NAME
mkavltree, insertavl, lookupavl, deleteavl, avlwalk, avlnext, avlprev, endwalk – AVL tree routines

SYNOPSIS
#include <u.h>
#include <libc.h>
#include <avl.h>
typedef struct Avl Avl;
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);
Avl       *searchavl(Avltree *tree, Avl *key, int neighbor);
Avltree *mkavltree(int(*cmp)(Avl*, Avl*));

DESCRIPTION
An AVL tree is a self–balancing binary search tree. These routines allow creation and maintenance of in–memory AVL trees.

An empty AVL tree is created by calling mkavltree with a comparison function as argument. This function should take two pointers to Avl objects and return –1, 0 or 1 as the first is respectively less than, equal to, or greater than, the second. Insertavl adds a new tree node into tree. If oldp is non–nil upon return, it points to storage for an old node with the same key that may now be freed. Lookupavl returns the tree node that matches key by tree's comparison function, or nil if none.

Searchavl returns the tree node that matches key by tree's comparison function, if it exists. If it does not, and neighbor is positive, it returns the nearest node whose key is greater or nil if there is none and, if neighbor is negative, it returns the nearest node whose key is less or nil if there is none. It is an error to set neighbor to values other than –1, 0, or +1.

Deleteavl removes the node matching key from tree; oldp is handled as per insertavl.

Avlwalk returns a pointer to a newly–allocated Avlwalk object. Endwalk frees such an object. Avlnext and avlprev walk the tree associated with walk, returning the next (respectively, previous) tree node in the comparison order defined by the comparison function associated with the tree associated with walk.

EXAMPLES
Intended usage seems to be to make an anonymous Avl the first member of the application's tree–node structure, then pass these routines tree–node pointers instead of Avl*s.
typedef struct Node {
Avl;
uchar     score[VtScoreSize];
int       type;
} Node;
Avltree *tree;
Avl *res;
Node *np;
...
res = lookupavl(tree, np);

SOURCE
/sys/src/libavl

SEE ALSO
G. M. Adelson–Velsky, E. M. Landis, ``An algorithm for the organization of information'', Soviet Mathematics, Vol. 3, pp. 1256—1263.

DIAGNOSTICS
Functions returning pointers return nil on error.
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