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/* A splay-tree datatype.
   Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.
   Contributed by Mark Mitchell (mark@markmitchell.com).
 
This file is part of GNU CC.
 
GNU CC is free software; you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.
 
GNU CC is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.
 
You should have received a copy of the GNU General Public License
along with GNU CC; see the file COPYING.  If not, write to
the Free Software Foundation, 59 Temple Place - Suite 330,
Boston, MA 02111-1307, USA.  */
 
/* For an easily readable description of splay-trees, see:
 
     Lewis, Harry R. and Denenberg, Larry.  Data Structures and Their
     Algorithms.  Harper-Collins, Inc.  1991.  */
 
#ifdef HAVE_CONFIG_H
#include "config.h"
#endif
 
#ifdef HAVE_STDLIB_H
#include <stdlib.h>
#endif
 
#include <stdio.h>
 
#include "libiberty.h"
#include "splay-tree.h"
 
static void splay_tree_delete_helper    PARAMS((splay_tree,
                                                splay_tree_node));
static void splay_tree_splay            PARAMS((splay_tree,
                                                splay_tree_key));
static splay_tree_node splay_tree_splay_helper
                                        PARAMS((splay_tree,
                                                splay_tree_key,
                                                splay_tree_node*,
                                                splay_tree_node*,
                                                splay_tree_node*));
static int splay_tree_foreach_helper    PARAMS((splay_tree,
                                                splay_tree_node,
                                                splay_tree_foreach_fn,
                                                void*));
 
/* Deallocate NODE (a member of SP), and all its sub-trees.  */
 
static void
splay_tree_delete_helper (sp, node)
     splay_tree sp;
     splay_tree_node node;
{
  if (!node)
    return;
 
  splay_tree_delete_helper (sp, node->left);
  splay_tree_delete_helper (sp, node->right);
 
  if (sp->delete_key)
    (*sp->delete_key)(node->key);
  if (sp->delete_value)
    (*sp->delete_value)(node->value);
 
  free ((char*) node);
}
 
/* Help splay SP around KEY.  PARENT and GRANDPARENT are the parent
   and grandparent, respectively, of NODE.  */
 
static splay_tree_node
splay_tree_splay_helper (sp, key, node, parent, grandparent)
     splay_tree sp;
     splay_tree_key key;
     splay_tree_node *node;
     splay_tree_node *parent;
     splay_tree_node *grandparent;
{
  splay_tree_node *next;
  splay_tree_node n;
  int comparison;
 
  n = *node;
 
  if (!n)
    return *parent;
 
  comparison = (*sp->comp) (key, n->key);
 
  if (comparison == 0)
    /* We've found the target.  */
    next = 0;
  else if (comparison < 0)
    /* The target is to the left.  */
    next = &n->left;
  else
    /* The target is to the right.  */
    next = &n->right;
 
  if (next)
    {
      /* Continue down the tree.  */
      n = splay_tree_splay_helper (sp, key, next, node, parent);
 
      /* The recursive call will change the place to which NODE
         points.  */
      if (*node != n)
        return n;
    }
 
  if (!parent)
    /* NODE is the root.  We are done.  */
    return n;
 
  /* First, handle the case where there is no grandparent (i.e.,
     *PARENT is the root of the tree.)  */
  if (!grandparent)
    {
      if (n == (*parent)->left)
        {
          *node = n->right;
          n->right = *parent;
        }
      else
        {
          *node = n->left;
          n->left = *parent;
        }
      *parent = n;
      return n;
    }
 
  /* Next handle the cases where both N and *PARENT are left children,
     or where both are right children.  */
  if (n == (*parent)->left && *parent == (*grandparent)->left)
    {
      splay_tree_node p = *parent;
 
      (*grandparent)->left = p->right;
      p->right = *grandparent;
      p->left = n->right;
      n->right = p;
      *grandparent = n;
      return n;
    }
  else if  (n == (*parent)->right && *parent == (*grandparent)->right)
    {
      splay_tree_node p = *parent;
 
      (*grandparent)->right = p->left;
      p->left = *grandparent;
      p->right = n->left;
      n->left = p;
      *grandparent = n;
      return n;
    }
 
  /* Finally, deal with the case where N is a left child, but *PARENT
     is a right child, or vice versa.  */
  if (n == (*parent)->left)
    {
      (*parent)->left = n->right;
      n->right = *parent;
      (*grandparent)->right = n->left;
      n->left = *grandparent;
      *grandparent = n;
      return n;
    }
  else
    {
      (*parent)->right = n->left;
      n->left = *parent;
      (*grandparent)->left = n->right;
      n->right = *grandparent;
      *grandparent = n;
      return n;
    }
}
 
/* Splay SP around KEY.  */
 
static void
splay_tree_splay (sp, key)
     splay_tree sp;
     splay_tree_key key;
{
  if (sp->root == 0)
    return;
 
  splay_tree_splay_helper (sp, key, &sp->root,
                           /*grandparent=*/0, /*parent=*/0);
}
 
/* Call FN, passing it the DATA, for every node below NODE, all of
   which are from SP, following an in-order traversal.  If FN every
   returns a non-zero value, the iteration ceases immediately, and the
   value is returned.  Otherwise, this function returns 0.  */
 
static int
splay_tree_foreach_helper (sp, node, fn, data)
     splay_tree sp;
     splay_tree_node node;
     splay_tree_foreach_fn fn;
     void* data;
{
  int val;
 
  if (!node)
    return 0;
 
  val = splay_tree_foreach_helper (sp, node->left, fn, data);
  if (val)
    return val;
 
  val = (*fn)(node, data);
  if (val)
    return val;
 
  return splay_tree_foreach_helper (sp, node->right, fn, data);
}
 
/* Allocate a new splay tree, using COMPARE_FN to compare nodes,
   DELETE_KEY_FN to deallocate keys, and DELETE_VALUE_FN to deallocate
   values.  */
 
splay_tree
splay_tree_new (compare_fn, delete_key_fn, delete_value_fn)
     splay_tree_compare_fn compare_fn;
     splay_tree_delete_key_fn delete_key_fn;
     splay_tree_delete_value_fn delete_value_fn;
{
  splay_tree sp = (splay_tree) xmalloc (sizeof (struct splay_tree_s));
  sp->root = 0;
  sp->comp = compare_fn;
  sp->delete_key = delete_key_fn;
  sp->delete_value = delete_value_fn;
 
  return sp;
}
 
/* Deallocate SP.  */
 
void
splay_tree_delete (sp)
     splay_tree sp;
{
  splay_tree_delete_helper (sp, sp->root);
  free ((char*) sp);
}
 
/* Insert a new node (associating KEY with DATA) into SP.  If a
   previous node with the indicated KEY exists, its data is replaced
   with the new value.  Returns the new node.  */
 
splay_tree_node
splay_tree_insert (sp, key, value)
     splay_tree sp;
     splay_tree_key key;
     splay_tree_value value;
{
  int comparison = 0;
 
  splay_tree_splay (sp, key);
 
  if (sp->root)
    comparison = (*sp->comp)(sp->root->key, key);
 
  if (sp->root && comparison == 0)
    {
      /* If the root of the tree already has the indicated KEY, just
         replace the value with VALUE.  */
      if (sp->delete_value)
        (*sp->delete_value)(sp->root->value);
      sp->root->value = value;
    }
  else
    {
      /* Create a new node, and insert it at the root.  */
      splay_tree_node node;
 
      node = (splay_tree_node) xmalloc (sizeof (struct splay_tree_node_s));
      node->key = key;
      node->value = value;
 
      if (!sp->root)
        node->left = node->right = 0;
      else if (comparison < 0)
        {
          node->left = sp->root;
          node->right = node->left->right;
          node->left->right = 0;
        }
      else
        {
          node->right = sp->root;
          node->left = node->right->left;
          node->right->left = 0;
        }
 
      sp->root = node;
    }
 
  return sp->root;
}
 
/* Remove KEY from SP.  It is not an error if it did not exist.  */
 
void
splay_tree_remove (sp, key)
     splay_tree sp;
     splay_tree_key key;
{
  splay_tree_splay (sp, key);
 
  if (sp->root && (*sp->comp) (sp->root->key, key) == 0)
    {
      splay_tree_node left, right;
 
      left = sp->root->left;
      right = sp->root->right;
 
      /* Delete the root node itself.  */
      if (sp->delete_value)
        (*sp->delete_value) (sp->root->value);
      free (sp->root);
 
      /* One of the children is now the root.  Doesn't matter much
         which, so long as we preserve the properties of the tree.  */
      if (left)
        {
          sp->root = left;
 
          /* If there was a right child as well, hang it off the
             right-most leaf of the left child.  */
          if (right)
            {
              while (left->right)
                left = left->right;
              left->right = right;
            }
        }
      else
        sp->root = right;
    }
}
 
/* Lookup KEY in SP, returning VALUE if present, and NULL
   otherwise.  */
 
splay_tree_node
splay_tree_lookup (sp, key)
     splay_tree sp;
     splay_tree_key key;
{
  splay_tree_splay (sp, key);
 
  if (sp->root && (*sp->comp)(sp->root->key, key) == 0)
    return sp->root;
  else
    return 0;
}
 
/* Return the node in SP with the greatest key.  */
 
splay_tree_node
splay_tree_max (sp)
     splay_tree sp;
{
  splay_tree_node n = sp->root;
 
  if (!n)
    return NULL;
 
  while (n->right)
    n = n->right;
 
  return n;
}
 
/* Return the node in SP with the smallest key.  */
 
splay_tree_node
splay_tree_min (sp)
     splay_tree sp;
{
  splay_tree_node n = sp->root;
 
  if (!n)
    return NULL;
 
  while (n->left)
    n = n->left;
 
  return n;
}
 
/* Return the immediate predecessor KEY, or NULL if there is no
   predecessor.  KEY need not be present in the tree.  */
 
splay_tree_node
splay_tree_predecessor (sp, key)
     splay_tree sp;
     splay_tree_key key;
{
  int comparison;
  splay_tree_node node;
 
  /* If the tree is empty, there is certainly no predecessor.  */
  if (!sp->root)
    return NULL;
 
  /* Splay the tree around KEY.  That will leave either the KEY
     itself, its predecessor, or its successor at the root.  */
  splay_tree_splay (sp, key);
  comparison = (*sp->comp)(sp->root->key, key);
 
  /* If the predecessor is at the root, just return it.  */
  if (comparison < 0)
    return sp->root;
 
  /* Otherwise, find the leftmost element of the right subtree.  */
  node = sp->root->left;
  if (node)
    while (node->right)
      node = node->right;
 
  return node;
}
 
/* Return the immediate successor KEY, or NULL if there is no
   predecessor.  KEY need not be present in the tree.  */
 
splay_tree_node
splay_tree_successor (sp, key)
     splay_tree sp;
     splay_tree_key key;
{
  int comparison;
  splay_tree_node node;
 
  /* If the tree is empty, there is certainly no predecessor.  */
  if (!sp->root)
    return NULL;
 
  /* Splay the tree around KEY.  That will leave either the KEY
     itself, its predecessor, or its successor at the root.  */
  splay_tree_splay (sp, key);
  comparison = (*sp->comp)(sp->root->key, key);
 
  /* If the successor is at the root, just return it.  */
  if (comparison > 0)
    return sp->root;
 
  /* Otherwise, find the rightmost element of the left subtree.  */
  node = sp->root->right;
  if (node)
    while (node->left)
      node = node->left;
 
  return node;
}
 
/* Call FN, passing it the DATA, for every node in SP, following an
   in-order traversal.  If FN every returns a non-zero value, the
   iteration ceases immediately, and the value is returned.
   Otherwise, this function returns 0.  */
 
int
splay_tree_foreach (sp, fn, data)
     splay_tree sp;
     splay_tree_foreach_fn fn;
     void *data;
{
  return splay_tree_foreach_helper (sp, sp->root, fn, data);
}
 
/* Splay-tree comparison function, treating the keys as ints.  */
 
int
splay_tree_compare_ints (k1, k2)
     splay_tree_key k1;
     splay_tree_key k2;
{
  if ((int) k1 < (int) k2)
    return -1;
  else if ((int) k1 > (int) k2)
    return 1;
  else
    return 0;
}
 
/* Splay-tree comparison function, treating the keys as pointers.  */
 
int
splay_tree_compare_pointers (k1, k2)
     splay_tree_key k1;
     splay_tree_key k2;
{
  if ((char*) k1 < (char*) k2)
    return -1;
  else if ((char*) k1 > (char*) k2)
    return 1;
  else
    return 0;
}

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[/] [or1k/] [tags/] [start/] [insight/] [libiberty/] [splay-tree.c] - Blame information for rev 1765

Line No.	Rev	Author	Line
1	578	markom	`/* A splay-tree datatype.`
2			`Copyright (C) 1998, 1999, 2000, 2001 Free Software Foundation, Inc.`
3			`Contributed by Mark Mitchell (mark@markmitchell.com).`
4
5			`This file is part of GNU CC.`
6
7			`GNU CC is free software; you can redistribute it and/or modify it`
8			`under the terms of the GNU General Public License as published by`
9			`the Free Software Foundation; either version 2, or (at your option)`
10			`any later version.`
11
12			`GNU CC is distributed in the hope that it will be useful, but`
13			`WITHOUT ANY WARRANTY; without even the implied warranty of`
14			`MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU`
15			`General Public License for more details.`
16
17			`You should have received a copy of the GNU General Public License`
18			`along with GNU CC; see the file COPYING. If not, write to`
19			`the Free Software Foundation, 59 Temple Place - Suite 330,`
20			`Boston, MA 02111-1307, USA. */`
21
22			`/* For an easily readable description of splay-trees, see:`
23
24			`Lewis, Harry R. and Denenberg, Larry. Data Structures and Their`
25			`Algorithms. Harper-Collins, Inc. 1991. */`
26
27			`#ifdef HAVE_CONFIG_H`
28			`#include "config.h"`
29			`#endif`
30
31			`#ifdef HAVE_STDLIB_H`
32			`#include <stdlib.h>`
33			`#endif`
34
35			`#include <stdio.h>`
36
37			`#include "libiberty.h"`
38			`#include "splay-tree.h"`
39
40			`static void splay_tree_delete_helper PARAMS((splay_tree,`
41			`splay_tree_node));`
42			`static void splay_tree_splay PARAMS((splay_tree,`
43			`splay_tree_key));`
44			`static splay_tree_node splay_tree_splay_helper`
45			`PARAMS((splay_tree,`
46			`splay_tree_key,`
47			`splay_tree_node*,`
48			`splay_tree_node*,`
49			`splay_tree_node*));`
50			`static int splay_tree_foreach_helper PARAMS((splay_tree,`
51			`splay_tree_node,`
52			`splay_tree_foreach_fn,`
53			`void*));`
54
55			`/* Deallocate NODE (a member of SP), and all its sub-trees. */`
56
57			`static void`
58			`splay_tree_delete_helper (sp, node)`
59			`splay_tree sp;`
60			`splay_tree_node node;`
61			`{`
62			`if (!node)`
63			`return;`
64
65			`splay_tree_delete_helper (sp, node->left);`
66			`splay_tree_delete_helper (sp, node->right);`
67
68			`if (sp->delete_key)`
69			`(*sp->delete_key)(node->key);`
70			`if (sp->delete_value)`
71			`(*sp->delete_value)(node->value);`
72
73			`free ((char*) node);`
74			`}`
75
76			`/* Help splay SP around KEY. PARENT and GRANDPARENT are the parent`
77			`and grandparent, respectively, of NODE. */`
78
79			`static splay_tree_node`
80			`splay_tree_splay_helper (sp, key, node, parent, grandparent)`
81			`splay_tree sp;`
82			`splay_tree_key key;`
83			`splay_tree_node *node;`
84			`splay_tree_node *parent;`
85			`splay_tree_node *grandparent;`
86			`{`
87			`splay_tree_node *next;`
88			`splay_tree_node n;`
89			`int comparison;`
90
91			`n = *node;`
92
93			`if (!n)`
94			`return *parent;`
95
96			`comparison = (*sp->comp) (key, n->key);`
97
98			`if (comparison == 0)`
99			`/* We've found the target. */`
100			`next = 0;`
101			`else if (comparison < 0)`
102			`/* The target is to the left. */`
103			`next = &n->left;`
104			`else`
105			`/* The target is to the right. */`
106			`next = &n->right;`
107
108			`if (next)`
109			`{`
110			`/* Continue down the tree. */`
111			`n = splay_tree_splay_helper (sp, key, next, node, parent);`
112
113			`/* The recursive call will change the place to which NODE`
114			`points. */`
115			`if (*node != n)`
116			`return n;`
117			`}`
118
119			`if (!parent)`
120			`/* NODE is the root. We are done. */`
121			`return n;`
122
123			`/* First, handle the case where there is no grandparent (i.e.,`
124			`PARENT is the root of the tree.) /`
125			`if (!grandparent)`
126			`{`
127			`if (n == (*parent)->left)`
128			`{`
129			`*node = n->right;`
130			`n->right = *parent;`
131			`}`
132			`else`
133			`{`
134			`*node = n->left;`
135			`n->left = *parent;`
136			`}`
137			`*parent = n;`
138			`return n;`
139			`}`
140
141			`/* Next handle the cases where both N and *PARENT are left children,`
142			`or where both are right children. */`
143			`if (n == (parent)->left && parent == (*grandparent)->left)`
144			`{`
145			`splay_tree_node p = *parent;`
146
147			`(*grandparent)->left = p->right;`
148			`p->right = *grandparent;`
149			`p->left = n->right;`
150			`n->right = p;`
151			`*grandparent = n;`
152			`return n;`
153			`}`
154			`else if (n == (parent)->right && parent == (*grandparent)->right)`
155			`{`
156			`splay_tree_node p = *parent;`
157
158			`(*grandparent)->right = p->left;`
159			`p->left = *grandparent;`
160			`p->right = n->left;`
161			`n->left = p;`
162			`*grandparent = n;`
163			`return n;`
164			`}`
165
166			`/* Finally, deal with the case where N is a left child, but *PARENT`
167			`is a right child, or vice versa. */`
168			`if (n == (*parent)->left)`
169			`{`
170			`(*parent)->left = n->right;`
171			`n->right = *parent;`
172			`(*grandparent)->right = n->left;`
173			`n->left = *grandparent;`
174			`*grandparent = n;`
175			`return n;`
176			`}`
177			`else`
178			`{`
179			`(*parent)->right = n->left;`
180			`n->left = *parent;`
181			`(*grandparent)->left = n->right;`
182			`n->right = *grandparent;`
183			`*grandparent = n;`
184			`return n;`
185			`}`
186			`}`
187
188			`/* Splay SP around KEY. */`
189
190			`static void`
191			`splay_tree_splay (sp, key)`
192			`splay_tree sp;`
193			`splay_tree_key key;`
194			`{`
195			`if (sp->root == 0)`
196			`return;`
197
198			`splay_tree_splay_helper (sp, key, &sp->root,`
199			`/grandparent=/0, /parent=/0);`
200			`}`
201
202			`/* Call FN, passing it the DATA, for every node below NODE, all of`
203			`which are from SP, following an in-order traversal. If FN every`
204			`returns a non-zero value, the iteration ceases immediately, and the`
205			`value is returned. Otherwise, this function returns 0. */`
206
207			`static int`
208			`splay_tree_foreach_helper (sp, node, fn, data)`
209			`splay_tree sp;`
210			`splay_tree_node node;`
211			`splay_tree_foreach_fn fn;`
212			`void* data;`
213			`{`
214			`int val;`
215
216			`if (!node)`
217			`return 0;`
218
219			`val = splay_tree_foreach_helper (sp, node->left, fn, data);`
220			`if (val)`
221			`return val;`
222
223			`val = (*fn)(node, data);`
224			`if (val)`
225			`return val;`
226
227			`return splay_tree_foreach_helper (sp, node->right, fn, data);`
228			`}`
229
230			`/* Allocate a new splay tree, using COMPARE_FN to compare nodes,`
231			`DELETE_KEY_FN to deallocate keys, and DELETE_VALUE_FN to deallocate`
232			`values. */`
233
234			`splay_tree`
235			`splay_tree_new (compare_fn, delete_key_fn, delete_value_fn)`
236			`splay_tree_compare_fn compare_fn;`
237			`splay_tree_delete_key_fn delete_key_fn;`
238			`splay_tree_delete_value_fn delete_value_fn;`
239			`{`
240			`splay_tree sp = (splay_tree) xmalloc (sizeof (struct splay_tree_s));`
241			`sp->root = 0;`
242			`sp->comp = compare_fn;`
243			`sp->delete_key = delete_key_fn;`
244			`sp->delete_value = delete_value_fn;`
245
246			`return sp;`
247			`}`
248
249			`/* Deallocate SP. */`
250
251			`void`
252			`splay_tree_delete (sp)`
253			`splay_tree sp;`
254			`{`
255			`splay_tree_delete_helper (sp, sp->root);`
256			`free ((char*) sp);`
257			`}`
258
259			`/* Insert a new node (associating KEY with DATA) into SP. If a`
260			`previous node with the indicated KEY exists, its data is replaced`
261			`with the new value. Returns the new node. */`
262
263			`splay_tree_node`
264			`splay_tree_insert (sp, key, value)`
265			`splay_tree sp;`
266			`splay_tree_key key;`
267			`splay_tree_value value;`
268			`{`
269			`int comparison = 0;`
270
271			`splay_tree_splay (sp, key);`
272
273			`if (sp->root)`
274			`comparison = (*sp->comp)(sp->root->key, key);`
275
276			`if (sp->root && comparison == 0)`
277			`{`
278			`/* If the root of the tree already has the indicated KEY, just`
279			`replace the value with VALUE. */`
280			`if (sp->delete_value)`
281			`(*sp->delete_value)(sp->root->value);`
282			`sp->root->value = value;`
283			`}`
284			`else`
285			`{`
286			`/* Create a new node, and insert it at the root. */`
287			`splay_tree_node node;`
288
289			`node = (splay_tree_node) xmalloc (sizeof (struct splay_tree_node_s));`
290			`node->key = key;`
291			`node->value = value;`
292
293			`if (!sp->root)`
294			`node->left = node->right = 0;`
295			`else if (comparison < 0)`
296			`{`
297			`node->left = sp->root;`
298			`node->right = node->left->right;`
299			`node->left->right = 0;`
300			`}`
301			`else`
302			`{`
303			`node->right = sp->root;`
304			`node->left = node->right->left;`
305			`node->right->left = 0;`
306			`}`
307
308			`sp->root = node;`
309			`}`
310
311			`return sp->root;`
312			`}`
313
314			`/* Remove KEY from SP. It is not an error if it did not exist. */`
315
316			`void`
317			`splay_tree_remove (sp, key)`
318			`splay_tree sp;`
319			`splay_tree_key key;`
320			`{`
321			`splay_tree_splay (sp, key);`
322
323			`if (sp->root && (*sp->comp) (sp->root->key, key) == 0)`
324			`{`
325			`splay_tree_node left, right;`
326
327			`left = sp->root->left;`
328			`right = sp->root->right;`
329
330			`/* Delete the root node itself. */`
331			`if (sp->delete_value)`
332			`(*sp->delete_value) (sp->root->value);`
333			`free (sp->root);`
334
335			`/* One of the children is now the root. Doesn't matter much`
336			`which, so long as we preserve the properties of the tree. */`
337			`if (left)`
338			`{`
339			`sp->root = left;`
340
341			`/* If there was a right child as well, hang it off the`
342			`right-most leaf of the left child. */`
343			`if (right)`
344			`{`
345			`while (left->right)`
346			`left = left->right;`
347			`left->right = right;`
348			`}`
349			`}`
350			`else`
351			`sp->root = right;`
352			`}`
353			`}`
354
355			`/* Lookup KEY in SP, returning VALUE if present, and NULL`
356			`otherwise. */`
357
358			`splay_tree_node`
359			`splay_tree_lookup (sp, key)`
360			`splay_tree sp;`
361			`splay_tree_key key;`
362			`{`
363			`splay_tree_splay (sp, key);`
364
365			`if (sp->root && (*sp->comp)(sp->root->key, key) == 0)`
366			`return sp->root;`
367			`else`
368			`return 0;`
369			`}`
370
371			`/* Return the node in SP with the greatest key. */`
372
373			`splay_tree_node`
374			`splay_tree_max (sp)`
375			`splay_tree sp;`
376			`{`
377			`splay_tree_node n = sp->root;`
378
379			`if (!n)`
380			`return NULL;`
381
382			`while (n->right)`
383			`n = n->right;`
384
385			`return n;`
386			`}`
387
388			`/* Return the node in SP with the smallest key. */`
389
390			`splay_tree_node`
391			`splay_tree_min (sp)`
392			`splay_tree sp;`
393			`{`
394			`splay_tree_node n = sp->root;`
395
396			`if (!n)`
397			`return NULL;`
398
399			`while (n->left)`
400			`n = n->left;`
401
402			`return n;`
403			`}`
404
405			`/* Return the immediate predecessor KEY, or NULL if there is no`
406			`predecessor. KEY need not be present in the tree. */`
407
408			`splay_tree_node`
409			`splay_tree_predecessor (sp, key)`
410			`splay_tree sp;`
411			`splay_tree_key key;`
412			`{`
413			`int comparison;`
414			`splay_tree_node node;`
415
416			`/* If the tree is empty, there is certainly no predecessor. */`
417			`if (!sp->root)`
418			`return NULL;`
419
420			`/* Splay the tree around KEY. That will leave either the KEY`
421			`itself, its predecessor, or its successor at the root. */`
422			`splay_tree_splay (sp, key);`
423			`comparison = (*sp->comp)(sp->root->key, key);`
424
425			`/* If the predecessor is at the root, just return it. */`
426			`if (comparison < 0)`
427			`return sp->root;`
428
429			`/* Otherwise, find the leftmost element of the right subtree. */`
430			`node = sp->root->left;`
431			`if (node)`
432			`while (node->right)`
433			`node = node->right;`
434
435			`return node;`
436			`}`
437
438			`/* Return the immediate successor KEY, or NULL if there is no`
439			`predecessor. KEY need not be present in the tree. */`
440
441			`splay_tree_node`
442			`splay_tree_successor (sp, key)`
443			`splay_tree sp;`
444			`splay_tree_key key;`
445			`{`
446			`int comparison;`
447			`splay_tree_node node;`
448
449			`/* If the tree is empty, there is certainly no predecessor. */`
450			`if (!sp->root)`
451			`return NULL;`
452
453			`/* Splay the tree around KEY. That will leave either the KEY`
454			`itself, its predecessor, or its successor at the root. */`
455			`splay_tree_splay (sp, key);`
456			`comparison = (*sp->comp)(sp->root->key, key);`
457
458			`/* If the successor is at the root, just return it. */`
459			`if (comparison > 0)`
460			`return sp->root;`
461
462			`/* Otherwise, find the rightmost element of the left subtree. */`
463			`node = sp->root->right;`
464			`if (node)`
465			`while (node->left)`
466			`node = node->left;`
467
468			`return node;`
469			`}`
470
471			`/* Call FN, passing it the DATA, for every node in SP, following an`
472			`in-order traversal. If FN every returns a non-zero value, the`
473			`iteration ceases immediately, and the value is returned.`
474			`Otherwise, this function returns 0. */`
475
476			`int`
477			`splay_tree_foreach (sp, fn, data)`
478			`splay_tree sp;`
479			`splay_tree_foreach_fn fn;`
480			`void *data;`
481			`{`
482			`return splay_tree_foreach_helper (sp, sp->root, fn, data);`
483			`}`
484
485			`/* Splay-tree comparison function, treating the keys as ints. */`
486
487			`int`
488			`splay_tree_compare_ints (k1, k2)`
489			`splay_tree_key k1;`
490			`splay_tree_key k2;`
491			`{`
492			`if ((int) k1 < (int) k2)`
493			`return -1;`
494			`else if ((int) k1 > (int) k2)`
495			`return 1;`
496			`else`
497			`return 0;`
498			`}`
499
500			`/* Splay-tree comparison function, treating the keys as pointers. */`
501
502			`int`
503			`splay_tree_compare_pointers (k1, k2)`
504			`splay_tree_key k1;`
505			`splay_tree_key k2;`
506			`{`
507			`if ((char) k1 < (char) k2)`
508			`return -1;`
509			`else if ((char) k1 > (char) k2)`
510			`return 1;`
511			`else`
512			`return 0;`
513			`}`