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-rw-r--r--numlib/aatree.c432
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diff --git a/numlib/aatree.c b/numlib/aatree.c
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+
+/*
+ Andersson binary balanced tree library
+
+ > Created (Julienne Walker): September 10, 2005
+ > Corrections (James Bucanek): April 10, 2006
+ 1) Typo in jsw_aerase:
+ up != 0 should be top != 0
+ 2) Bug in jsw_aerase:
+ skew ( path[top] ) should be skew ( up )
+ split ( path[top] ) should be split ( up )
+ 3) Bug in skew and split macros:
+ Condition should test for nil
+ 4) Bug in jsw_aerase:
+ Search for successor should save the path
+ > Fixed duplicate handling (Graeme W. Gill): August 16, 2009
+*/
+
+#include "aatree.h"
+
+#ifdef __cplusplus
+#include <cstdlib>
+
+using std::malloc;
+using std::free;
+using std::size_t;
+#else
+#include <stdlib.h>
+#endif
+
+#ifndef HEIGHT_LIMIT
+#define HEIGHT_LIMIT 64 /* Tallest allowable tree */
+#endif
+
+typedef struct aat_anode {
+ int level; /* Horizontal level for balance */
+ void *data; /* User-defined content */
+ struct aat_anode *link[2]; /* Left (0) and right (1) links */
+} aat_anode_t;
+
+struct aat_atree {
+ aat_anode_t *root; /* Top of the tree */
+ aat_anode_t *nil; /* End of tree sentinel */
+ cmp_f cmp; /* Compare two items */
+ size_t size; /* Number of items (user-defined) */
+};
+
+struct aat_atrav {
+ aat_atree_t *tree; /* Paired tree */
+ aat_anode_t *it; /* Current node */
+ aat_anode_t *path[HEIGHT_LIMIT]; /* Traversal path */
+ size_t top; /* Top of stack */
+};
+
+/* Remove left horizontal links */
+#define skew(t) do { \
+ if ( t->link[0]->level == t->level && t->level != 0 ) { \
+ aat_anode_t *save = t->link[0]; \
+ t->link[0] = save->link[1]; \
+ save->link[1] = t; \
+ t = save; \
+ } \
+} while(0)
+
+/* Remove consecutive horizontal links */
+#define split(t) do { \
+ if ( t->link[1]->link[1]->level == t->level && t->level != 0 ) { \
+ aat_anode_t *save = t->link[1]; \
+ t->link[1] = save->link[0]; \
+ save->link[0] = t; \
+ t = save; \
+ ++t->level; \
+ } \
+} while(0)
+
+/* Version of cmp that ensure there are no duplicates */
+/* Set res to comparison result */
+#define AAT_CMP( res, tree, p1, p2) \
+{ \
+ if ((res = tree->cmp ( p1, p2 )) == 0) { \
+ if (p1 < p2) \
+ res = -1; \
+ else if (p1 > p2) \
+ res = 1; \
+ } \
+}
+
+/* Create a new node that points to our data */
+/* Return tree-nil if malloc failed. */
+static aat_anode_t *new_node ( aat_atree_t *tree, void *data )
+{
+ aat_anode_t *rn = (aat_anode_t *)malloc ( sizeof *rn );
+
+ if ( rn == NULL )
+ return tree->nil;
+
+ rn->level = 1;
+ rn->data = data;
+ rn->link[0] = rn->link[1] = tree->nil;
+
+ return rn;
+}
+
+/* Create a new empty tree */
+aat_atree_t *aat_anew ( cmp_f cmp )
+{
+ aat_atree_t *rt = (aat_atree_t *)malloc ( sizeof *rt );
+
+ if ( rt == NULL )
+ return NULL;
+
+ /* Initialize sentinel */
+ rt->nil = (aat_anode_t *)malloc ( sizeof *rt->nil );
+ if ( rt->nil == NULL ) {
+ free ( rt );
+ return NULL;
+ }
+
+ rt->nil->data = NULL; /* Simplifies some ops */
+ rt->nil->level = 0;
+ rt->nil->link[0] = rt->nil->link[1] = rt->nil;
+
+ /* Initialize tree */
+ rt->root = rt->nil;
+ rt->cmp = cmp;
+ rt->size = 0;
+
+ return rt;
+}
+
+/* Delete the whole tree (but not the data) */
+void aat_adelete ( aat_atree_t *tree )
+{
+ aat_anode_t *it = tree->root;
+ aat_anode_t *save;
+
+ /* Destruction by rotation */
+ while ( it != tree->nil ) {
+ if ( it->link[0] == tree->nil ) {
+ /* Remove node */
+ save = it->link[1];
+ free ( it );
+ }
+ else {
+ /* Rotate right */
+ save = it->link[0];
+ it->link[0] = save->link[1];
+ save->link[1] = it;
+ }
+
+ it = save;
+ }
+
+ /* Finalize destruction */
+ free ( tree->nil );
+ free ( tree );
+}
+
+/* Locate a entry based on the data's value */
+void *aat_afind ( aat_atree_t *tree, void *data )
+{
+ aat_anode_t *it = tree->root;
+
+ while ( it != tree->nil ) {
+ int cmp;
+ AAT_CMP(cmp, tree, it->data, data);
+
+ if ( cmp == 0 )
+ break;
+
+ it = it->link[cmp < 0];
+ }
+
+ /* nil->data == NULL */
+ return it->data;
+}
+
+/* Insert an entry based on the data's value. */
+/* Take a copy of the pointer to the entry. */
+/* Return 0 if malloc failed */
+int aat_ainsert ( aat_atree_t *tree, void *data )
+{
+ if ( tree->root == tree->nil ) {
+ /* Empty tree case */
+ tree->root = new_node ( tree, data );
+ if ( tree->root == tree->nil )
+ return 0;
+ }
+ else {
+ aat_anode_t *it = tree->root;
+ aat_anode_t *path[HEIGHT_LIMIT];
+ int top = 0, dir;
+
+ /* Find a spot and save the path */
+ for ( ; ; ) {
+ int cmp;
+
+ path[top++] = it;
+ AAT_CMP(cmp, tree, it->data, data);
+ dir = cmp < 0;
+
+ if ( it->link[dir] == tree->nil )
+ break;
+
+ it = it->link[dir];
+ }
+
+ /* Create a new item */
+ it->link[dir] = new_node ( tree, data );
+ if ( it->link[dir] == tree->nil )
+ return 0;
+
+ /* Walk back and rebalance */
+ while ( --top >= 0 ) {
+ /* Which child? */
+ if ( top != 0 )
+ dir = path[top - 1]->link[1] == path[top];
+
+ skew ( path[top] );
+ split ( path[top] );
+
+ /* Fix the parent */
+ if ( top != 0 )
+ path[top - 1]->link[dir] = path[top];
+ else
+ tree->root = path[top];
+ }
+ }
+
+ ++tree->size;
+
+ return 1;
+}
+
+/* Delete an given entry by locating it by */
+/* its value, then removing it from the tree. */
+/* The item itself isn't deleted. */
+/* Return 0 if the item wasn't found */
+int aat_aerase ( aat_atree_t *tree, void *data )
+{
+ if ( tree->root == tree->nil )
+ return 0;
+ else {
+ aat_anode_t *it = tree->root;
+ aat_anode_t *path[HEIGHT_LIMIT];
+ int top = 0, dir, cmp;
+
+ /* Find node to remove and save path */
+ for ( ; ; ) {
+ path[top++] = it;
+
+ if ( it == tree->nil )
+ return 0;
+
+ AAT_CMP(cmp, tree, it->data, data);
+ if ( cmp == 0 )
+ break;
+
+ dir = cmp < 0;
+ it = it->link[dir];
+ }
+
+ /* Remove the found node */
+ if ( it->link[0] == tree->nil
+ || it->link[1] == tree->nil )
+ {
+ /* Single child case */
+ int dir2 = it->link[0] == tree->nil;
+
+ /* Unlink the item */
+ if ( --top != 0 )
+ path[top - 1]->link[dir] = it->link[dir2];
+ else
+ tree->root = it->link[1];
+
+ free ( it );
+ }
+ else {
+ /* Two child case */
+ aat_anode_t *heir = it->link[1];
+ aat_anode_t *prev = it;
+
+ while ( heir->link[0] != tree->nil ) {
+ path[top++] = prev = heir;
+ heir = heir->link[0];
+ }
+
+ /*
+ Order is important!
+ (free item, replace item, free heir)
+ */
+ it->data = heir->data;
+ prev->link[prev == it] = heir->link[1];
+ free ( heir );
+ }
+
+ /* Walk back up and rebalance */
+ while ( --top >= 0 ) {
+ aat_anode_t *up = path[top];
+
+ if ( top != 0 )
+ dir = path[top - 1]->link[1] == up;
+
+ /* Rebalance (aka. black magic) */
+ if ( up->link[0]->level < up->level - 1
+ || up->link[1]->level < up->level - 1 )
+ {
+ if ( up->link[1]->level > --up->level )
+ up->link[1]->level = up->level;
+
+ /* Order is important! */
+ skew ( up );
+ skew ( up->link[1] );
+ skew ( up->link[1]->link[1] );
+ split ( up );
+ split ( up->link[1] );
+ }
+
+ /* Fix the parent */
+ if ( top != 0 )
+ path[top - 1]->link[dir] = up;
+ else
+ tree->root = up;
+ }
+ }
+
+ --tree->size;
+
+ return 1;
+}
+
+/* Return the current number of items */
+size_t aat_asize ( aat_atree_t *tree )
+{
+ return tree->size;
+}
+
+/* Return a traversal object */
+aat_atrav_t *aat_atnew ( void )
+{
+ return malloc ( sizeof ( aat_atrav_t ) );
+}
+
+/* Destroy a traversal object */
+void aat_atdelete ( aat_atrav_t *trav )
+{
+ free ( trav );
+}
+
+/*
+ First step in traversal,
+ handles min and max
+*/
+static void *start ( aat_atrav_t *trav,
+ aat_atree_t *tree, int dir )
+{
+ trav->tree = tree;
+ trav->it = tree->root;
+ trav->top = 0;
+
+ /* Build a path to work with */
+ if ( trav->it != tree->nil ) {
+ while ( trav->it->link[dir] != tree->nil ) {
+ trav->path[trav->top++] = trav->it;
+ trav->it = trav->it->link[dir];
+ }
+ }
+
+ /* Could be nil, but nil->data == NULL */
+ return trav->it->data;
+}
+
+/*
+ Subsequent traversal steps,
+ handles ascending and descending
+*/
+static void *move ( aat_atrav_t *trav, int dir )
+{
+ aat_anode_t *nil = trav->tree->nil;
+
+ if ( trav->it->link[dir] != nil ) {
+ /* Continue down this branch */
+ trav->path[trav->top++] = trav->it;
+ trav->it = trav->it->link[dir];
+
+ while ( trav->it->link[!dir] != nil ) {
+ trav->path[trav->top++] = trav->it;
+ trav->it = trav->it->link[!dir];
+ }
+ }
+ else {
+ /* Move to the next branch */
+ aat_anode_t *last;
+
+ do {
+ if ( trav->top == 0 ) {
+ trav->it = nil;
+ break;
+ }
+
+ last = trav->it;
+ trav->it = trav->path[--trav->top];
+ } while ( last == trav->it->link[dir] );
+ }
+
+ /* Could be nil, but nil->data == NULL */
+ return trav->it->data;
+}
+
+/* Return first item */
+void *aat_atfirst ( aat_atrav_t *trav, aat_atree_t *tree )
+{
+ return start ( trav, tree, 0 ); /* Min value */
+}
+
+/* Return last item */
+void *aat_atlast ( aat_atrav_t *trav, aat_atree_t *tree )
+{
+ return start ( trav, tree, 1 ); /* Max value */
+}
+
+/* Move to next */
+void *aat_atnext ( aat_atrav_t *trav )
+{
+ return move ( trav, 1 ); /* Toward larger items */
+}
+
+/* Move to previous */
+void *aat_atprev ( aat_atrav_t *trav )
+{
+ return move ( trav, 0 ); /* Toward smaller items */
+}
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