ref: 9f50ee06f3a78af3767ec061f4647b5446c8619e
dir: /sys/src/libavl/avl.c/
#include <u.h>
#include <libc.h>
#include <bio.h>
#include <avl.h>
/*
* In-memory database stored as self-balancing AVL tree.
* See Lewis & Denenberg, Data Structures and Their Algorithms.
*/
static void
singleleft(Avl **tp, Avl *p)
{
int l, r2;
Avl *a, *c;
a = *tp;
c = a->n[1];
r2 = c->bal;
l = (r2 > 0? r2: 0)+1 - a->bal;
if((a->n[1] = c->n[0]) != nil)
a->n[1]->p = a;
if((c->n[0] = a) != nil)
c->n[0]->p = c;
if((*tp = c) != nil)
(*tp)->p = p;
a->bal = -l;
c->bal = r2 - ((l > 0? l: 0)+1);
}
static void
singleright(Avl **tp, Avl *p)
{
int l2, r;
Avl *a, *c;
a = *tp;
c = a->n[0];
l2 = - c->bal;
r = a->bal + ((l2 > 0? l2: 0)+1);
if((a->n[0] = c->n[1]) != nil)
a->n[0]->p = a;
if((c->n[1] = a) != nil)
c->n[1]->p = c;
if((*tp = c) != nil)
(*tp)->p = p;
a->bal = r;
c->bal = ((r > 0? r: 0)+1) - l2;
}
static void
doublerightleft(Avl **tp, Avl *p)
{
singleright(&(*tp)->n[1], *tp);
singleleft(tp, p);
}
static void
doubleleftright(Avl **tp, Avl *p)
{
singleleft(&(*tp)->n[0], *tp);
singleright(tp, p);
}
static void
balance(Avl **tp, Avl *p)
{
switch((*tp)->bal){
case -2:
if((*tp)->n[0]->bal <= 0)
singleright(tp, p);
else if((*tp)->n[0]->bal == 1)
doubleleftright(tp, p);
else
assert(0);
break;
case 2:
if((*tp)->n[1]->bal >= 0)
singleleft(tp, p);
else if((*tp)->n[1]->bal == -1)
doublerightleft(tp, p);
else
assert(0);
break;
}
}
static int
canoncmp(int cmp)
{
if(cmp < 0)
return -1;
else if(cmp > 0)
return 1;
return 0;
}
static int
_insertavl(Avl **tp, Avl *p, Avl *r, int (*cmp)(Avl*,Avl*), Avl **rfree)
{
int i, ob;
if(*tp == nil){
r->bal = 0;
r->n[0] = nil;
r->n[1] = nil;
r->p = p;
*tp = r;
return 1;
}
ob = (*tp)->bal;
if((i = canoncmp(cmp(r, *tp))) != 0){
(*tp)->bal += i * _insertavl(&(*tp)->n[(i+1)/2], *tp, r, cmp,
rfree);
balance(tp, p);
return ob == 0 && (*tp)->bal != 0;
}
/* install new entry */
*rfree = *tp; /* save old node for freeing */
*tp = r; /* insert new node */
**tp = **rfree; /* copy old node's Avl contents */
if(r->n[0]) /* fix node's children's parent pointers */
r->n[0]->p = r;
if(r->n[1])
r->n[1]->p = r;
return 0;
}
static int
successor(Avl **tp, Avl *p, Avl **r)
{
int ob;
if((*tp)->n[0] == nil){
*r = *tp;
*tp = (*r)->n[1];
if(*tp)
(*tp)->p = p;
return -1;
}
ob = (*tp)->bal;
(*tp)->bal -= successor(&(*tp)->n[0], *tp, r);
balance(tp, p);
return -(ob != 0 && (*tp)->bal == 0);
}
static int
_deleteavl(Avl **tp, Avl *p, Avl *rx, int(*cmp)(Avl*,Avl*), Avl **del,
void (*predel)(Avl*, void*), void *arg)
{
int i, ob;
Avl *r, *or;
if(*tp == nil)
return 0;
ob = (*tp)->bal;
if((i=canoncmp(cmp(rx, *tp))) != 0){
(*tp)->bal += i * _deleteavl(&(*tp)->n[(i+1)/2], *tp, rx, cmp,
del, predel, arg);
balance(tp, p);
return -(ob != 0 && (*tp)->bal == 0);
}
if(predel)
(*predel)(*tp, arg);
or = *tp;
if(or->n[i=0] == nil || or->n[i=1] == nil){
*tp = or->n[1-i];
if(*tp)
(*tp)->p = p;
*del = or;
return -1;
}
/* deleting node with two kids, find successor */
or->bal += successor(&or->n[1], or, &r);
r->bal = or->bal;
r->n[0] = or->n[0];
r->n[1] = or->n[1];
*tp = r;
(*tp)->p = p;
/* node has changed; fix children's parent pointers */
if(r->n[0])
r->n[0]->p = r;
if(r->n[1])
r->n[1]->p = r;
*del = or;
balance(tp, p);
return -(ob != 0 && (*tp)->bal == 0);
}
static void
checkparents(Avl *a, Avl *p)
{
if(a == nil)
return;
if(a->p != p)
print("bad parent\n");
checkparents(a->n[0], a);
checkparents(a->n[1], a);
}
struct Avltree
{
Avl *root;
int (*cmp)(Avl*, Avl*);
Avlwalk *walks;
};
struct Avlwalk
{
int started;
int moved;
Avlwalk *next;
Avltree *tree;
Avl *node;
};
Avltree*
mkavltree(int (*cmp)(Avl*, Avl*))
{
Avltree *t;
t = malloc(sizeof *t);
if(t == nil)
return nil;
memset(t, 0, sizeof *t);
t->cmp = cmp;
return t;
}
void
insertavl(Avltree *t, Avl *new, Avl **oldp)
{
*oldp = nil;
_insertavl(&t->root, nil, new, t->cmp, oldp);
}
static Avl*
findpredecessor(Avl *a)
{
if(a == nil)
return nil;
if(a->n[0] != nil){
/* predecessor is rightmost descendant of left child */
for(a = a->n[0]; a->n[1]; a = a->n[1])
;
return a;
}else{
/* we're at a leaf, successor is a parent we enter from the right */
while(a->p && a->p->n[0] == a)
a = a->p;
return a->p;
}
}
static Avl*
findsuccessor(Avl *a)
{
if(a == nil)
return nil;
if(a->n[1] != nil){
/* successor is leftmost descendant of right child */
for(a = a->n[1]; a->n[0]; a = a->n[0])
;
return a;
}else{
/* we're at a leaf, successor is a parent we enter from the left going up */
while(a->p && a->p->n[1] == a)
a = a->p;
return a->p;
}
}
static Avl*
_lookupavl(Avl *t, Avl *r, int (*cmp)(Avl*,Avl*), int neighbor)
{
int i;
Avl *p;
p = nil;
if(t == nil)
return nil;
do{
assert(t->p == p);
if((i = canoncmp(cmp(r, t))) == 0)
return t;
p = t;
t = t->n[(i+1)/2];
}while(t);
if(neighbor == 0)
return nil;
if(neighbor < 0)
return i > 0 ? p : findpredecessor(p);
return i < 0 ? p : findsuccessor(p);
}
Avl*
searchavl(Avltree *t, Avl *key, int neighbor)
{
return _lookupavl(t->root, key, t->cmp, neighbor);
}
Avl*
lookupavl(Avltree *t, Avl *key)
{
return _lookupavl(t->root, key, t->cmp, 0);
}
static void
walkdel(Avl *a, void *v)
{
Avl *p;
Avlwalk *w;
Avltree *t;
if(a == nil)
return;
p = findpredecessor(a);
t = v;
for(w = t->walks; w; w = w->next){
if(w->node == a){
/* back pointer to predecessor; not perfect but adequate */
w->moved = 1;
w->node = p;
if(p == nil)
w->started = 0;
}
}
}
void
deleteavl(Avltree *t, Avl *key, Avl **oldp)
{
*oldp = nil;
_deleteavl(&t->root, nil, key, t->cmp, oldp, walkdel, t);
}
Avlwalk*
avlwalk(Avltree *t)
{
Avlwalk *w;
w = malloc(sizeof *w);
if(w == nil)
return nil;
memset(w, 0, sizeof *w);
w->tree = t;
w->next = t->walks;
t->walks = w;
return w;
}
Avl*
avlnext(Avlwalk *w)
{
Avl *a;
if(w->started==0){
for(a = w->tree->root; a && a->n[0]; a = a->n[0])
;
w->node = a;
w->started = 1;
}else{
a = findsuccessor(w->node);
if(a == w->node)
abort();
w->node = a;
}
return w->node;
}
Avl*
avlprev(Avlwalk *w)
{
Avl *a;
if(w->started == 0){
for(a = w->tree->root; a && a->n[1]; a = a->n[1])
;
w->node = a;
w->started = 1;
}else if(w->moved){
w->moved = 0;
return w->node;
}else{
a = findpredecessor(w->node);
if(a == w->node)
abort();
w->node = a;
}
return w->node;
}
void
endwalk(Avlwalk *w)
{
Avltree *t;
Avlwalk **l;
t = w->tree;
for(l = &t->walks; *l; l = &(*l)->next){
if(*l == w){
*l = w->next;
break;
}
}
free(w);
}
static void
walkavl(Avl *t, void (*f)(Avl*, void*), void *v)
{
if(t == nil)
return;
walkavl(t->n[0], f, v);
f(t, v);
walkavl(t->n[1], f, v);
}