft;
unsigned char uchRightLeftHeight = AVL_HEIGHTOF(pRightLeftNode);
PAVLNODECORE pRightRightNode = pRightNode->pRight;
if (AVL_HEIGHTOF(pRightRightNode) >= uchRightLeftHeight)
{
pNode->pRight = pRightLeftNode;
pRightNode->pLeft = pNode;
pRightNode->uchHeight = (unsigned char)(1 + (pNode->uchHeight = (unsigned char)(1 + uchRightLeftHeight)));
*ppNode = pRightNode;
}
else
{
pRightNode->pLeft = pRightLeftNode->pRight;
pNode->pRight = pRightLeftNode->pLeft;
pRightLeftNode->pRight = pRightNode;
pRightLeftNode->pLeft = pNode;
pRightNode->uchHeight = pNode->uchHeight = uchRightLeftHeight;
pRightLeftNode->uchHeight = uchRightHeight;
*ppNode = pRightLeftNode;
}
}
else
{
register unsigned char uchHeight = (unsigned char)(max(uchLeftHeight, uchRightHeight) + 1);
if (uchHeight == pNode->uchHeight)
break;
pNode->uchHeight = uchHeight;
}
}
}
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