static void verify_tree (c_avl_node_t *n)
{
if (n == NULL)
return;
verify_tree (n->left);
verify_tree (n->right);
assert ((BALANCE (n) >= -1) && (BALANCE (n) <= 1));
assert ((n->parent == NULL) || (n->parent->right == n) || (n->parent->left == n));
} /* void verify_tree */
static void balance(t_avl const *const avl, t_node **const root) {
int b = BALANCE(*root) / 2;
if (b) {
int const side = (1 - b) / 2;
if (BALANCE((*root)->node[side]) == -b)
rotate(avl, &(*root)->node[side], !side);
*root = rotate(avl, root, side);
}
if (*root != nil)
(*root)->height = 1 + MAX((*root)->node[0]->height, (*root)->node[1]->height);
}
static void rebalance (c_avl_tree_t *t, c_avl_node_t *n)
{
int b_top;
int b_bottom;
while (n != NULL)
{
b_top = BALANCE (n);
assert ((b_top >= -2) && (b_top <= 2));
if (b_top == -2)
{
assert (n->right != NULL);
b_bottom = BALANCE (n->right);
assert ((b_bottom >= -1) && (b_bottom <= 1));
if (b_bottom == 1)
n = rotate_right_left (t, n);
else
n = rotate_left (t, n);
}
else if (b_top == 2)
{
assert (n->left != NULL);
b_bottom = BALANCE (n->left);
assert ((b_bottom >= -1) && (b_bottom <= 1));
if (b_bottom == -1)
n = rotate_left_right (t, n);
else
n = rotate_right (t, n);
}
else
{
int height = calc_height (n);
if (height == n->height)
break;
n->height = height;
}
assert (n->height == calc_height (n));
n = n->parent;
} /* while (n != NULL) */
} /* void rebalance */
/* deletion */
static void __remove(t_avl const *const avl, t_node **const root, void *val) {
if (*root == nil)
return;
if (!avl->hook_cmp((*root)->val, val)) {
if ((*root = rotate(avl, root, BALANCE(*root) < 0)) == nil)
return;
}
__remove(avl, &(*root)->node[avl->hook_cmp(val, (*root)->val) < 0], val);
balance(avl, root);
}
static node_t *
avl_single(node_t *root, int dir)
{
node_t *save = root->link[!dir];
int rlh, rrh, slh;
root->link[!dir] = save->link[dir];
save->link[dir] = root;
rlh = height(root->link[0]);
rrh = height(root->link[1]);
slh = height(save->link[!dir]);
BALANCE(root) = avl_max(rlh, rrh) + 1;
BALANCE(save) = avl_max(slh, BALANCE(root)) + 1;
return save;
}
LIB_EXPORT rc_t CC BSTreeInsert ( BSTree *bt, BSTNode *n,
int64_t ( CC * sort ) ( const BSTNode *n, const BSTNode *p ) )
{
if ( bt != NULL && n != NULL )
{
int64_t diff;
BSTNode *p = bt -> root;
BSTNode *q = NULL;
BSTNode *y = NULL;
while ( p != NULL )
{
diff = ( * sort ) ( n, p );
q = p;
if ( BALANCE ( p ) != 0 )
y = p;
p = p -> child [ diff > 0 ];
}
n -> par = q;
n -> child [ 0 ] = n -> child [ 1 ] = NULL;
if ( q == NULL )
bt -> root = n;
else
{
q -> child [ diff > 0 ] = n;
/* run a trace-back */
for ( p = n; q != y; )
{
/* this is safe because q has 0 balance */
BSTNode *z = q -> par;
if ( q -> child [ 0 ] == p )
SET_BALANCE ( q, LEFT );
else
SET_BALANCE ( q, RIGHT );
p = q;
q = z;
}
/* rebalance */
if ( q != NULL )
RebalanceAfterInsert ( & bt -> root, q, p );
}
}
/* never fails in this implementation */
return 0;
}
static
void CC RebalanceAfterInsert ( BSTNode **root, BSTNode *y, BSTNode *x )
{
BSTNode *w, *z;
/* detect left insertion */
if ( y -> child [ 0 ] == x )
{
/* if y was right-heavy, done */
if ( RIGHT_HEAVY ( y ) )
{
CLR_BALANCE ( y, RIGHT );
return;
}
/* rebalance left insertion */
w = RebalanceLeft ( y, x );
}
/* right insertion */
else
{
/* if y was left-heavy, done */
if ( LEFT_HEAVY ( y ) )
{
CLR_BALANCE ( y, LEFT );
return;
}
/* rebalance right insertion */
w = RebalanceRight ( y, x );
}
/* fix parent to child */
assert ( BALANCE ( w ) == 0 );
z = w -> par;
if ( z == 0 )
* root = w;
else
z -> child [ z -> child [ 1 ] == y ] = w;
}
BSTNode* CC RotateRightAtXLeftAtY ( BSTNode *y, BSTNode *x )
{
BSTNode *w = x -> child [ 0 ];
BSTNode *z = w -> child [ 1 ];
x -> child [ 0 ] = z;
if ( z != 0 )
SET_PARENT ( z, x );
z = w -> child [ 0 ];
w -> child [ 1 ] = x;
y -> child [ 1 ] = z;
w -> child [ 0 ] = y;
switch ( BALANCE ( w ) )
{
case 0:
w -> par = PARENT ( y );
x -> par = w;
y -> par = w;
break;
case LEFT:
w -> par = PARENT ( y );
SET_PARBAL ( x, w, RIGHT );
y -> par = w;
break;
case RIGHT:
w -> par = PARENT ( y );
x -> par = w;
SET_PARBAL ( y, w, LEFT );
break;
}
/* patch parent link */
if ( z != 0 )
SET_PARENT ( z, y );
return w;
}
static int _remove (c_avl_tree_t *t, c_avl_node_t *n)
{
assert ((t != NULL) && (n != NULL));
if ((n->left != NULL) && (n->right != NULL))
{
c_avl_node_t *r; /* replacement node */
if (BALANCE (n) > 0) /* left subtree is higher */
{
assert (n->left != NULL);
r = c_avl_node_prev (n);
}
else /* right subtree is higher */
{
assert (n->right != NULL);
r = c_avl_node_next (n);
}
assert ((r->left == NULL) || (r->right == NULL));
/* copy content */
n->key = r->key;
n->value = r->value;
n = r;
}
assert ((n->left == NULL) || (n->right == NULL));
if ((n->left == NULL) && (n->right == NULL))
{
/* Deleting a leave is easy */
if (n->parent == NULL)
{
assert (t->root == n);
t->root = NULL;
}
else
{
assert ((n->parent->left == n)
|| (n->parent->right == n));
if (n->parent->left == n)
n->parent->left = NULL;
else
n->parent->right = NULL;
rebalance (t, n->parent);
}
free_node (n);
}
else if (n->left == NULL)
{
assert (BALANCE (n) == -1);
assert ((n->parent == NULL) || (n->parent->left == n) || (n->parent->right == n));
if (n->parent == NULL)
{
assert (t->root == n);
t->root = n->right;
}
else if (n->parent->left == n)
{
n->parent->left = n->right;
}
else
{
n->parent->right = n->right;
}
n->right->parent = n->parent;
if (n->parent != NULL)
rebalance (t, n->parent);
n->right = NULL;
free_node (n);
}
else if (n->right == NULL)
{
assert (BALANCE (n) == 1);
assert ((n->parent == NULL) || (n->parent->left == n) || (n->parent->right == n));
if (n->parent == NULL)
{
assert (t->root == n);
t->root = n->left;
}
else if (n->parent->left == n)
{
n->parent->left = n->left;
}
else
{
n->parent->right = n->left;
}
n->left->parent = n->parent;
if (n->parent != NULL)
rebalance (t, n->parent);
n->left = NULL;
free_node (n);
}
else
{
assert (0);
}
return (0);
} /* void *_remove */
extern int
avl_remove(node_t **rootaddr, PyObject *key)
{
node_t *root = *rootaddr;
int cmp_res;
if (root != NULL) {
node_t *it, *up[32];
int upd[32], top = 0;
it = root;
for (;;) {
if (it == NULL)
return 0;
cmp_res = ct_compare(KEY(it), key);
if (cmp_res == 0)
break;
upd[top] = (cmp_res < 0);
up[top++] = it;
it = it->link[upd[top - 1]];
}
if (it->link[0] == NULL ||
it->link[1] == NULL) {
int dir = it->link[0] == NULL;
if (top != 0)
up[top - 1]->link[upd[top - 1]] = it->link[dir];
else
root = it->link[dir];
ct_delete_node(it);
}
else {
node_t *heir = it->link[1];
upd[top] = 1;
up[top++] = it;
while ( heir->link[0] != NULL ) {
upd[top] = 0;
up[top++] = heir;
heir = heir->link[0];
}
ct_swap_data(it, heir);
up[top - 1]->link[up[top - 1] == it] = heir->link[1];
ct_delete_node(heir);
}
while (--top >= 0) {
int lh = height(up[top]->link[upd[top]]);
int rh = height(up[top]->link[!upd[top]]);
int max = avl_max(lh, rh);
BALANCE(up[top]) = max + 1;
if (lh - rh == -1)
break;
if (lh - rh <= -2) {
node_t *a = up[top]->link[!upd[top]]->link[upd[top]];
node_t *b = up[top]->link[!upd[top]]->link[!upd[top]];
if (height(a) <= height(b))
up[top] = avl_single(up[top], upd[top]);
else
up[top] = avl_double(up[top], upd[top]);
if (top != 0)
up[top - 1]->link[upd[top - 1]] = up[top];
else
root = up[0];
}
}
}
(*rootaddr) = root;
return 1;
}
extern int
avl_insert(node_t **rootaddr, PyObject *key, PyObject *value)
{
node_t *root = *rootaddr;
if (root == NULL) {
root = avl_new_node(key, value);
if (root == NULL)
return -1;
}
else {
node_t *it, *up[32];
int upd[32], top = 0;
int done = 0;
int cmp_res;
it = root;
for (;;) {
cmp_res = ct_compare(KEY(it), key);
if (cmp_res == 0) {
Py_XDECREF(VALUE(it));
VALUE(it) = value;
Py_INCREF(value);
return 0;
}
upd[top] = (cmp_res < 0);
up[top++] = it;
if (it->link[upd[top - 1]] == NULL)
break;
it = it->link[upd[top - 1]];
}
it->link[upd[top - 1]] = avl_new_node(key, value);
if (it->link[upd[top - 1]] == NULL)
return -1;
while (--top >= 0 && !done) {
int lh, rh, max;
cmp_res = ct_compare(KEY(up[top]), key);
lh = height(up[top]->link[upd[top]]);
rh = height(up[top]->link[!upd[top]]);
if (lh - rh == 0)
done = 1;
if (lh - rh >= 2) {
node_t *a = up[top]->link[upd[top]]->link[upd[top]];
node_t *b = up[top]->link[upd[top]]->link[!upd[top]];
if (height( a ) >= height( b ))
up[top] = avl_single(up[top], !upd[top]);
else
up[top] = avl_double(up[top], !upd[top]);
if (top != 0)
up[top - 1]->link[upd[top - 1]] = up[top];
else
root = up[0];
done = 1;
}
lh = height(up[top]->link[upd[top]]);
rh = height(up[top]->link[!upd[top]]);
max = avl_max(lh, rh);
BALANCE(up[top]) = max + 1;
}
}
(*rootaddr) = root;
return 1;
}
/* BSTreeUnlink
* removes a node from tree
*/
static
void CC RebalanceAfterUnlink ( BSTNode **root, BSTNode *q, int dir )
{
while ( q != 0 )
{
BSTNode *w, *x, *y = q;
q = PARENT ( q );
if ( ! dir )
{
if ( q && q -> child [ 1 ] == y )
dir = 1;
/* simulate an increment of balance */
switch ( BALANCE ( y ) )
{
case 0:
SET_BALANCE ( y, RIGHT );
return;
case LEFT:
CLR_BALANCE ( y, LEFT );
break;
case RIGHT:
/* y has just become ++ */
x = y -> child [ 1 ];
if ( LEFT_HEAVY ( x ) )
{
w = RotateRightAtXLeftAtY ( y, x );
if ( q == 0 )
* root = w;
else
q -> child [ dir ] = w;
}
else
{
w = y -> child [ 1 ] = x -> child [ 0 ];
x -> child [ 0 ] = y;
SET_PARENT ( x, q );
SET_PARENT ( y, x );
if ( w != 0 )
SET_PARENT ( w, y );
if ( q == 0 )
* root = x;
else
q -> child [ dir ] = x;
if ( BALANCE ( x ) == 0 )
{
SET_BALANCE ( x, LEFT );
SET_PARBAL ( y, x, RIGHT );
return;
}
ZERO_BALANCE ( x );
ZERO_BALANCE ( y );
/* y = x; */
}
break;
}
}
/* symmetric case */
else
{
if ( q && q -> child [ 0 ] == y )
dir = 0;
switch ( BALANCE ( y ) )
{
case 0:
SET_BALANCE ( y, LEFT );
return;
case LEFT:
/* y has just become -- */
x = y -> child [ 0 ];
if ( RIGHT_HEAVY ( x ) )
{
w = RotateLeftAtXRightAtY ( y, x );
if ( q == 0 )
* root = w;
else
q -> child [ dir ] = w;
}
else
{
w = x -> child [ 1 ];
y -> child [ 0 ] = w;
x -> child [ 1 ] = y;
SET_PARENT ( x, q );
SET_PARENT ( y, x );
if ( w != 0 )
SET_PARENT ( w, y );
if ( q == 0 )
* root = x;
else
q -> child [ dir ] = x;
if ( BALANCE ( x ) == 0 )
{
SET_BALANCE ( x, RIGHT );
SET_PARBAL ( y, x, LEFT );
return;
}
ZERO_BALANCE ( x );
ZERO_BALANCE ( y );
/* y = x; */
}
break;
case RIGHT:
CLR_BALANCE ( y, RIGHT );
break;
}
}
}
}
/* BSTreeInsertUnique
* insert an object within tree, but only if unique
* "sort" function returns equivalent of "item" - "n"
* returns non-NULL "n" upon match or NULL on success
*/
LIB_EXPORT rc_t CC BSTreeInsertUnique ( BSTree *bt, BSTNode *n, BSTNode **exist,
int64_t ( CC * sort ) ( const BSTNode *n, const BSTNode *p ) )
{
if ( bt != NULL && n != NULL )
{
int64_t diff;
BSTNode *p = bt -> root;
BSTNode *q = NULL;
BSTNode *y = NULL;
while ( p != NULL )
{
diff = ( * sort ) ( n, p );
if ( diff == 0 )
{
/* fail to insert */
if ( exist != NULL )
* exist = p;
return RC ( rcCont, rcTree, rcInserting, rcNode, rcExists );
}
q = p;
if ( BALANCE ( p ) != 0 )
y = p;
p = p -> child [ diff > 0 ];
}
n -> par = q;
n -> child [ 0 ] = n -> child [ 1 ] = NULL;
if ( q == NULL )
bt -> root = n;
else
{
q -> child [ diff > 0 ] = n;
/* run a trace-back */
for ( p = n; q != y; )
{
/* this is safe because q has 0 balance */
BSTNode *z = q -> par;
if ( q -> child [ 0 ] == p )
SET_BALANCE ( q, LEFT );
else
SET_BALANCE ( q, RIGHT );
p = q;
q = z;
}
/* rebalance */
if ( q != NULL )
RebalanceAfterInsert ( & bt -> root, q, p );
}
}
/* only fails on existing item in this implementation */
return 0;
}
