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minix3/servers/vm/cavl_impl.h

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/* Abstract AVL Tree Generic C Package.
** Implementation generation header file.
**
** This code is in the public domain. See cavl_tree.html for interface
** documentation.
**
** Version: 1.5 Author: Walt Karas
*/
#include <string.h>
#undef L__
#undef L__EST_LONG_BIT
#undef L__SIZE
#undef L__tree
#undef L__MASK_HIGH_BIT
#undef L__LONG_BIT
#undef L__BIT_ARR_DEFN
#undef L__BIT_ARR_CLEAR
#undef L__BIT_ARR_VAL
#undef L__BIT_ARR_0
#undef L__BIT_ARR_1
#undef L__BIT_ARR_ALL
#undef L__BIT_ARR_LONGS
#undef L__IMPL_MASK
#undef L__CHECK_READ_ERROR
#undef L__CHECK_READ_ERROR_INV_DEPTH
#undef L__SC
#undef L__BALANCE_PARAM_PREFIX
#ifdef AVL_UNIQUE
#define L__ AVL_UNIQUE
#else
#define L__(X) X
#endif
/* Determine correct storage class for functions */
#ifdef AVL_PRIVATE
#define L__SC static
#else
#define L__SC
#endif
#ifdef AVL_SIZE
#define L__SIZE AVL_SIZE
#else
#define L__SIZE unsigned long
#endif
#define L__MASK_HIGH_BIT ((int) ~ ((~ (unsigned) 0) >> 1))
/* ANSI C/ISO C++ require that a long have at least 32 bits. Set
** L__EST_LONG_BIT to be the greatest multiple of 8 in the range
** 32 - 64 (inclusive) that is less than or equal to the number of
** bits in a long.
*/
#if (((LONG_MAX >> 31) >> 7) == 0)
#define L__EST_LONG_BIT 32
#elif (((LONG_MAX >> 31) >> 15) == 0)
#define L__EST_LONG_BIT 40
#elif (((LONG_MAX >> 31) >> 23) == 0)
#define L__EST_LONG_BIT 48
#elif (((LONG_MAX >> 31) >> 31) == 0)
#define L__EST_LONG_BIT 56
#else
#define L__EST_LONG_BIT 64
#endif
#define L__LONG_BIT (sizeof(long) * CHAR_BIT)
#if ((AVL_MAX_DEPTH) > L__EST_LONG_BIT)
/* The maximum depth may be greater than the number of bits in a long,
** so multiple longs are needed to hold a bit array indexed by node
** depth. */
#define L__BIT_ARR_LONGS (((AVL_MAX_DEPTH) + L__LONG_BIT - 1) / L__LONG_BIT)
#define L__BIT_ARR_DEFN(NAME) unsigned long NAME[L__BIT_ARR_LONGS];
#define L__BIT_ARR_CLEAR(NAME) memset(NAME, 0, sizeof(NAME));
#define L__BIT_ARR_VAL(BIT_ARR, BIT_NUM) \
((BIT_ARR)[(BIT_NUM) / L__LONG_BIT] & (1L << ((BIT_NUM) % L__LONG_BIT)))
#define L__BIT_ARR_0(BIT_ARR, BIT_NUM) \
(BIT_ARR)[(BIT_NUM) / L__LONG_BIT] &= ~(1L << ((BIT_NUM) % L__LONG_BIT));
#define L__BIT_ARR_1(BIT_ARR, BIT_NUM) \
(BIT_ARR)[(BIT_NUM) / L__LONG_BIT] |= 1L << ((BIT_NUM) % L__LONG_BIT);
#define L__BIT_ARR_ALL(BIT_ARR, BIT_VAL) \
{ int i = L__BIT_ARR_LONGS; do (BIT_ARR)[--i] = 0L - (BIT_VAL); while(i); }
#else /* The bit array can definitely fit in one long */
#define L__BIT_ARR_DEFN(NAME) unsigned long NAME;
#define L__BIT_ARR_CLEAR(NAME) NAME = 0;
#define L__BIT_ARR_VAL(BIT_ARR, BIT_NUM) ((BIT_ARR) & (1L << (BIT_NUM)))
#define L__BIT_ARR_0(BIT_ARR, BIT_NUM) (BIT_ARR) &= ~(1L << (BIT_NUM));
#define L__BIT_ARR_1(BIT_ARR, BIT_NUM) (BIT_ARR) |= 1L << (BIT_NUM);
#define L__BIT_ARR_ALL(BIT_ARR, BIT_VAL) (BIT_ARR) = 0L - (BIT_VAL);
#endif
#ifdef AVL_READ_ERRORS_HAPPEN
#define L__CHECK_READ_ERROR(ERROR_RETURN) \
{ if (AVL_READ_ERROR) return(ERROR_RETURN); }
#else
#define L__CHECK_READ_ERROR(ERROR_RETURN)
#endif
/* The presumed reason that an instantiation places additional fields
** inside the AVL tree structure is that the SET_ and GET_ macros
** need these fields. The "balance" function does not explicitly use
** any fields in the AVL tree structure, so only pass an AVL tree
** structure pointer to "balance" if it has instantiation-specific
** fields that are (presumably) needed by the SET_/GET_ calls within
** "balance".
*/
#ifdef AVL_INSIDE_STRUCT
#define L__BALANCE_PARAM_CALL_PREFIX L__tree,
#define L__BALANCE_PARAM_DECL_PREFIX L__(avl) *L__tree,
#else
#define L__BALANCE_PARAM_CALL_PREFIX
#define L__BALANCE_PARAM_DECL_PREFIX
#endif
#ifdef AVL_IMPL_MASK
#define L__IMPL_MASK (AVL_IMPL_MASK)
#else
/* Define all functions. */
#define L__IMPL_MASK AVL_IMPL_ALL
#endif
#if (L__IMPL_MASK & AVL_IMPL_INIT)
L__SC void L__(init)(L__(avl) *L__tree) { AVL_SET_ROOT(L__tree, AVL_NULL); }
#endif
#if (L__IMPL_MASK & AVL_IMPL_IS_EMPTY)
L__SC int L__(is_empty)(L__(avl) *L__tree)
{ return(L__tree->root == AVL_NULL); }
#endif
/* Put the private balance function in the same compilation module as
** the insert function. */
#if (L__IMPL_MASK & AVL_IMPL_INSERT)
/* Balances subtree, returns handle of root node of subtree after balancing.
*/
static L__SC AVL_HANDLE L__(balance)(L__BALANCE_PARAM_DECL_PREFIX AVL_HANDLE bal_h)
{
AVL_HANDLE deep_h;
/* Either the "greater than" or the "less than" subtree of
** this node has to be 2 levels deeper (or else it wouldn't
** need balancing).
*/
if (AVL_GET_BALANCE_FACTOR(bal_h) > 0)
{
/* "Greater than" subtree is deeper. */
deep_h = AVL_GET_GREATER(bal_h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
if (AVL_GET_BALANCE_FACTOR(deep_h) < 0)
{
int bf;
AVL_HANDLE old_h = bal_h;
bal_h = AVL_GET_LESS(deep_h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
AVL_SET_GREATER(old_h, AVL_GET_LESS(bal_h, 1))
AVL_SET_LESS(deep_h, AVL_GET_GREATER(bal_h, 1))
AVL_SET_LESS(bal_h, old_h)
AVL_SET_GREATER(bal_h, deep_h)
bf = AVL_GET_BALANCE_FACTOR(bal_h);
if (bf != 0)
{
if (bf > 0)
{
AVL_SET_BALANCE_FACTOR(old_h, -1)
AVL_SET_BALANCE_FACTOR(deep_h, 0)
}
else
{
AVL_SET_BALANCE_FACTOR(deep_h, 1)
AVL_SET_BALANCE_FACTOR(old_h, 0)
}
AVL_SET_BALANCE_FACTOR(bal_h, 0)
}
else
{
AVL_SET_BALANCE_FACTOR(old_h, 0)
AVL_SET_BALANCE_FACTOR(deep_h, 0)
}
}
else
{
AVL_SET_GREATER(bal_h, AVL_GET_LESS(deep_h, 0))
AVL_SET_LESS(deep_h, bal_h)
if (AVL_GET_BALANCE_FACTOR(deep_h) == 0)
{
AVL_SET_BALANCE_FACTOR(deep_h, -1)
AVL_SET_BALANCE_FACTOR(bal_h, 1)
}
else
{
AVL_SET_BALANCE_FACTOR(deep_h, 0)
AVL_SET_BALANCE_FACTOR(bal_h, 0)
}
bal_h = deep_h;
}
}
else
{
/* "Less than" subtree is deeper. */
deep_h = AVL_GET_LESS(bal_h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
if (AVL_GET_BALANCE_FACTOR(deep_h) > 0)
{
int bf;
AVL_HANDLE old_h = bal_h;
bal_h = AVL_GET_GREATER(deep_h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
AVL_SET_LESS(old_h, AVL_GET_GREATER(bal_h, 0))
AVL_SET_GREATER(deep_h, AVL_GET_LESS(bal_h, 0))
AVL_SET_GREATER(bal_h, old_h)
AVL_SET_LESS(bal_h, deep_h)
bf = AVL_GET_BALANCE_FACTOR(bal_h);
if (bf != 0)
{
if (bf < 0)
{
AVL_SET_BALANCE_FACTOR(old_h, 1)
AVL_SET_BALANCE_FACTOR(deep_h, 0)
}
else
{
AVL_SET_BALANCE_FACTOR(deep_h, -1)
AVL_SET_BALANCE_FACTOR(old_h, 0)
}
AVL_SET_BALANCE_FACTOR(bal_h, 0)
}
else
{
AVL_SET_BALANCE_FACTOR(old_h, 0)
AVL_SET_BALANCE_FACTOR(deep_h, 0)
}
}
else
{
AVL_SET_LESS(bal_h, AVL_GET_GREATER(deep_h, 0))
AVL_SET_GREATER(deep_h, bal_h)
if (AVL_GET_BALANCE_FACTOR(deep_h) == 0)
{
AVL_SET_BALANCE_FACTOR(deep_h, 1)
AVL_SET_BALANCE_FACTOR(bal_h, -1)
}
else
{
AVL_SET_BALANCE_FACTOR(deep_h, 0)
AVL_SET_BALANCE_FACTOR(bal_h, 0)
}
bal_h = deep_h;
}
}
return(bal_h);
}
L__SC AVL_HANDLE L__(insert)(L__(avl) *L__tree, AVL_HANDLE h)
{
AVL_SET_LESS(h, AVL_NULL)
AVL_SET_GREATER(h, AVL_NULL)
AVL_SET_BALANCE_FACTOR(h, 0)
if (L__tree->root == AVL_NULL) {
AVL_SET_ROOT(L__tree, h);
} else
{
/* Last unbalanced node encountered in search for insertion point. */
AVL_HANDLE unbal = AVL_NULL;
/* Parent of last unbalanced node. */
AVL_HANDLE parent_unbal = AVL_NULL;
/* Balance factor of last unbalanced node. */
int unbal_bf;
/* Zero-based depth in tree. */
unsigned depth = 0, unbal_depth = 0;
/* Records a path into the tree. If bit n is true, indicates
** take greater branch from the nth node in the path, otherwise
** take the less branch. bit 0 gives branch from root, and
** so on. */
L__BIT_ARR_DEFN(branch)
AVL_HANDLE hh = L__tree->root;
AVL_HANDLE parent = AVL_NULL;
int cmp;
L__BIT_ARR_CLEAR(branch)
do
{
if (AVL_GET_BALANCE_FACTOR(hh) != 0)
{
unbal = hh;
parent_unbal = parent;
unbal_depth = depth;
}
cmp = AVL_COMPARE_NODE_NODE(h, hh);
if (cmp == 0)
/* Duplicate key. */
return(hh);
parent = hh;
if (cmp > 0)
{
hh = AVL_GET_GREATER(hh, 1);
L__BIT_ARR_1(branch, depth)
}
else
{
hh = AVL_GET_LESS(hh, 1);
L__BIT_ARR_0(branch, depth)
}
L__CHECK_READ_ERROR(AVL_NULL)
depth++;
}
while (hh != AVL_NULL);
/* Add node to insert as leaf of tree. */
if (cmp < 0)
AVL_SET_LESS(parent, h)
else
AVL_SET_GREATER(parent, h)
depth = unbal_depth;
if (unbal == AVL_NULL)
hh = L__tree->root;
else
{
cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
depth++;
unbal_bf = AVL_GET_BALANCE_FACTOR(unbal);
if (cmp < 0)
unbal_bf--;
else /* cmp > 0 */
unbal_bf++;
hh = cmp < 0 ? AVL_GET_LESS(unbal, 1) : AVL_GET_GREATER(unbal, 1);
L__CHECK_READ_ERROR(AVL_NULL)
if ((unbal_bf != -2) && (unbal_bf != 2))
{
/* No rebalancing of tree is necessary. */
AVL_SET_BALANCE_FACTOR(unbal, unbal_bf)
unbal = AVL_NULL;
}
}
if (hh != AVL_NULL)
while (h != hh)
{
cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
depth++;
if (cmp < 0)
{
AVL_SET_BALANCE_FACTOR(hh, -1)
hh = AVL_GET_LESS(hh, 1);
}
else /* cmp > 0 */
{
AVL_SET_BALANCE_FACTOR(hh, 1)
hh = AVL_GET_GREATER(hh, 1);
}
L__CHECK_READ_ERROR(AVL_NULL)
}
if (unbal != AVL_NULL)
{
unbal = L__(balance)(L__BALANCE_PARAM_CALL_PREFIX unbal);
L__CHECK_READ_ERROR(AVL_NULL)
if (parent_unbal == AVL_NULL)
{
AVL_SET_ROOT(L__tree, unbal);
}
else
{
depth = unbal_depth - 1;
cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
if (cmp < 0)
AVL_SET_LESS(parent_unbal, unbal)
else /* cmp > 0 */
AVL_SET_GREATER(parent_unbal, unbal)
}
}
}
return(h);
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_SEARCH)
L__SC AVL_HANDLE L__(search)(L__(avl) *L__tree, AVL_KEY k, avl_search_type st)
{
int cmp, target_cmp;
AVL_HANDLE match_h = AVL_NULL;
AVL_HANDLE h = L__tree->root;
if (st & AVL_LESS)
target_cmp = 1;
else if (st & AVL_GREATER)
target_cmp = -1;
else
target_cmp = 0;
while (h != AVL_NULL)
{
cmp = AVL_COMPARE_KEY_NODE(k, h);
if (cmp == 0)
{
if (st & AVL_EQUAL)
{
match_h = h;
break;
}
cmp = -target_cmp;
}
else if (target_cmp != 0)
if (!((cmp ^ target_cmp) & L__MASK_HIGH_BIT))
/* cmp and target_cmp are both positive or both negative. */
match_h = h;
h = cmp < 0 ? AVL_GET_LESS(h, 1) : AVL_GET_GREATER(h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
}
return(match_h);
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_SEARCH_LEAST)
L__SC AVL_HANDLE L__(search_least)(L__(avl) *L__tree)
{
AVL_HANDLE h = L__tree->root;
AVL_HANDLE parent = AVL_NULL;
while (h != AVL_NULL)
{
parent = h;
h = AVL_GET_LESS(h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
}
return(parent);
}
#endif
L__SC AVL_HANDLE L__(search_root)(L__(avl) *L__tree)
{
return L__tree->root;
}
#if (L__IMPL_MASK & AVL_IMPL_SEARCH_GREATEST)
L__SC AVL_HANDLE L__(search_greatest)(L__(avl) *L__tree)
{
AVL_HANDLE h = L__tree->root;
AVL_HANDLE parent = AVL_NULL;
while (h != AVL_NULL)
{
parent = h;
h = AVL_GET_GREATER(h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
}
return(parent);
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_REMOVE)
/* Prototype of balance function (called by remove) in case not in
** same compilation unit.
*/
L__SC AVL_HANDLE L__(balance)(L__BALANCE_PARAM_DECL_PREFIX AVL_HANDLE bal_h);
L__SC AVL_HANDLE L__(remove)(L__(avl) *L__tree, AVL_KEY k)
{
/* Zero-based depth in tree. */
unsigned depth = 0, rm_depth;
/* Records a path into the tree. If bit n is true, indicates
** take greater branch from the nth node in the path, otherwise
** take the less branch. bit 0 gives branch from root, and
** so on. */
L__BIT_ARR_DEFN(branch)
AVL_HANDLE h = L__tree->root;
AVL_HANDLE parent = AVL_NULL;
AVL_HANDLE child;
AVL_HANDLE path;
int cmp, cmp_shortened_sub_with_path = 0;
int reduced_depth;
int bf;
AVL_HANDLE rm;
AVL_HANDLE parent_rm;
L__BIT_ARR_CLEAR(branch)
for ( ; ; )
{
if (h == AVL_NULL)
/* No node in tree with given key. */
return(AVL_NULL);
cmp = AVL_COMPARE_KEY_NODE(k, h);
if (cmp == 0)
/* Found node to remove. */
break;
parent = h;
if (cmp > 0)
{
h = AVL_GET_GREATER(h, 1);
L__BIT_ARR_1(branch, depth)
}
else
{
h = AVL_GET_LESS(h, 1);
L__BIT_ARR_0(branch, depth)
}
L__CHECK_READ_ERROR(AVL_NULL)
depth++;
cmp_shortened_sub_with_path = cmp;
}
rm = h;
parent_rm = parent;
rm_depth = depth;
/* If the node to remove is not a leaf node, we need to get a
** leaf node, or a node with a single leaf as its child, to put
** in the place of the node to remove. We will get the greatest
** node in the less subtree (of the node to remove), or the least
** node in the greater subtree. We take the leaf node from the
** deeper subtree, if there is one. */
if (AVL_GET_BALANCE_FACTOR(h) < 0)
{
child = AVL_GET_LESS(h, 1);
L__BIT_ARR_0(branch, depth)
cmp = -1;
}
else
{
child = AVL_GET_GREATER(h, 1);
L__BIT_ARR_1(branch, depth)
cmp = 1;
}
L__CHECK_READ_ERROR(AVL_NULL)
depth++;
if (child != AVL_NULL)
{
cmp = -cmp;
do
{
parent = h;
h = child;
if (cmp < 0)
{
child = AVL_GET_LESS(h, 1);
L__BIT_ARR_0(branch, depth)
}
else
{
child = AVL_GET_GREATER(h, 1);
L__BIT_ARR_1(branch, depth)
}
L__CHECK_READ_ERROR(AVL_NULL)
depth++;
}
while (child != AVL_NULL);
if (parent == rm)
/* Only went through do loop once. Deleted node will be replaced
** in the tree structure by one of its immediate children. */
cmp_shortened_sub_with_path = -cmp;
else
cmp_shortened_sub_with_path = cmp;
/* Get the handle of the opposite child, which may not be null. */
child = cmp > 0 ? AVL_GET_LESS(h, 0) : AVL_GET_GREATER(h, 0);
}
if (parent == AVL_NULL) {
/* There were only 1 or 2 nodes in this tree. */
AVL_SET_ROOT(L__tree, child);
}
else if (cmp_shortened_sub_with_path < 0)
AVL_SET_LESS(parent, child)
else
AVL_SET_GREATER(parent, child)
/* "path" is the parent of the subtree being eliminated or reduced
** from a depth of 2 to 1. If "path" is the node to be removed, we
** set path to the node we're about to poke into the position of the
** node to be removed. */
path = parent == rm ? h : parent;
if (h != rm)
{
/* Poke in the replacement for the node to be removed. */
AVL_SET_LESS(h, AVL_GET_LESS(rm, 0))
AVL_SET_GREATER(h, AVL_GET_GREATER(rm, 0))
AVL_SET_BALANCE_FACTOR(h, AVL_GET_BALANCE_FACTOR(rm))
if (parent_rm == AVL_NULL) {
AVL_SET_ROOT(L__tree, h);
}
else
{
depth = rm_depth - 1;
if (L__BIT_ARR_VAL(branch, depth))
AVL_SET_GREATER(parent_rm, h)
else
AVL_SET_LESS(parent_rm, h)
}
}
if (path != AVL_NULL)
{
/* Create a temporary linked list from the parent of the path node
** to the root node. */
h = L__tree->root;
parent = AVL_NULL;
depth = 0;
while (h != path)
{
if (L__BIT_ARR_VAL(branch, depth))
{
child = AVL_GET_GREATER(h, 1);
AVL_SET_GREATER(h, parent)
}
else
{
child = AVL_GET_LESS(h, 1);
AVL_SET_LESS(h, parent)
}
L__CHECK_READ_ERROR(AVL_NULL)
depth++;
parent = h;
h = child;
}
/* Climb from the path node to the root node using the linked
** list, restoring the tree structure and rebalancing as necessary.
*/
reduced_depth = 1;
cmp = cmp_shortened_sub_with_path;
for ( ; ; )
{
if (reduced_depth)
{
bf = AVL_GET_BALANCE_FACTOR(h);
if (cmp < 0)
bf++;
else /* cmp > 0 */
bf--;
if ((bf == -2) || (bf == 2))
{
h = L__(balance)(L__BALANCE_PARAM_CALL_PREFIX h);
L__CHECK_READ_ERROR(AVL_NULL)
bf = AVL_GET_BALANCE_FACTOR(h);
}
else
AVL_SET_BALANCE_FACTOR(h, bf)
reduced_depth = (bf == 0);
}
if (parent == AVL_NULL)
break;
child = h;
h = parent;
depth--;
cmp = L__BIT_ARR_VAL(branch, depth) ? 1 : -1;
if (cmp < 0)
{
parent = AVL_GET_LESS(h, 1);
AVL_SET_LESS(h, child)
}
else
{
parent = AVL_GET_GREATER(h, 1);
AVL_SET_GREATER(h, child)
}
L__CHECK_READ_ERROR(AVL_NULL)
}
AVL_SET_ROOT(L__tree, h);
}
return(rm);
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_SUBST)
L__SC AVL_HANDLE L__(subst)(L__(avl) *L__tree, AVL_HANDLE new_node)
{
AVL_HANDLE h = L__tree->root;
AVL_HANDLE parent = AVL_NULL;
int cmp, last_cmp = 0;
/* Search for node already in tree with same key. */
for ( ; ; )
{
if (h == AVL_NULL)
/* No node in tree with same key as new node. */
return(AVL_NULL);
cmp = AVL_COMPARE_NODE_NODE(new_node, h);
if (cmp == 0)
/* Found the node to substitute new one for. */
break;
last_cmp = cmp;
parent = h;
h = cmp < 0 ? AVL_GET_LESS(h, 1) : AVL_GET_GREATER(h, 1);
L__CHECK_READ_ERROR(AVL_NULL)
}
/* Copy tree housekeeping fields from node in tree to new node. */
AVL_SET_LESS(new_node, AVL_GET_LESS(h, 0))
AVL_SET_GREATER(new_node, AVL_GET_GREATER(h, 0))
AVL_SET_BALANCE_FACTOR(new_node, AVL_GET_BALANCE_FACTOR(h))
if (parent == AVL_NULL)
{
/* New node is also new root. */
AVL_SET_ROOT(L__tree, new_node);
}
else
{
/* Make parent point to new node. */
if (last_cmp < 0)
AVL_SET_LESS(parent, new_node)
else
AVL_SET_GREATER(parent, new_node)
}
return(h);
}
#endif
#ifdef AVL_BUILD_ITER_TYPE
#if (L__IMPL_MASK & AVL_IMPL_BUILD)
L__SC int L__(build)(
L__(avl) *L__tree, AVL_BUILD_ITER_TYPE p, L__SIZE num_nodes)
{
/* Gives path to subtree being built. If bit n is false, branch
** less from the node at depth n, if true branch greater. */
L__BIT_ARR_DEFN(branch)
/* If bit n is true, then for the current subtree at depth n, its
** greater subtree has one more node than its less subtree. */
L__BIT_ARR_DEFN(rem)
/* Depth of root node of current subtree. */
unsigned depth = 0;
/* Number of nodes in current subtree. */
L__SIZE num_sub = num_nodes;
/* The algorithm relies on a stack of nodes whose less subtree has
** been built, but whose greater subtree has not yet been built.
** The stack is implemented as linked list. The nodes are linked
** together by having the "greater" handle of a node set to the
** next node in the list. "less_parent" is the handle of the first
** node in the list. */
AVL_HANDLE less_parent = AVL_NULL;
/* h is root of current subtree, child is one of its children. */
AVL_HANDLE h;
AVL_HANDLE child;
if (num_nodes == 0)
{
AVL_SET_ROOT(L__tree, AVL_NULL);
return(1);
}
L__BIT_ARR_CLEAR(branch)
L__BIT_ARR_CLEAR(rem)
for ( ; ; )
{
while (num_sub > 2)
{
/* Subtract one for root of subtree. */
num_sub--;
if (num_sub & 1)
L__BIT_ARR_1(rem, depth)
else
L__BIT_ARR_0(rem, depth)
L__BIT_ARR_0(branch, depth)
depth++;
num_sub >>= 1;
}
if (num_sub == 2)
{
/* Build a subtree with two nodes, slanting to greater.
** I arbitrarily chose to always have the extra node in the
** greater subtree when there is an odd number of nodes to
** split between the two subtrees. */
h = AVL_BUILD_ITER_VAL(p);
L__CHECK_READ_ERROR(0)
AVL_BUILD_ITER_INCR(p)
child = AVL_BUILD_ITER_VAL(p);
L__CHECK_READ_ERROR(0)
AVL_BUILD_ITER_INCR(p)
AVL_SET_LESS(child, AVL_NULL)
AVL_SET_GREATER(child, AVL_NULL)
AVL_SET_BALANCE_FACTOR(child, 0)
AVL_SET_GREATER(h, child)
AVL_SET_LESS(h, AVL_NULL)
AVL_SET_BALANCE_FACTOR(h, 1)
}
else /* num_sub == 1 */
{
/* Build a subtree with one node. */
h = AVL_BUILD_ITER_VAL(p);
L__CHECK_READ_ERROR(0)
AVL_BUILD_ITER_INCR(p)
AVL_SET_LESS(h, AVL_NULL)
AVL_SET_GREATER(h, AVL_NULL)
AVL_SET_BALANCE_FACTOR(h, 0)
}
while (depth)
{
depth--;
if (!L__BIT_ARR_VAL(branch, depth))
/* We've completed a less subtree. */
break;
/* We've completed a greater subtree, so attach it to
** its parent (that is less than it). We pop the parent
** off the stack of less parents. */
child = h;
h = less_parent;
less_parent = AVL_GET_GREATER(h, 1);
L__CHECK_READ_ERROR(0)
AVL_SET_GREATER(h, child)
/* num_sub = 2 * (num_sub - rem[depth]) + rem[depth] + 1 */
num_sub <<= 1;
num_sub += L__BIT_ARR_VAL(rem, depth) ? 0 : 1;
if (num_sub & (num_sub - 1))
/* num_sub is not a power of 2. */
AVL_SET_BALANCE_FACTOR(h, 0)
else
/* num_sub is a power of 2. */
AVL_SET_BALANCE_FACTOR(h, 1)
}
if (num_sub == num_nodes)
/* We've completed the full tree. */
break;
/* The subtree we've completed is the less subtree of the
** next node in the sequence. */
child = h;
h = AVL_BUILD_ITER_VAL(p);
L__CHECK_READ_ERROR(0)
AVL_BUILD_ITER_INCR(p)
AVL_SET_LESS(h, child)
/* Put h into stack of less parents. */
AVL_SET_GREATER(h, less_parent)
less_parent = h;
/* Proceed to creating greater than subtree of h. */
L__BIT_ARR_1(branch, depth)
num_sub += L__BIT_ARR_VAL(rem, depth) ? 1 : 0;
depth++;
} /* end for ( ; ; ) */
AVL_SET_ROOT(L__tree, h);
return(1);
}
#endif
#endif
#if (L__IMPL_MASK & AVL_IMPL_INIT_ITER)
/* Initialize depth to invalid value, to indicate iterator is
** invalid. (Depth is zero-base.) It's not necessary to initialize
** iterators prior to passing them to the "start" function.
*/
L__SC void L__(init_iter)(L__(iter) *iter) { iter->depth = ~0; }
#endif
#ifdef AVL_READ_ERRORS_HAPPEN
#define L__CHECK_READ_ERROR_INV_DEPTH \
{ if (AVL_READ_ERROR) { iter->depth = ~0; return; } }
#else
#define L__CHECK_READ_ERROR_INV_DEPTH
#endif
#if (L__IMPL_MASK & AVL_IMPL_START_ITER)
L__SC void L__(start_iter)(
L__(avl) *L__tree, L__(iter) *iter, AVL_KEY k, avl_search_type st)
{
AVL_HANDLE h = L__tree->root;
unsigned d = 0;
int cmp, target_cmp;
/* Save the tree that we're going to iterate through in a
** member variable. */
iter->tree_ = L__tree;
iter->depth = ~0;
if (h == AVL_NULL)
/* Tree is empty. */
return;
if (st & AVL_LESS)
/* Key can be greater than key of starting node. */
target_cmp = 1;
else if (st & AVL_GREATER)
/* Key can be less than key of starting node. */
target_cmp = -1;
else
/* Key must be same as key of starting node. */
target_cmp = 0;
for ( ; ; )
{
cmp = AVL_COMPARE_KEY_NODE(k, h);
if (cmp == 0)
{
if (st & AVL_EQUAL)
{
/* Equal node was sought and found as starting node. */
iter->depth = d;
break;
}
cmp = -target_cmp;
}
else if (target_cmp != 0)
if (!((cmp ^ target_cmp) & L__MASK_HIGH_BIT))
/* cmp and target_cmp are both negative or both positive. */
iter->depth = d;
h = cmp < 0 ? AVL_GET_LESS(h, 1) : AVL_GET_GREATER(h, 1);
L__CHECK_READ_ERROR_INV_DEPTH
if (h == AVL_NULL)
break;
if (cmp > 0)
L__BIT_ARR_1(iter->branch, d)
else
L__BIT_ARR_0(iter->branch, d)
iter->path_h[d++] = h;
}
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_START_ITER_LEAST)
L__SC void L__(start_iter_least)(L__(avl) *L__tree, L__(iter) *iter)
{
AVL_HANDLE h = L__tree->root;
iter->tree_ = L__tree;
iter->depth = ~0;
L__BIT_ARR_ALL(iter->branch, 0)
while (h != AVL_NULL)
{
if (iter->depth != ~0)
iter->path_h[iter->depth] = h;
iter->depth++;
h = AVL_GET_LESS(h, 1);
L__CHECK_READ_ERROR_INV_DEPTH
}
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_START_ITER_GREATEST)
L__SC void L__(start_iter_greatest)(L__(avl) *L__tree, L__(iter) *iter)
{
AVL_HANDLE h = L__tree->root;
iter->tree_ = L__tree;
iter->depth = ~0;
L__BIT_ARR_ALL(iter->branch, 1)
while (h != AVL_NULL)
{
if (iter->depth != ~0)
iter->path_h[iter->depth] = h;
iter->depth++;
h = AVL_GET_GREATER(h, 1);
L__CHECK_READ_ERROR_INV_DEPTH
}
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_GET_ITER)
L__SC AVL_HANDLE L__(get_iter)(L__(iter) *iter)
{
if (iter->depth == ~0)
return(AVL_NULL);
return(iter->depth == 0 ?
iter->tree_->root : iter->path_h[iter->depth - 1]);
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_INCR_ITER)
L__SC void L__(incr_iter)(L__(iter) *iter)
{
#define L__tree (iter->tree_)
if (iter->depth != ~0)
{
AVL_HANDLE h =
AVL_GET_GREATER((iter->depth == 0 ?
iter->tree_->root : iter->path_h[iter->depth - 1]), 1);
L__CHECK_READ_ERROR_INV_DEPTH
if (h == AVL_NULL)
do
{
if (iter->depth == 0)
{
iter->depth = ~0;
break;
}
iter->depth--;
}
while (L__BIT_ARR_VAL(iter->branch, iter->depth));
else
{
L__BIT_ARR_1(iter->branch, iter->depth)
iter->path_h[iter->depth++] = h;
for ( ; ; )
{
h = AVL_GET_LESS(h, 1);
L__CHECK_READ_ERROR_INV_DEPTH
if (h == AVL_NULL)
break;
L__BIT_ARR_0(iter->branch, iter->depth)
iter->path_h[iter->depth++] = h;
}
}
}
#undef L__tree
}
#endif
#if (L__IMPL_MASK & AVL_IMPL_DECR_ITER)
L__SC void L__(decr_iter)(L__(iter) *iter)
{
#define L__tree (iter->tree_)
if (iter->depth != ~0)
{
AVL_HANDLE h =
AVL_GET_LESS((iter->depth == 0 ?
iter->tree_->root : iter->path_h[iter->depth - 1]), 1);
L__CHECK_READ_ERROR_INV_DEPTH
if (h == AVL_NULL)
do
{
if (iter->depth == 0)
{
iter->depth = ~0;
break;
}
iter->depth--;
}
while (!L__BIT_ARR_VAL(iter->branch, iter->depth));
else
{
L__BIT_ARR_0(iter->branch, iter->depth)
iter->path_h[iter->depth++] = h;
for ( ; ; )
{
h = AVL_GET_GREATER(h, 1);
L__CHECK_READ_ERROR_INV_DEPTH
if (h == AVL_NULL)
break;
L__BIT_ARR_1(iter->branch, iter->depth)
iter->path_h[iter->depth++] = h;
}
}
}
#undef L__tree
}
#endif
/* Tidy up the preprocessor symbol name space. */
#undef L__
#undef L__EST_LONG_BIT
#undef L__SIZE
#undef L__MASK_HIGH_BIT
#undef L__LONG_BIT
#undef L__BIT_ARR_DEFN
#undef L__BIT_ARR_CLEAR
#undef L__BIT_ARR_VAL
#undef L__BIT_ARR_0
#undef L__BIT_ARR_1
#undef L__BIT_ARR_ALL
#undef L__CHECK_READ_ERROR
#undef L__CHECK_READ_ERROR_INV_DEPTH
#undef L__BIT_ARR_LONGS
#undef L__IMPL_MASK
#undef L__CHECK_READ_ERROR
#undef L__CHECK_READ_ERROR_INV_DEPTH
#undef L__SC
#undef L__BALANCE_PARAM_CALL_PREFIX
#undef L__BALANCE_PARAM_DECL_PREFIX
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