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.\" Copyright (c) 1997 Todd C. Miller <Todd.Miller@courtesan.com>
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.\"	OpenBSD: tsearch.3,v 1.2 1998/06/21 22:13:49 millert Exp
.\" $FreeBSD: src/lib/libc/stdlib/tsearch.3,v 1.15 2006/06/23 13:36:33 keramida Exp $
.\"
.Dd June 15, 1997
.Dt TSEARCH 3
.Os
.Sh NAME
.Nm tdelete ,
.Nm tfind ,
.Nm tsearch ,
.Nm twalk
.Nd manipulate binary search trees
.Sh SYNOPSIS
.In search.h
.Ft void *
.Fo tdelete
.Fa "const void *restrict key"
.Fa "void **restrict rootp"
.Fa "int (*compar) (const void *key1, const void *key2)"
.Fc
.Ft void *
.Fo tfind
.Fa "const void *key"
.Fa "void *const *rootp"
.Fa "int (*compar) (const void *key1, const void *key2)"
.Fc
.Ft void *
.Fo tsearch
.Fa "const void *key"
.Fa "void **rootp"
.Fa "int (*compar) (const void *key1, const void *key2)"
.Fc
.Ft void
.Fo twalk
.Fa "const void *root"
.Fa "void (*action) (const void *node, VISIT order, int level)"
.Fc
.Sh DESCRIPTION
The
.Fn tdelete ,
.Fn tfind ,
.Fn tsearch ,
and
.Fn twalk
functions manage binary search trees, based on algorithms T and D
from Knuth (6.2.2).
The comparison function passed in by
the user takes two arguments, each of which is a key
pointer.
This function has the same style of return values as
.Xr strcmp 3 .
.Pp
The
.Fn tfind
function
searches for a node whose key matches the argument
.Fa key
in the binary tree rooted at
.Fa rootp ,
returning a pointer to the node if it is found and NULL
if it is not.
.Pp
Note that a node is itself a pointer to the key of the node.
Thus, you should generally cast this result to a
double pointer to the data type stored in the tree, for example
(struct myType **), and use double indirection to retrieve the
original key value.
.Pp
The
.Fn tsearch
function is identical to
.Fn tfind
except that, if no match is found,
it inserts a new node for the
.Fa key
into the tree and returns a pointer to the node.
If
.Fa rootp
points to a NULL value, a new binary search tree is created.
.Pp
The
.Fn tdelete
function deletes a node from the specified binary search tree
and returns a pointer to the parent of the node that was deleted.
It takes the same arguments as
.Fn tfind
and
.Fn tsearch .
If the node to be deleted is the root of the binary search tree,
.Fa rootp
will be adjusted.
.Pp
The
.Fn twalk
function walks the binary search tree rooted in
.Fa root
and calls the function
.Fa action
on each node.
The
.Fa action
function is called with three arguments: a pointer to the current node,
a value from the enum
.Sy "typedef enum { preorder, postorder, endorder, leaf } VISIT;"
specifying the traversal type, and a node level (where level
zero is the root of the tree).
.Pp
As
.Fn twalk
traverses the tree, it calls the
.Fa action
function with the traversal type "preorder"
before visiting the left subtree of the
.Fa node ,
with the
traversal type "postorder" before visiting the right subtree
of the
.Fa node ,
and with the traversal type "endorder" after
visiting the right subtree of the
.Fa node .
.Pp.
The
.Fa action
function is called only once for a leaf-node, with the
traversal type "leaf."
.Pp
Note: the names for the traversal types differ somewhat from
common parlance.  The traversal type "postorder" corresponds
to what would typically be referred to as in-order, and the
traversal type "endorder" corresponds to what would typically
be referred to as post-order.
.Sh RETURN VALUES
The
.Fn tsearch
function returns NULL if allocation of a new node fails (usually
due to a lack of free memory).
.Pp
The
.Fn tfind ,
.Fn tsearch ,
and
.Fn tdelete
functions
return NULL if
.Fa rootp
is NULL or the node cannot be found.
.Pp
The
.Fn twalk
function returns no value.
.Sh SEE ALSO
.Xr bsearch 3 ,
.Xr hsearch 3 ,
.Xr lsearch 3