stdlib: Remove use of mergesort on qsort (BZ 21719)

[glibc.git] / manual / search.texi

@node Searching and Sorting, Pattern Matching, Message Translation, Top
@c %MENU% General searching and sorting functions
@chapter Searching and Sorting

This chapter describes functions for searching and sorting arrays of
arbitrary objects.  You pass the appropriate comparison function to be
applied as an argument, along with the size of the objects in the array
and the total number of elements.

@menu
* Comparison Functions::        Defining how to compare two objects.
                                 Since the sort and search facilities
                                 are general, you have to specify the
                                 ordering.
* Array Search Function::       The @code{bsearch} function.
* Array Sort Function::         The @code{qsort} function.
* Search/Sort Example::         An example program.
* Hash Search Function::        The @code{hsearch} function.
* Tree Search Function::        The @code{tsearch} function.
@end menu

@node Comparison Functions
@section Defining the Comparison Function
@cindex Comparison Function

In order to use the sorted array library functions, you have to describe
how to compare the elements of the array.

To do this, you supply a comparison function to compare two elements of
the array.  The library will call this function, passing as arguments
pointers to two array elements to be compared.  Your comparison function
should return a value the way @code{strcmp} (@pxref{String/Array
Comparison}) does: negative if the first argument is ``less'' than the
second, zero if they are ``equal'', and positive if the first argument
is ``greater''.

Here is an example of a comparison function which works with an array of
numbers of type @code{double}:

@smallexample
int
compare_doubles (const void *a, const void *b)
@{
  const double *da = (const double *) a;
  const double *db = (const double *) b;

  return (*da > *db) - (*da < *db);
@}
@end smallexample

The header file @file{stdlib.h} defines a name for the data type of
comparison functions.  This type is a GNU extension.

@comment stdlib.h
@comment GNU
@tindex comparison_fn_t
@smallexample
int comparison_fn_t (const void *, const void *);
@end smallexample

@node Array Search Function
@section Array Search Function
@cindex search function (for arrays)
@cindex binary search function (for arrays)
@cindex array search function

Generally searching for a specific element in an array means that
potentially all elements must be checked.  @Theglibc{} contains
functions to perform linear search.  The prototypes for the following
two functions can be found in @file{search.h}.

@deftypefun {void *} lfind (const void *@var{key}, const void *@var{base}, size_t *@var{nmemb}, size_t @var{size}, comparison_fn_t @var{compar})
@standards{SVID, search.h}
@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{lfind} function searches in the array with @code{*@var{nmemb}}
elements of @var{size} bytes pointed to by @var{base} for an element
which matches the one pointed to by @var{key}.  The function pointed to
by @var{compar} is used to decide whether two elements match.

The return value is a pointer to the matching element in the array
starting at @var{base} if it is found.  If no matching element is
available @code{NULL} is returned.

The mean runtime of this function is @code{*@var{nmemb}}/2.  This
function should only be used if elements often get added to or deleted from
the array in which case it might not be useful to sort the array before
searching.
@end deftypefun

@deftypefun {void *} lsearch (const void *@var{key}, void *@var{base}, size_t *@var{nmemb}, size_t @var{size}, comparison_fn_t @var{compar})
@standards{SVID, search.h}
@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
@c A signal handler that interrupted an insertion and performed an
@c insertion itself would leave the array in a corrupt state (e.g. one
@c new element initialized twice, with parts of both initializations
@c prevailing, and another uninitialized element), but this is just a
@c special case of races on user-controlled objects, that have to be
@c avoided by users.

@c In case of cancellation, we know the array won't be left in a corrupt
@c state; the new element is initialized before the element count is
@c incremented, and the compiler can't reorder these operations because
@c it can't know that they don't alias.  So, we'll either cancel after
@c the increment and the initialization are both complete, or the
@c increment won't have taken place, and so how far the initialization
@c got doesn't matter.
The @code{lsearch} function is similar to the @code{lfind} function.  It
searches the given array for an element and returns it if found.  The
difference is that if no matching element is found the @code{lsearch}
function adds the object pointed to by @var{key} (with a size of
@var{size} bytes) at the end of the array and it increments the value of
@code{*@var{nmemb}} to reflect this addition.

This means for the caller that if it is not sure that the array contains
the element one is searching for the memory allocated for the array
starting at @var{base} must have room for at least @var{size} more
bytes.  If one is sure the element is in the array it is better to use
@code{lfind} so having more room in the array is always necessary when
calling @code{lsearch}.
@end deftypefun

To search a sorted array for an element matching the key, use the
@code{bsearch} function.  The prototype for this function is in
the header file @file{stdlib.h}.
@pindex stdlib.h

@deftypefun {void *} bsearch (const void *@var{key}, const void *@var{array}, size_t @var{count}, size_t @var{size}, comparison_fn_t @var{compare})
@standards{ISO, stdlib.h}
@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{bsearch} function searches the sorted array @var{array} for an object
that is equivalent to @var{key}.  The array contains @var{count} elements,
each of which is of size @var{size} bytes.

The @var{compare} function is used to perform the comparison.  This
function is called with two pointer arguments and should return an
integer less than, equal to, or greater than zero corresponding to
whether its first argument is considered less than, equal to, or greater
than its second argument.  The elements of the @var{array} must already
be sorted in ascending order according to this comparison function.

The return value is a pointer to the matching array element, or a null
pointer if no match is found.  If the array contains more than one element
that matches, the one that is returned is unspecified.

This function derives its name from the fact that it is implemented
using the binary search algorithm.
@end deftypefun

@node Array Sort Function
@section Array Sort Function
@cindex sort function (for arrays)
@cindex quick sort function (for arrays)
@cindex array sort function

To sort an array using an arbitrary comparison function, use the
@code{qsort} function.  The prototype for this function is in
@file{stdlib.h}.
@pindex stdlib.h

@deftypefun void qsort (void *@var{array}, size_t @var{count}, size_t @var{size}, comparison_fn_t @var{compare})
@standards{ISO, stdlib.h}
@safety{@prelim{}@mtsafe{}@assafe{}@acsafe{}}
The @code{qsort} function sorts the array @var{array}.  The array
contains @var{count} elements, each of which is of size @var{size}.

The @var{compare} function is used to perform the comparison on the
array elements.  This function is called with two pointer arguments and
should return an integer less than, equal to, or greater than zero
corresponding to whether its first argument is considered less than,
equal to, or greater than its second argument.

@cindex stable sorting
@strong{Warning:} If two objects compare as equal, their order after
sorting is unpredictable.  That is to say, the sorting is not stable.
This can make a difference when the comparison considers only part of
the elements.  Two elements with the same sort key may differ in other
respects.

Although the object addresses passed to the comparison function lie
within the array, they need not correspond with the original locations
of those objects because the sorting algorithm may swap around objects
in the array before making some comparisons.  The only way to perform
a stable sort with @code{qsort} is to first augment the objects with a
monotonic counter of some kind.

Here is a simple example of sorting an array of doubles in numerical
order, using the comparison function defined above (@pxref{Comparison
Functions}):

@smallexample
@{
  double *array;
  int size;
  @dots{}
  qsort (array, size, sizeof (double), compare_doubles);
@}
@end smallexample

The @code{qsort} function derives its name from the fact that it was
originally implemented using the ``quick sort'' algorithm.

The implementation of @code{qsort} in this library is an in-place sort
and uses a constant extra space (allocated on the stack).
@end deftypefun

@node Search/Sort Example
@section Searching and Sorting Example

Here is an example showing the use of @code{qsort} and @code{bsearch}
with an array of structures.  The objects in the array are sorted
by comparing their @code{name} fields with the @code{strcmp} function.
Then, we can look up individual objects based on their names.

@comment This example is dedicated to the memory of Jim Henson.  RIP.
@smallexample
@include search.c.texi
@end smallexample

@cindex Kermit the frog
The output from this program looks like:

@smallexample
Kermit, the frog
Piggy, the pig
Gonzo, the whatever
Fozzie, the bear
Sam, the eagle
Robin, the frog
Animal, the animal
Camilla, the chicken
Sweetums, the monster
Dr. Strangepork, the pig
Link Hogthrob, the pig
Zoot, the human
Dr. Bunsen Honeydew, the human
Beaker, the human
Swedish Chef, the human

Animal, the animal
Beaker, the human
Camilla, the chicken
Dr. Bunsen Honeydew, the human
Dr. Strangepork, the pig
Fozzie, the bear
Gonzo, the whatever
Kermit, the frog
Link Hogthrob, the pig
Piggy, the pig
Robin, the frog
Sam, the eagle
Swedish Chef, the human
Sweetums, the monster
Zoot, the human

Kermit, the frog
Gonzo, the whatever
Couldn't find Janice.
@end smallexample


@node Hash Search Function
@section The @code{hsearch} function.

The functions mentioned so far in this chapter are for searching in a sorted
or unsorted array.  There are other methods to organize information
which later should be searched.  The costs of insert, delete and search
differ.  One possible implementation is using hashing tables.
The following functions are declared in the header file @file{search.h}.

@deftypefun int hcreate (size_t @var{nel})
@standards{SVID, search.h}
@safety{@prelim{}@mtunsafe{@mtasurace{:hsearch}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}}
@c hcreate @mtasurace:hsearch @ascuheap @acucorrupt @acsmem
@c  hcreate_r dup @mtsrace:htab @ascuheap @acucorrupt @acsmem
The @code{hcreate} function creates a hashing table which can contain at
least @var{nel} elements.  There is no possibility to grow this table so
it is necessary to choose the value for @var{nel} wisely.  The method
used to implement this function might make it necessary to make the
number of elements in the hashing table larger than the expected maximal
number of elements.  Hashing tables usually work inefficiently if they are
filled 80% or more.  The constant access time guaranteed by hashing can
only be achieved if few collisions exist.  See Knuth's ``The Art of
Computer Programming, Part 3: Searching and Sorting'' for more
information.

The weakest aspect of this function is that there can be at most one
hashing table used through the whole program.  The table is allocated
in local memory out of control of the programmer.  As an extension @theglibc{}
provides an additional set of functions with a reentrant
interface which provides a similar interface but which allows keeping
arbitrarily many hashing tables.

It is possible to use more than one hashing table in the program run if
the former table is first destroyed by a call to @code{hdestroy}.

The function returns a non-zero value if successful.  If it returns zero,
something went wrong.  This could either mean there is already a hashing
table in use or the program ran out of memory.
@end deftypefun

@deftypefun void hdestroy (void)
@standards{SVID, search.h}
@safety{@prelim{}@mtunsafe{@mtasurace{:hsearch}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}}
@c hdestroy @mtasurace:hsearch @ascuheap @acucorrupt @acsmem
@c  hdestroy_r dup @mtsrace:htab @ascuheap @acucorrupt @acsmem
The @code{hdestroy} function can be used to free all the resources
allocated in a previous call of @code{hcreate}.  After a call to this
function it is again possible to call @code{hcreate} and allocate a new
table with possibly different size.

It is important to remember that the elements contained in the hashing
table at the time @code{hdestroy} is called are @emph{not} freed by this
function.  It is the responsibility of the program code to free those
strings (if necessary at all).  Freeing all the element memory is not
possible without extra, separately kept information since there is no
function to iterate through all available elements in the hashing table.
If it is really necessary to free a table and all elements the
programmer has to keep a list of all table elements and before calling
@code{hdestroy} s/he has to free all element's data using this list.
This is a very unpleasant mechanism and it also shows that this kind of
hashing table is mainly meant for tables which are created once and
used until the end of the program run.
@end deftypefun

Entries of the hashing table and keys for the search are defined using
this type:

@deftp {Data type} ENTRY
@table @code
@item char *key
Pointer to a zero-terminated string of characters describing the key for
the search or the element in the hashing table.

This is a limiting restriction of the functionality of the
@code{hsearch} functions: They can only be used for data sets which
use the NUL character always and solely to terminate keys.  It is not
possible to handle general binary data for keys.

@item void *data
Generic pointer for use by the application.  The hashing table
implementation preserves this pointer in entries, but does not use it
in any way otherwise.
@end table
@end deftp

@deftp {Data type} {struct entry}
The underlying type of @code{ENTRY}.
@end deftp

@deftypefun {ENTRY *} hsearch (ENTRY @var{item}, ACTION @var{action})
@standards{SVID, search.h}
@safety{@prelim{}@mtunsafe{@mtasurace{:hsearch}}@asunsafe{}@acunsafe{@acucorrupt{/action==ENTER}}}
@c hsearch @mtasurace:hsearch @acucorrupt/action==ENTER
@c  hsearch_r dup @mtsrace:htab @acucorrupt/action==ENTER
To search in a hashing table created using @code{hcreate} the
@code{hsearch} function must be used.  This function can perform a simple
search for an element (if @var{action} has the value @code{FIND}) or it can
alternatively insert the key element into the hashing table.  Entries
are never replaced.

The key is denoted by a pointer to an object of type @code{ENTRY}.  For
locating the corresponding position in the hashing table only the
@code{key} element of the structure is used.

If an entry with a matching key is found the @var{action} parameter is
irrelevant.  The found entry is returned.  If no matching entry is found
and the @var{action} parameter has the value @code{FIND} the function
returns a @code{NULL} pointer.  If no entry is found and the
@var{action} parameter has the value @code{ENTER} a new entry is added
to the hashing table which is initialized with the parameter @var{item}.
A pointer to the newly added entry is returned.
@end deftypefun

As mentioned before, the hashing table used by the functions described so
far is global and there can be at any time at most one hashing table in
the program.  A solution is to use the following functions which are a
GNU extension.  All have in common that they operate on a hashing table
which is described by the content of an object of the type @code{struct
hsearch_data}.  This type should be treated as opaque, none of its
members should be changed directly.

@deftypefun int hcreate_r (size_t @var{nel}, struct hsearch_data *@var{htab})
@standards{GNU, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:htab}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}}
@c Unlike the lsearch array, the htab is (at least in part) opaque, so
@c let's make it absolutely clear that ensuring exclusive access is a
@c caller responsibility.

@c Cancellation is unlikely to leave the htab in a corrupt state: the
@c last field to be initialized is the one that tells whether the entire
@c data structure was initialized, and there's a function call (calloc)
@c in between that will often ensure all other fields are written before
@c the table.  However, should this call be inlined (say with LTO), this
@c assumption may not hold.  The calloc call doesn't cross our library
@c interface barrier, so let's consider this could happen and mark this
@c with @acucorrupt.  It's no safety loss, since we already have
@c @ascuheap anyway...

@c hcreate_r @mtsrace:htab @ascuheap @acucorrupt @acsmem
@c  isprime ok
@c  calloc dup @ascuheap @acsmem
The @code{hcreate_r} function initializes the object pointed to by
@var{htab} to contain a hashing table with at least @var{nel} elements.
So this function is equivalent to the @code{hcreate} function except
that the initialized data structure is controlled by the user.

This allows having more than one hashing table at one time.  The memory
necessary for the @code{struct hsearch_data} object can be allocated
dynamically.  It must be initialized with zero before calling this
function.

The return value is non-zero if the operation was successful.  If the
return value is zero, something went wrong, which probably means the
program ran out of memory.
@end deftypefun

@deftypefun void hdestroy_r (struct hsearch_data *@var{htab})
@standards{GNU, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:htab}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}}
@c The table is released while the table pointer still points to it.
@c Async cancellation is thus unsafe, but it already was because we call
@c free().  Using the table in a handler while it's being released would
@c also be dangerous, but calling free() already makes it unsafe, and
@c the requirement on the caller to ensure exclusive access already
@c guarantees this doesn't happen, so we don't get @asucorrupt.

@c hdestroy_r @mtsrace:htab @ascuheap @acucorrupt @acsmem
@c  free dup @ascuheap @acsmem
The @code{hdestroy_r} function frees all resources allocated by the
@code{hcreate_r} function for this very same object @var{htab}.  As for
@code{hdestroy} it is the program's responsibility to free the strings
for the elements of the table.
@end deftypefun

@deftypefun int hsearch_r (ENTRY @var{item}, ACTION @var{action}, ENTRY **@var{retval}, struct hsearch_data *@var{htab})
@standards{GNU, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:htab}}@assafe{}@acunsafe{@acucorrupt{/action==ENTER}}}
@c Callers have to ensure mutual exclusion; insertion, if cancelled,
@c leaves the table in a corrupt state.

@c hsearch_r @mtsrace:htab @acucorrupt/action==ENTER
@c  strlen dup ok
@c  strcmp dup ok
The @code{hsearch_r} function is equivalent to @code{hsearch}.  The
meaning of the first two arguments is identical.  But instead of
operating on a single global hashing table the function works on the
table described by the object pointed to by @var{htab} (which is
initialized by a call to @code{hcreate_r}).

Another difference to @code{hcreate} is that the pointer to the found
entry in the table is not the return value of the function.  It is
returned by storing it in a pointer variable pointed to by the
@var{retval} parameter.  The return value of the function is an integer
value indicating success if it is non-zero and failure if it is zero.
In the latter case the global variable @code{errno} signals the reason for
the failure.

@table @code
@item ENOMEM
The table is filled and @code{hsearch_r} was called with a so far
unknown key and @var{action} set to @code{ENTER}.
@item ESRCH
The @var{action} parameter is @code{FIND} and no corresponding element
is found in the table.
@end table
@end deftypefun


@node Tree Search Function
@section The @code{tsearch} function.

Another common form to organize data for efficient search is to use
trees.  The @code{tsearch} function family provides a nice interface to
functions to organize possibly large amounts of data by providing a mean
access time proportional to the logarithm of the number of elements.
@Theglibc{} implementation even guarantees that this bound is
never exceeded even for input data which cause problems for simple
binary tree implementations.

The functions described in the chapter are all described in the @w{System
V} and X/Open specifications and are therefore quite portable.

In contrast to the @code{hsearch} functions the @code{tsearch} functions
can be used with arbitrary data and not only zero-terminated strings.

The @code{tsearch} functions have the advantage that no function to
initialize data structures is necessary.  A simple pointer of type
@code{void *} initialized to @code{NULL} is a valid tree and can be
extended or searched.  The prototypes for these functions can be found
in the header file @file{search.h}.

@deftypefun {void *} tsearch (const void *@var{key}, void **@var{rootp}, comparison_fn_t @var{compar})
@standards{SVID, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:rootp}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}}
@c The tree is not modified in a thread-safe manner, and rotations may
@c leave the tree in an inconsistent state that could be observed in an
@c asynchronous signal handler (except for the caller-synchronization
@c requirement) or after asynchronous cancellation of the thread
@c performing the rotation or the insertion.
The @code{tsearch} function searches in the tree pointed to by
@code{*@var{rootp}} for an element matching @var{key}.  The function
pointed to by @var{compar} is used to determine whether two elements
match.  @xref{Comparison Functions}, for a specification of the functions
which can be used for the @var{compar} parameter.

If the tree does not contain a matching entry the @var{key} value will
be added to the tree.  @code{tsearch} does not make a copy of the object
pointed to by @var{key} (how could it since the size is unknown).
Instead it adds a reference to this object which means the object must
be available as long as the tree data structure is used.

The tree is represented by a pointer to a pointer since it is sometimes
necessary to change the root node of the tree.  So it must not be
assumed that the variable pointed to by @var{rootp} has the same value
after the call.  This also shows that it is not safe to call the
@code{tsearch} function more than once at the same time using the same
tree.  It is no problem to run it more than once at a time on different
trees.

The return value is a pointer to the matching element in the tree.  If a
new element was created the pointer points to the new data (which is in
fact @var{key}).  If an entry had to be created and the program ran out
of space @code{NULL} is returned.
@end deftypefun

@deftypefun {void *} tfind (const void *@var{key}, void *const *@var{rootp}, comparison_fn_t @var{compar})
@standards{SVID, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:rootp}}@assafe{}@acsafe{}}
The @code{tfind} function is similar to the @code{tsearch} function.  It
locates an element matching the one pointed to by @var{key} and returns
a pointer to this element.  But if no matching element is available no
new element is entered (note that the @var{rootp} parameter points to a
constant pointer).  Instead the function returns @code{NULL}.
@end deftypefun

Another advantage of the @code{tsearch} functions in contrast to the
@code{hsearch} functions is that there is an easy way to remove
elements.

@deftypefun {void *} tdelete (const void *@var{key}, void **@var{rootp}, comparison_fn_t @var{compar})
@standards{SVID, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:rootp}}@asunsafe{@ascuheap{}}@acunsafe{@acucorrupt{} @acsmem{}}}
To remove a specific element matching @var{key} from the tree
@code{tdelete} can be used.  It locates the matching element using the
same method as @code{tfind}.  The corresponding element is then removed
and a pointer to the parent of the deleted node is returned by the
function.  If there is no matching entry in the tree nothing can be
deleted and the function returns @code{NULL}.  If the root of the tree
is deleted @code{tdelete} returns some unspecified value not equal to
@code{NULL}.
@end deftypefun

@deftypefun void tdestroy (void *@var{vroot}, __free_fn_t @var{freefct})
@standards{GNU, search.h}
@safety{@prelim{}@mtsafe{}@asunsafe{@ascuheap{}}@acunsafe{@acsmem{}}}
If the complete search tree has to be removed one can use
@code{tdestroy}.  It frees all resources allocated by the @code{tsearch}
functions to generate the tree pointed to by @var{vroot}.

For the data in each tree node the function @var{freefct} is called.
The pointer to the data is passed as the argument to the function.  If
no such work is necessary @var{freefct} must point to a function doing
nothing.  It is called in any case.

This function is a GNU extension and not covered by the @w{System V} or
X/Open specifications.
@end deftypefun

In addition to the functions to create and destroy the tree data
structure, there is another function which allows you to apply a
function to all elements of the tree.  The function must have this type:

@smallexample
void __action_fn_t (const void *nodep, VISIT value, int level);
@end smallexample

The @var{nodep} is the data value of the current node (once given as the
@var{key} argument to @code{tsearch}).  @var{level} is a numeric value
which corresponds to the depth of the current node in the tree.  The
root node has the depth @math{0} and its children have a depth of
@math{1} and so on.  The @code{VISIT} type is an enumeration type.

@deftp {Data Type} VISIT
The @code{VISIT} value indicates the status of the current node in the
tree and how the function is called.  The status of a node is either
`leaf' or `internal node'.  For each leaf node the function is called
exactly once, for each internal node it is called three times: before
the first child is processed, after the first child is processed and
after both children are processed.  This makes it possible to handle all
three methods of tree traversal (or even a combination of them).

@vtable @code
@item preorder
The current node is an internal node and the function is called before
the first child was processed.
@item postorder
The current node is an internal node and the function is called after
the first child was processed.
@item endorder
The current node is an internal node and the function is called after
the second child was processed.
@item leaf
The current node is a leaf.
@end vtable
@end deftp

@deftypefun void twalk (const void *@var{root}, __action_fn_t @var{action})
@standards{SVID, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:root}}@assafe{}@acsafe{}}
For each node in the tree with a node pointed to by @var{root}, the
@code{twalk} function calls the function provided by the parameter
@var{action}.  For leaf nodes the function is called exactly once with
@var{value} set to @code{leaf}.  For internal nodes the function is
called three times, setting the @var{value} parameter or @var{action} to
the appropriate value.  The @var{level} argument for the @var{action}
function is computed while descending the tree by increasing the value
by one for each descent to a child, starting with the value @math{0} for
the root node.

Since the functions used for the @var{action} parameter to @code{twalk}
must not modify the tree data, it is safe to run @code{twalk} in more
than one thread at the same time, working on the same tree.  It is also
safe to call @code{tfind} in parallel.  Functions which modify the tree
must not be used, otherwise the behavior is undefined.  However, it is
difficult to pass data external to the tree to the callback function
without resorting to global variables (and thread safety issues), so
see the @code{twalk_r} function below.
@end deftypefun

@deftypefun void twalk_r (const void *@var{root}, void (*@var{action}) (const void *@var{key}, VISIT @var{which}, void *@var{closure}), void *@var{closure})
@standards{GNU, search.h}
@safety{@prelim{}@mtsafe{@mtsrace{:root}}@assafe{}@acsafe{}}
For each node in the tree with a node pointed to by @var{root}, the
@code{twalk_r} function calls the function provided by the parameter
@var{action}.  For leaf nodes the function is called exactly once with
@var{which} set to @code{leaf}.  For internal nodes the function is
called three times, setting the @var{which} parameter of @var{action} to
the appropriate value.  The @var{closure} parameter is passed down to
each call of the @var{action} function, unmodified.

It is possible to implement the @code{twalk} function on top of the
@code{twalk_r} function, which is why there is no separate level
parameter.

@smallexample
@include twalk.c.texi
@end smallexample
@end deftypefun