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-@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}.
-
-@comment search.h
-@comment SVID
-@deftypefun {void *} lfind (const void *@var{key}, const void *@var{base}, size_t *@var{nmemb}, size_t @var{size}, comparison_fn_t @var{compar})
-@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
-
-@comment search.h
-@comment SVID
-@deftypefun {void *} lsearch (const void *@var{key}, void *@var{base}, size_t *@var{nmemb}, size_t @var{size}, comparison_fn_t @var{compar})
-@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
-
-@comment stdlib.h
-@comment ISO
-@deftypefun {void *} bsearch (const void *@var{key}, const void *@var{array}, size_t @var{count}, size_t @var{size}, comparison_fn_t @var{compare})
-@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
-
-@comment stdlib.h
-@comment ISO
-@deftypefun void qsort (void *@var{array}, size_t @var{count}, size_t @var{size}, comparison_fn_t @var{compare})
-@safety{@prelim{}@mtsafe{}@assafe{}@acunsafe{@acucorrupt{}}}
-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 might not be an
-in-place sort and might thereby use an extra amount of memory to store
-the array.
-@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}.
-
-@comment search.h
-@comment SVID
-@deftypefun int hcreate (size_t @var{nel})
-@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
-
-@comment search.h
-@comment SVID
-@deftypefun void hdestroy (void)
-@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} {struct ENTRY}
-Both elements of this structure are pointers to zero-terminated strings.
-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 the records. It is not
-possible to handle general binary data.
-
-@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.
-@item char *data
-Pointer to a zero-terminated string of characters describing the data.
-If the functions will be called only for searching an existing entry
-this element might stay undefined since it is not used.
-@end table
-@end deftp
-
-@comment search.h
-@comment SVID
-@deftypefun {ENTRY *} hsearch (ENTRY @var{item}, ACTION @var{action})
-@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.
-
-@comment search.h
-@comment GNU
-@deftypefun int hcreate_r (size_t @var{nel}, struct hsearch_data *@var{htab})
-@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
-
-@comment search.h
-@comment GNU
-@deftypefun void hdestroy_r (struct hsearch_data *@var{htab})
-@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
-
-@comment search.h
-@comment GNU
-@deftypefun int hsearch_r (ENTRY @var{item}, ACTION @var{action}, ENTRY **@var{retval}, struct hsearch_data *@var{htab})
-@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 @var{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}.
-
-@comment search.h
-@comment SVID
-@deftypefun {void *} tsearch (const void *@var{key}, void **@var{rootp}, comparison_fn_t @var{compar})
-@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
-
-@comment search.h
-@comment SVID
-@deftypefun {void *} tfind (const void *@var{key}, void *const *@var{rootp}, comparison_fn_t @var{compar})
-@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.
-
-@comment search.h
-@comment SVID
-@deftypefun {void *} tdelete (const void *@var{key}, void **@var{rootp}, comparison_fn_t @var{compar})
-@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
-
-@comment search.h
-@comment GNU
-@deftypefun void tdestroy (void *@var{vroot}, __free_fn_t @var{freefct})
-@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
-
-@comment search.h
-@comment SVID
-@deftypefun void twalk (const void *@var{root}, __action_fn_t @var{action})
-@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.
-@end deftypefun