commit - da0a205ed60d81a85e1c71e0f31571337ba390a5
commit + 375b78fb110b7e1dd3686bc43aba38cf45c606e9
blob - /dev/null
blob + d118ffd16d3d776be746bfb5943cb2c3238eb9f0 (mode 644)
--- /dev/null
+++ include/avl.h
+/* #pragma lib "libavl.a" */
+/* #pragma src "/sys/src/libavl" */
+
+AUTOLIB(avl)
+
+typedef struct Avl Avl;
+typedef struct Avltree Avltree;
+typedef struct Avlwalk Avlwalk;
+
+/* #pragma incomplete Avltree */
+/* #pragma incomplete Avlwalk */
+
+struct Avl
+{
+ Avl *p; /* parent */
+ Avl *n[2]; /* children */
+ int bal; /* balance bits */
+};
+
+Avl *avlnext(Avlwalk *walk);
+Avl *avlprev(Avlwalk *walk);
+Avlwalk *avlwalk(Avltree *tree);
+void deleteavl(Avltree *tree, Avl *key, Avl **oldp);
+void endwalk(Avlwalk *walk);
+void insertavl(Avltree *tree, Avl *new, Avl **oldp);
+Avl *lookupavl(Avltree *tree, Avl *key);
+Avltree *mkavltree(int(*cmp)(Avl*, Avl*));
blob - /dev/null
blob + f87fd97cd456993173da185f2c819056c8e88748 (mode 644)
--- /dev/null
+++ man/man3/avl.3
+.TH AVL 3
+.SH NAME
+mkavltree, insertavl, lookupavl, deleteavl, avlwalk, avlnext, avlprev, endwalk - AVL tree routines
+.SH SYNOPSIS
+.\" .ta 0.75i 1.5i 2.25i 3i 3.75i 4.5i
+.ta 0.7i +0.7i +0.7i +0.7i +0.7i +0.7i +0.7i
+.EX
+#include <u.h>
+#include <libc.h>
+#include <avl.h>
+.sp 0.3v
+typedef struct Avl Avl;
+struct Avl
+{
+ Avl *p; /* parent */
+ Avl *n[2]; /* children */
+ int bal; /* balance bits */
+};
+.sp 0.3v
+Avl *avlnext(Avlwalk *walk);
+Avl *avlprev(Avlwalk *walk);
+Avlwalk *avlwalk(Avltree *tree);
+void deleteavl(Avltree *tree, Avl *key, Avl **oldp);
+void endwalk(Avlwalk *walk);
+void insertavl(Avltree *tree, Avl *new, Avl **oldp);
+Avl *lookupavl(Avltree *tree, Avl *key);
+Avltree *mkavltree(int(*cmp)(Avl*, Avl*));
+.EE
+.SH DESCRIPTION
+An AVL tree is a self-balancing binary search tree.
+These routines allow creation and maintenance of in-memory AVL trees.
+.PP
+An empty AVL tree is created by calling
+.I mkavltree
+with a comparison function as argument.
+This function should take two pointers to
+.B Avl
+objects and return -1, 0 or 1 as the first is
+respectively less than,
+equal to, or greater than,
+the second.
+.I Insertavl
+adds a
+.I new
+tree node into
+.IR tree .
+If
+.I oldp
+is non-nil upon return,
+it points to storage for an old node
+with the same key that may now be freed.
+.I Lookupavl
+returns the
+.I tree
+node that matches
+.I key
+by
+.IR tree 's
+comparison function,
+or
+.B nil
+if none.
+.I Deleteavl
+removes the node matching
+.I key
+from
+.IR tree ;
+.I oldp
+is handled as per
+.IR insertavl .
+.PP
+.I Avlwalk
+returns a pointer to a newly-allocated
+.B Avlwalk
+object.
+.I Endwalk
+frees such an object.
+.I Avlnext
+and
+.I avlprev
+walk the tree associated with
+.IR walk ,
+returning the next
+(respectively, previous)
+tree node in the comparison order
+defined by the comparison function
+associated with the tree associated with
+.IR walk .
+.SH EXAMPLES
+Intended usage seems to be to make an anonymous
+.B Avl
+the first member of the application's tree-node structure,
+then pass these routines tree-node pointers instead of
+.BR Avl* s.
+.IP
+.EX
+typedef struct Node {
+ Avl;
+ uchar score[VtScoreSize];
+ int type;
+} Node;
+.sp 0.3v
+Avltree *tree;
+Avl *res;
+Node *np;
+\fI\&...\fP
+ res = lookupavl(tree, np);
+.EE
+.SH SOURCE
+.B \*9/src/libavl
+.SH SEE ALSO
+G. M. Adelson-Velsky,
+E. M. Landis,
+``An algorithm for the organization of information'',
+.IR "Soviet Mathematics" ,
+Vol. 3, pp. 1256—1263.
+.SH DIAGNOSTICS
+Functions returning pointers return
+.B nil
+on error.
blob - /dev/null
blob + 2567c98dddde2166f41adf8d71071d1df0d07602 (mode 644)
--- /dev/null
+++ 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
+_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 = 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 Avl*
+_lookupavl(Avl *t, Avl *r, int (*cmp)(Avl*,Avl*))
+{
+ int i;
+ Avl *p;
+
+ p = nil;
+ while(t != nil){
+ assert(t->p == p);
+ if((i = cmp(r, t)) == 0)
+ return t;
+ p = t;
+ t = t->n[(i+1)/2];
+ }
+ return nil;
+}
+
+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=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);
+}
+
+Avl*
+lookupavl(Avltree *t, Avl *key)
+{
+ return _lookupavl(t->root, key, t->cmp);
+}
+
+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 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);
+}
blob - /dev/null
blob + 1970b186c8c95689f1a0bd25d18aba69fee47222 (mode 644)
--- /dev/null
+++ src/libavl/mkfile
+<$PLAN9/src/mkhdr
+
+LIB=libavl.a
+OFILES=\
+ avl.$O\
+
+HFILES=$PLAN9/include/avl.h
+
+<$PLAN9/src/mksyslib
