ref: a45f1830cf4af0fbaf2fad448f717a6458b48b24
dir: /tree234.c/
/*
* tree234.c: reasonably generic counted 2-3-4 tree routines.
*
* This file is copyright 1999-2001 Simon Tatham.
*
* Permission is hereby granted, free of charge, to any person
* obtaining a copy of this software and associated documentation
* files (the "Software"), to deal in the Software without
* restriction, including without limitation the rights to use,
* copy, modify, merge, publish, distribute, sublicense, and/or
* sell copies of the Software, and to permit persons to whom the
* Software is furnished to do so, subject to the following
* conditions:
*
* The above copyright notice and this permission notice shall be
* included in all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
* EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
* OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
* NONINFRINGEMENT. IN NO EVENT SHALL SIMON TATHAM BE LIABLE FOR
* ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
* CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
* CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
* SOFTWARE.
*/
#include <stdio.h>
#include <stdlib.h>
#include <assert.h>
#include "tree234.h"
#include "puzzles.h" /* for smalloc/sfree */
#ifdef TEST
#include <stdarg.h>
static void logprintf(const char *fmt, ...)
{
va_list ap;
va_start(ap, fmt);
vprintf(fmt, ap);
va_end(ap);
}
#define LOG(x) (logprintf x)
#else
#define LOG(x)
#endif
typedef struct node234_Tag node234;
struct tree234_Tag {
node234 *root;
cmpfn234 cmp;
};
struct node234_Tag {
node234 *parent;
node234 *kids[4];
int counts[4];
void *elems[3];
};
/*
* Create a 2-3-4 tree.
*/
tree234 *newtree234(cmpfn234 cmp) {
tree234 *ret = snew(tree234);
LOG(("created tree %p\n", ret));
ret->root = NULL;
ret->cmp = cmp;
return ret;
}
/*
* Free a 2-3-4 tree (not including freeing the elements).
*/
static void freenode234(node234 *n) {
if (!n)
return;
freenode234(n->kids[0]);
freenode234(n->kids[1]);
freenode234(n->kids[2]);
freenode234(n->kids[3]);
sfree(n);
}
void freetree234(tree234 *t) {
freenode234(t->root);
sfree(t);
}
/*
* Internal function to count a node.
*/
static int countnode234(node234 *n) {
int count = 0;
int i;
if (!n)
return 0;
for (i = 0; i < 4; i++)
count += n->counts[i];
for (i = 0; i < 3; i++)
if (n->elems[i])
count++;
return count;
}
/*
* Count the elements in a tree.
*/
int count234(tree234 *t) {
if (t->root)
return countnode234(t->root);
else
return 0;
}
/*
* Propagate a node overflow up a tree until it stops. Returns 0 or
* 1, depending on whether the root had to be split or not.
*/
static int add234_insert(node234 *left, void *e, node234 *right,
node234 **root, node234 *n, int ki) {
int lcount, rcount;
/*
* We need to insert the new left/element/right set in n at
* child position ki.
*/
lcount = countnode234(left);
rcount = countnode234(right);
while (n) {
LOG((" at %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" need to insert %p/%d \"%s\" %p/%d at position %d\n",
left, lcount, e, right, rcount, ki));
if (n->elems[1] == NULL) {
/*
* Insert in a 2-node; simple.
*/
if (ki == 0) {
LOG((" inserting on left of 2-node\n"));
n->kids[2] = n->kids[1]; n->counts[2] = n->counts[1];
n->elems[1] = n->elems[0];
n->kids[1] = right; n->counts[1] = rcount;
n->elems[0] = e;
n->kids[0] = left; n->counts[0] = lcount;
} else { /* ki == 1 */
LOG((" inserting on right of 2-node\n"));
n->kids[2] = right; n->counts[2] = rcount;
n->elems[1] = e;
n->kids[1] = left; n->counts[1] = lcount;
}
if (n->kids[0]) n->kids[0]->parent = n;
if (n->kids[1]) n->kids[1]->parent = n;
if (n->kids[2]) n->kids[2]->parent = n;
LOG((" done\n"));
break;
} else if (n->elems[2] == NULL) {
/*
* Insert in a 3-node; simple.
*/
if (ki == 0) {
LOG((" inserting on left of 3-node\n"));
n->kids[3] = n->kids[2]; n->counts[3] = n->counts[2];
n->elems[2] = n->elems[1];
n->kids[2] = n->kids[1]; n->counts[2] = n->counts[1];
n->elems[1] = n->elems[0];
n->kids[1] = right; n->counts[1] = rcount;
n->elems[0] = e;
n->kids[0] = left; n->counts[0] = lcount;
} else if (ki == 1) {
LOG((" inserting in middle of 3-node\n"));
n->kids[3] = n->kids[2]; n->counts[3] = n->counts[2];
n->elems[2] = n->elems[1];
n->kids[2] = right; n->counts[2] = rcount;
n->elems[1] = e;
n->kids[1] = left; n->counts[1] = lcount;
} else { /* ki == 2 */
LOG((" inserting on right of 3-node\n"));
n->kids[3] = right; n->counts[3] = rcount;
n->elems[2] = e;
n->kids[2] = left; n->counts[2] = lcount;
}
if (n->kids[0]) n->kids[0]->parent = n;
if (n->kids[1]) n->kids[1]->parent = n;
if (n->kids[2]) n->kids[2]->parent = n;
if (n->kids[3]) n->kids[3]->parent = n;
LOG((" done\n"));
break;
} else {
node234 *m = snew(node234);
m->parent = n->parent;
LOG((" splitting a 4-node; created new node %p\n", m));
/*
* Insert in a 4-node; split into a 2-node and a
* 3-node, and move focus up a level.
*
* I don't think it matters which way round we put the
* 2 and the 3. For simplicity, we'll put the 3 first
* always.
*/
if (ki == 0) {
m->kids[0] = left; m->counts[0] = lcount;
m->elems[0] = e;
m->kids[1] = right; m->counts[1] = rcount;
m->elems[1] = n->elems[0];
m->kids[2] = n->kids[1]; m->counts[2] = n->counts[1];
e = n->elems[1];
n->kids[0] = n->kids[2]; n->counts[0] = n->counts[2];
n->elems[0] = n->elems[2];
n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3];
} else if (ki == 1) {
m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0];
m->elems[0] = n->elems[0];
m->kids[1] = left; m->counts[1] = lcount;
m->elems[1] = e;
m->kids[2] = right; m->counts[2] = rcount;
e = n->elems[1];
n->kids[0] = n->kids[2]; n->counts[0] = n->counts[2];
n->elems[0] = n->elems[2];
n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3];
} else if (ki == 2) {
m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0];
m->elems[0] = n->elems[0];
m->kids[1] = n->kids[1]; m->counts[1] = n->counts[1];
m->elems[1] = n->elems[1];
m->kids[2] = left; m->counts[2] = lcount;
/* e = e; */
n->kids[0] = right; n->counts[0] = rcount;
n->elems[0] = n->elems[2];
n->kids[1] = n->kids[3]; n->counts[1] = n->counts[3];
} else { /* ki == 3 */
m->kids[0] = n->kids[0]; m->counts[0] = n->counts[0];
m->elems[0] = n->elems[0];
m->kids[1] = n->kids[1]; m->counts[1] = n->counts[1];
m->elems[1] = n->elems[1];
m->kids[2] = n->kids[2]; m->counts[2] = n->counts[2];
n->kids[0] = left; n->counts[0] = lcount;
n->elems[0] = e;
n->kids[1] = right; n->counts[1] = rcount;
e = n->elems[2];
}
m->kids[3] = n->kids[3] = n->kids[2] = NULL;
m->counts[3] = n->counts[3] = n->counts[2] = 0;
m->elems[2] = n->elems[2] = n->elems[1] = NULL;
if (m->kids[0]) m->kids[0]->parent = m;
if (m->kids[1]) m->kids[1]->parent = m;
if (m->kids[2]) m->kids[2]->parent = m;
if (n->kids[0]) n->kids[0]->parent = n;
if (n->kids[1]) n->kids[1]->parent = n;
LOG((" left (%p): %p/%d \"%s\" %p/%d \"%s\" %p/%d\n", m,
m->kids[0], m->counts[0], m->elems[0],
m->kids[1], m->counts[1], m->elems[1],
m->kids[2], m->counts[2]));
LOG((" right (%p): %p/%d \"%s\" %p/%d\n", n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1]));
left = m; lcount = countnode234(left);
right = n; rcount = countnode234(right);
}
if (n->parent)
ki = (n->parent->kids[0] == n ? 0 :
n->parent->kids[1] == n ? 1 :
n->parent->kids[2] == n ? 2 : 3);
n = n->parent;
}
/*
* If we've come out of here by `break', n will still be
* non-NULL and all we need to do is go back up the tree
* updating counts. If we've come here because n is NULL, we
* need to create a new root for the tree because the old one
* has just split into two. */
if (n) {
while (n->parent) {
int count = countnode234(n);
int childnum;
childnum = (n->parent->kids[0] == n ? 0 :
n->parent->kids[1] == n ? 1 :
n->parent->kids[2] == n ? 2 : 3);
n->parent->counts[childnum] = count;
n = n->parent;
}
return 0; /* root unchanged */
} else {
LOG((" root is overloaded, split into two\n"));
(*root) = snew(node234);
(*root)->kids[0] = left; (*root)->counts[0] = lcount;
(*root)->elems[0] = e;
(*root)->kids[1] = right; (*root)->counts[1] = rcount;
(*root)->elems[1] = NULL;
(*root)->kids[2] = NULL; (*root)->counts[2] = 0;
(*root)->elems[2] = NULL;
(*root)->kids[3] = NULL; (*root)->counts[3] = 0;
(*root)->parent = NULL;
if ((*root)->kids[0]) (*root)->kids[0]->parent = (*root);
if ((*root)->kids[1]) (*root)->kids[1]->parent = (*root);
LOG((" new root is %p/%d \"%s\" %p/%d\n",
(*root)->kids[0], (*root)->counts[0],
(*root)->elems[0],
(*root)->kids[1], (*root)->counts[1]));
return 1; /* root moved */
}
}
/*
* Add an element e to a 2-3-4 tree t. Returns e on success, or if
* an existing element compares equal, returns that.
*/
static void *add234_internal(tree234 *t, void *e, int index) {
node234 *n;
int ki;
void *orig_e = e;
int c;
LOG(("adding element \"%s\" to tree %p\n", e, t));
if (t->root == NULL) {
t->root = snew(node234);
t->root->elems[1] = t->root->elems[2] = NULL;
t->root->kids[0] = t->root->kids[1] = NULL;
t->root->kids[2] = t->root->kids[3] = NULL;
t->root->counts[0] = t->root->counts[1] = 0;
t->root->counts[2] = t->root->counts[3] = 0;
t->root->parent = NULL;
t->root->elems[0] = e;
LOG((" created root %p\n", t->root));
return orig_e;
}
n = t->root;
do {
LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
if (index >= 0) {
if (!n->kids[0]) {
/*
* Leaf node. We want to insert at kid position
* equal to the index:
*
* 0 A 1 B 2 C 3
*/
ki = index;
} else {
/*
* Internal node. We always descend through it (add
* always starts at the bottom, never in the
* middle).
*/
if (index <= n->counts[0]) {
ki = 0;
} else if (index -= n->counts[0] + 1, index <= n->counts[1]) {
ki = 1;
} else if (index -= n->counts[1] + 1, index <= n->counts[2]) {
ki = 2;
} else if (index -= n->counts[2] + 1, index <= n->counts[3]) {
ki = 3;
} else
return NULL; /* error: index out of range */
}
} else {
if ((c = t->cmp(e, n->elems[0])) < 0)
ki = 0;
else if (c == 0)
return n->elems[0]; /* already exists */
else if (n->elems[1] == NULL || (c = t->cmp(e, n->elems[1])) < 0)
ki = 1;
else if (c == 0)
return n->elems[1]; /* already exists */
else if (n->elems[2] == NULL || (c = t->cmp(e, n->elems[2])) < 0)
ki = 2;
else if (c == 0)
return n->elems[2]; /* already exists */
else
ki = 3;
}
LOG((" moving to child %d (%p)\n", ki, n->kids[ki]));
if (!n->kids[ki])
break;
n = n->kids[ki];
} while (n);
add234_insert(NULL, e, NULL, &t->root, n, ki);
return orig_e;
}
void *add234(tree234 *t, void *e) {
if (!t->cmp) /* tree is unsorted */
return NULL;
return add234_internal(t, e, -1);
}
void *addpos234(tree234 *t, void *e, int index) {
if (index < 0 || /* index out of range */
t->cmp) /* tree is sorted */
return NULL; /* return failure */
return add234_internal(t, e, index); /* this checks the upper bound */
}
/*
* Look up the element at a given numeric index in a 2-3-4 tree.
* Returns NULL if the index is out of range.
*/
void *index234(tree234 *t, int index) {
node234 *n;
if (!t->root)
return NULL; /* tree is empty */
if (index < 0 || index >= countnode234(t->root))
return NULL; /* out of range */
n = t->root;
while (n) {
if (index < n->counts[0])
n = n->kids[0];
else if (index -= n->counts[0] + 1, index < 0)
return n->elems[0];
else if (index < n->counts[1])
n = n->kids[1];
else if (index -= n->counts[1] + 1, index < 0)
return n->elems[1];
else if (index < n->counts[2])
n = n->kids[2];
else if (index -= n->counts[2] + 1, index < 0)
return n->elems[2];
else
n = n->kids[3];
}
/* We shouldn't ever get here. I wonder how we did. */
return NULL;
}
/*
* Find an element e in a sorted 2-3-4 tree t. Returns NULL if not
* found. e is always passed as the first argument to cmp, so cmp
* can be an asymmetric function if desired. cmp can also be passed
* as NULL, in which case the compare function from the tree proper
* will be used.
*/
void *findrelpos234(tree234 *t, void *e, cmpfn234 cmp,
int relation, int *index) {
node234 *n;
void *ret;
int c;
int idx, ecount, kcount, cmpret;
if (t->root == NULL)
return NULL;
if (cmp == NULL)
cmp = t->cmp;
n = t->root;
/*
* Attempt to find the element itself.
*/
idx = 0;
ecount = -1;
/*
* Prepare a fake `cmp' result if e is NULL.
*/
cmpret = 0;
if (e == NULL) {
assert(relation == REL234_LT || relation == REL234_GT);
if (relation == REL234_LT)
cmpret = +1; /* e is a max: always greater */
else if (relation == REL234_GT)
cmpret = -1; /* e is a min: always smaller */
}
while (1) {
for (kcount = 0; kcount < 4; kcount++) {
if (kcount >= 3 || n->elems[kcount] == NULL ||
(c = cmpret ? cmpret : cmp(e, n->elems[kcount])) < 0) {
break;
}
if (n->kids[kcount]) idx += n->counts[kcount];
if (c == 0) {
ecount = kcount;
break;
}
idx++;
}
if (ecount >= 0)
break;
if (n->kids[kcount])
n = n->kids[kcount];
else
break;
}
if (ecount >= 0) {
/*
* We have found the element we're looking for. It's
* n->elems[ecount], at tree index idx. If our search
* relation is EQ, LE or GE we can now go home.
*/
if (relation != REL234_LT && relation != REL234_GT) {
if (index) *index = idx;
return n->elems[ecount];
}
/*
* Otherwise, we'll do an indexed lookup for the previous
* or next element. (It would be perfectly possible to
* implement these search types in a non-counted tree by
* going back up from where we are, but far more fiddly.)
*/
if (relation == REL234_LT)
idx--;
else
idx++;
} else {
/*
* We've found our way to the bottom of the tree and we
* know where we would insert this node if we wanted to:
* we'd put it in in place of the (empty) subtree
* n->kids[kcount], and it would have index idx
*
* But the actual element isn't there. So if our search
* relation is EQ, we're doomed.
*/
if (relation == REL234_EQ)
return NULL;
/*
* Otherwise, we must do an index lookup for index idx-1
* (if we're going left - LE or LT) or index idx (if we're
* going right - GE or GT).
*/
if (relation == REL234_LT || relation == REL234_LE) {
idx--;
}
}
/*
* We know the index of the element we want; just call index234
* to do the rest. This will return NULL if the index is out of
* bounds, which is exactly what we want.
*/
ret = index234(t, idx);
if (ret && index) *index = idx;
return ret;
}
void *find234(tree234 *t, void *e, cmpfn234 cmp) {
return findrelpos234(t, e, cmp, REL234_EQ, NULL);
}
void *findrel234(tree234 *t, void *e, cmpfn234 cmp, int relation) {
return findrelpos234(t, e, cmp, relation, NULL);
}
void *findpos234(tree234 *t, void *e, cmpfn234 cmp, int *index) {
return findrelpos234(t, e, cmp, REL234_EQ, index);
}
/*
* Tree transformation used in delete and split: move a subtree
* right, from child ki of a node to the next child. Update k and
* index so that they still point to the same place in the
* transformed tree. Assumes the destination child is not full, and
* that the source child does have a subtree to spare. Can cope if
* the destination child is undersized.
*
* . C . . B .
* / \ -> / \
* [more] a A b B c d D e [more] a A b c C d D e
*
* . C . . B .
* / \ -> / \
* [more] a A b B c d [more] a A b c C d
*/
static void trans234_subtree_right(node234 *n, int ki, int *k, int *index) {
node234 *src, *dest;
int i, srclen, adjust;
src = n->kids[ki];
dest = n->kids[ki+1];
LOG((" trans234_subtree_right(%p, %d):\n", n, ki));
LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
src,
src->kids[0], src->counts[0], src->elems[0],
src->kids[1], src->counts[1], src->elems[1],
src->kids[2], src->counts[2], src->elems[2],
src->kids[3], src->counts[3]));
LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
dest,
dest->kids[0], dest->counts[0], dest->elems[0],
dest->kids[1], dest->counts[1], dest->elems[1],
dest->kids[2], dest->counts[2], dest->elems[2],
dest->kids[3], dest->counts[3]));
/*
* Move over the rest of the destination node to make space.
*/
dest->kids[3] = dest->kids[2]; dest->counts[3] = dest->counts[2];
dest->elems[2] = dest->elems[1];
dest->kids[2] = dest->kids[1]; dest->counts[2] = dest->counts[1];
dest->elems[1] = dest->elems[0];
dest->kids[1] = dest->kids[0]; dest->counts[1] = dest->counts[0];
/* which element to move over */
i = (src->elems[2] ? 2 : src->elems[1] ? 1 : 0);
dest->elems[0] = n->elems[ki];
n->elems[ki] = src->elems[i];
src->elems[i] = NULL;
dest->kids[0] = src->kids[i+1]; dest->counts[0] = src->counts[i+1];
src->kids[i+1] = NULL; src->counts[i+1] = 0;
if (dest->kids[0]) dest->kids[0]->parent = dest;
adjust = dest->counts[0] + 1;
n->counts[ki] -= adjust;
n->counts[ki+1] += adjust;
srclen = n->counts[ki];
if (k) {
LOG((" before: k,index = %d,%d\n", (*k), (*index)));
if ((*k) == ki && (*index) > srclen) {
(*index) -= srclen + 1;
(*k)++;
} else if ((*k) == ki+1) {
(*index) += adjust;
}
LOG((" after: k,index = %d,%d\n", (*k), (*index)));
}
LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
src,
src->kids[0], src->counts[0], src->elems[0],
src->kids[1], src->counts[1], src->elems[1],
src->kids[2], src->counts[2], src->elems[2],
src->kids[3], src->counts[3]));
LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
dest,
dest->kids[0], dest->counts[0], dest->elems[0],
dest->kids[1], dest->counts[1], dest->elems[1],
dest->kids[2], dest->counts[2], dest->elems[2],
dest->kids[3], dest->counts[3]));
}
/*
* Tree transformation used in delete and split: move a subtree
* left, from child ki of a node to the previous child. Update k
* and index so that they still point to the same place in the
* transformed tree. Assumes the destination child is not full, and
* that the source child does have a subtree to spare. Can cope if
* the destination child is undersized.
*
* . B . . C .
* / \ -> / \
* a A b c C d D e [more] a A b B c d D e [more]
*
* . A . . B .
* / \ -> / \
* a b B c C d [more] a A b c C d [more]
*/
static void trans234_subtree_left(node234 *n, int ki, int *k, int *index) {
node234 *src, *dest;
int i, adjust;
src = n->kids[ki];
dest = n->kids[ki-1];
LOG((" trans234_subtree_left(%p, %d):\n", n, ki));
LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
dest,
dest->kids[0], dest->counts[0], dest->elems[0],
dest->kids[1], dest->counts[1], dest->elems[1],
dest->kids[2], dest->counts[2], dest->elems[2],
dest->kids[3], dest->counts[3]));
LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
src,
src->kids[0], src->counts[0], src->elems[0],
src->kids[1], src->counts[1], src->elems[1],
src->kids[2], src->counts[2], src->elems[2],
src->kids[3], src->counts[3]));
/* where in dest to put it */
i = (dest->elems[1] ? 2 : dest->elems[0] ? 1 : 0);
dest->elems[i] = n->elems[ki-1];
n->elems[ki-1] = src->elems[0];
dest->kids[i+1] = src->kids[0]; dest->counts[i+1] = src->counts[0];
if (dest->kids[i+1]) dest->kids[i+1]->parent = dest;
/*
* Move over the rest of the source node.
*/
src->kids[0] = src->kids[1]; src->counts[0] = src->counts[1];
src->elems[0] = src->elems[1];
src->kids[1] = src->kids[2]; src->counts[1] = src->counts[2];
src->elems[1] = src->elems[2];
src->kids[2] = src->kids[3]; src->counts[2] = src->counts[3];
src->elems[2] = NULL;
src->kids[3] = NULL; src->counts[3] = 0;
adjust = dest->counts[i+1] + 1;
n->counts[ki] -= adjust;
n->counts[ki-1] += adjust;
if (k) {
LOG((" before: k,index = %d,%d\n", (*k), (*index)));
if ((*k) == ki) {
(*index) -= adjust;
if ((*index) < 0) {
(*index) += n->counts[ki-1] + 1;
(*k)--;
}
}
LOG((" after: k,index = %d,%d\n", (*k), (*index)));
}
LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" dest %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
dest,
dest->kids[0], dest->counts[0], dest->elems[0],
dest->kids[1], dest->counts[1], dest->elems[1],
dest->kids[2], dest->counts[2], dest->elems[2],
dest->kids[3], dest->counts[3]));
LOG((" src %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
src,
src->kids[0], src->counts[0], src->elems[0],
src->kids[1], src->counts[1], src->elems[1],
src->kids[2], src->counts[2], src->elems[2],
src->kids[3], src->counts[3]));
}
/*
* Tree transformation used in delete and split: merge child nodes
* ki and ki+1 of a node. Update k and index so that they still
* point to the same place in the transformed tree. Assumes both
* children _are_ sufficiently small.
*
* . B . .
* / \ -> |
* a A b c C d a A b B c C d
*
* This routine can also cope with either child being undersized:
*
* . A . .
* / \ -> |
* a b B c a A b B c
*
* . A . .
* / \ -> |
* a b B c C d a A b B c C d
*/
static void trans234_subtree_merge(node234 *n, int ki, int *k, int *index) {
node234 *left, *right;
int i, leftlen, rightlen, lsize, rsize;
left = n->kids[ki]; leftlen = n->counts[ki];
right = n->kids[ki+1]; rightlen = n->counts[ki+1];
LOG((" trans234_subtree_merge(%p, %d):\n", n, ki));
LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" left %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
left,
left->kids[0], left->counts[0], left->elems[0],
left->kids[1], left->counts[1], left->elems[1],
left->kids[2], left->counts[2], left->elems[2],
left->kids[3], left->counts[3]));
LOG((" right %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
right,
right->kids[0], right->counts[0], right->elems[0],
right->kids[1], right->counts[1], right->elems[1],
right->kids[2], right->counts[2], right->elems[2],
right->kids[3], right->counts[3]));
assert(!left->elems[2] && !right->elems[2]); /* neither is large! */
lsize = (left->elems[1] ? 2 : left->elems[0] ? 1 : 0);
rsize = (right->elems[1] ? 2 : right->elems[0] ? 1 : 0);
left->elems[lsize] = n->elems[ki];
for (i = 0; i < rsize+1; i++) {
left->kids[lsize+1+i] = right->kids[i];
left->counts[lsize+1+i] = right->counts[i];
if (left->kids[lsize+1+i])
left->kids[lsize+1+i]->parent = left;
if (i < rsize)
left->elems[lsize+1+i] = right->elems[i];
}
n->counts[ki] += rightlen + 1;
sfree(right);
/*
* Move the rest of n up by one.
*/
for (i = ki+1; i < 3; i++) {
n->kids[i] = n->kids[i+1];
n->counts[i] = n->counts[i+1];
}
for (i = ki; i < 2; i++) {
n->elems[i] = n->elems[i+1];
}
n->kids[3] = NULL;
n->counts[3] = 0;
n->elems[2] = NULL;
if (k) {
LOG((" before: k,index = %d,%d\n", (*k), (*index)));
if ((*k) == ki+1) {
(*k)--;
(*index) += leftlen + 1;
} else if ((*k) > ki+1) {
(*k)--;
}
LOG((" after: k,index = %d,%d\n", (*k), (*index)));
}
LOG((" parent %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" merged %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
left,
left->kids[0], left->counts[0], left->elems[0],
left->kids[1], left->counts[1], left->elems[1],
left->kids[2], left->counts[2], left->elems[2],
left->kids[3], left->counts[3]));
}
/*
* Delete an element e in a 2-3-4 tree. Does not free the element,
* merely removes all links to it from the tree nodes.
*/
static void *delpos234_internal(tree234 *t, int index) {
node234 *n;
void *retval;
int ki, i;
retval = NULL;
n = t->root; /* by assumption this is non-NULL */
LOG(("deleting item %d from tree %p\n", index, t));
while (1) {
node234 *sub;
LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d index=%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3],
index));
if (index <= n->counts[0]) {
ki = 0;
} else if (index -= n->counts[0]+1, index <= n->counts[1]) {
ki = 1;
} else if (index -= n->counts[1]+1, index <= n->counts[2]) {
ki = 2;
} else if (index -= n->counts[2]+1, index <= n->counts[3]) {
ki = 3;
} else {
assert(0); /* can't happen */
}
if (!n->kids[0])
break; /* n is a leaf node; we're here! */
/*
* Check to see if we've found our target element. If so,
* we must choose a new target (we'll use the old target's
* successor, which will be in a leaf), move it into the
* place of the old one, continue down to the leaf and
* delete the old copy of the new target.
*/
if (index == n->counts[ki]) {
node234 *m;
LOG((" found element in internal node, index %d\n", ki));
assert(n->elems[ki]); /* must be a kid _before_ an element */
ki++; index = 0;
for (m = n->kids[ki]; m->kids[0]; m = m->kids[0])
continue;
LOG((" replacing with element \"%s\" from leaf node %p\n",
m->elems[0], m));
retval = n->elems[ki-1];
n->elems[ki-1] = m->elems[0];
}
/*
* Recurse down to subtree ki. If it has only one element,
* we have to do some transformation to start with.
*/
LOG((" moving to subtree %d\n", ki));
sub = n->kids[ki];
if (!sub->elems[1]) {
LOG((" subtree has only one element!\n"));
if (ki > 0 && n->kids[ki-1]->elems[1]) {
/*
* Child ki has only one element, but child
* ki-1 has two or more. So we need to move a
* subtree from ki-1 to ki.
*/
trans234_subtree_right(n, ki-1, &ki, &index);
} else if (ki < 3 && n->kids[ki+1] &&
n->kids[ki+1]->elems[1]) {
/*
* Child ki has only one element, but ki+1 has
* two or more. Move a subtree from ki+1 to ki.
*/
trans234_subtree_left(n, ki+1, &ki, &index);
} else {
/*
* ki is small with only small neighbours. Pick a
* neighbour and merge with it.
*/
trans234_subtree_merge(n, ki>0 ? ki-1 : ki, &ki, &index);
sub = n->kids[ki];
if (!n->elems[0]) {
/*
* The root is empty and needs to be
* removed.
*/
LOG((" shifting root!\n"));
t->root = sub;
sub->parent = NULL;
sfree(n);
n = NULL;
}
}
}
if (n)
n->counts[ki]--;
n = sub;
}
/*
* Now n is a leaf node, and ki marks the element number we
* want to delete. We've already arranged for the leaf to be
* bigger than minimum size, so let's just go to it.
*/
assert(!n->kids[0]);
if (!retval)
retval = n->elems[ki];
for (i = ki; i < 2 && n->elems[i+1]; i++)
n->elems[i] = n->elems[i+1];
n->elems[i] = NULL;
/*
* It's just possible that we have reduced the leaf to zero
* size. This can only happen if it was the root - so destroy
* it and make the tree empty.
*/
if (!n->elems[0]) {
LOG((" removed last element in tree, destroying empty root\n"));
assert(n == t->root);
sfree(n);
t->root = NULL;
}
return retval; /* finished! */
}
void *delpos234(tree234 *t, int index) {
if (index < 0 || index >= countnode234(t->root))
return NULL;
return delpos234_internal(t, index);
}
void *del234(tree234 *t, void *e) {
int index;
if (!findrelpos234(t, e, NULL, REL234_EQ, &index))
return NULL; /* it wasn't in there anyway */
return delpos234_internal(t, index); /* it's there; delete it. */
}
/*
* Join two subtrees together with a separator element between
* them, given their relative height.
*
* (Height<0 means the left tree is shorter, >0 means the right
* tree is shorter, =0 means (duh) they're equal.)
*
* It is assumed that any checks needed on the ordering criterion
* have _already_ been done.
*
* The value returned in `height' is 0 or 1 depending on whether the
* resulting tree is the same height as the original larger one, or
* one higher.
*/
static node234 *join234_internal(node234 *left, void *sep,
node234 *right, int *height) {
node234 *root, *node;
int relht = *height;
int ki;
LOG((" join: joining %p \"%s\" %p, relative height is %d\n",
left, sep, right, relht));
if (relht == 0) {
/*
* The trees are the same height. Create a new one-element
* root containing the separator and pointers to the two
* nodes.
*/
node234 *newroot;
newroot = snew(node234);
newroot->kids[0] = left; newroot->counts[0] = countnode234(left);
newroot->elems[0] = sep;
newroot->kids[1] = right; newroot->counts[1] = countnode234(right);
newroot->elems[1] = NULL;
newroot->kids[2] = NULL; newroot->counts[2] = 0;
newroot->elems[2] = NULL;
newroot->kids[3] = NULL; newroot->counts[3] = 0;
newroot->parent = NULL;
if (left) left->parent = newroot;
if (right) right->parent = newroot;
*height = 1;
LOG((" join: same height, brand new root\n"));
return newroot;
}
/*
* This now works like the addition algorithm on the larger
* tree. We're replacing a single kid pointer with two kid
* pointers separated by an element; if that causes the node to
* overload, we split it in two, move a separator element up to
* the next node, and repeat.
*/
if (relht < 0) {
/*
* Left tree is shorter. Search down the right tree to find
* the pointer we're inserting at.
*/
node = root = right;
while (++relht < 0) {
node = node->kids[0];
}
ki = 0;
right = node->kids[ki];
} else {
/*
* Right tree is shorter; search down the left to find the
* pointer we're inserting at.
*/
node = root = left;
while (--relht > 0) {
if (node->elems[2])
node = node->kids[3];
else if (node->elems[1])
node = node->kids[2];
else
node = node->kids[1];
}
if (node->elems[2])
ki = 3;
else if (node->elems[1])
ki = 2;
else
ki = 1;
left = node->kids[ki];
}
/*
* Now proceed as for addition.
*/
*height = add234_insert(left, sep, right, &root, node, ki);
return root;
}
static int height234(tree234 *t) {
int level = 0;
node234 *n = t->root;
while (n) {
level++;
n = n->kids[0];
}
return level;
}
tree234 *join234(tree234 *t1, tree234 *t2) {
int size2 = countnode234(t2->root);
if (size2 > 0) {
void *element;
int relht;
if (t1->cmp) {
element = index234(t2, 0);
element = findrelpos234(t1, element, NULL, REL234_GE, NULL);
if (element)
return NULL;
}
element = delpos234(t2, 0);
relht = height234(t1) - height234(t2);
t1->root = join234_internal(t1->root, element, t2->root, &relht);
t2->root = NULL;
}
return t1;
}
tree234 *join234r(tree234 *t1, tree234 *t2) {
int size1 = countnode234(t1->root);
if (size1 > 0) {
void *element;
int relht;
if (t2->cmp) {
element = index234(t1, size1-1);
element = findrelpos234(t2, element, NULL, REL234_LE, NULL);
if (element)
return NULL;
}
element = delpos234(t1, size1-1);
relht = height234(t1) - height234(t2);
t2->root = join234_internal(t1->root, element, t2->root, &relht);
t1->root = NULL;
}
return t2;
}
/*
* Split out the first <index> elements in a tree and return a
* pointer to the root node. Leave the root node of the remainder
* in t.
*/
static node234 *split234_internal(tree234 *t, int index) {
node234 *halves[2] = { NULL, NULL }, *n, *sib, *sub;
node234 *lparent, *rparent;
int ki, pki, i, half, lcount, rcount;
n = t->root;
LOG(("splitting tree %p at point %d\n", t, index));
/*
* Easy special cases. After this we have also dealt completely
* with the empty-tree case and we can assume the root exists.
*/
if (index == 0) /* return nothing */
return NULL;
if (index == countnode234(t->root)) { /* return the whole tree */
node234 *ret = t->root;
t->root = NULL;
return ret;
}
/*
* Search down the tree to find the split point.
*/
halves[0] = halves[1] = NULL;
lparent = rparent = NULL;
pki = -1;
while (n) {
LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d index=%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3],
index));
lcount = index;
rcount = countnode234(n) - lcount;
if (index <= n->counts[0]) {
ki = 0;
} else if (index -= n->counts[0]+1, index <= n->counts[1]) {
ki = 1;
} else if (index -= n->counts[1]+1, index <= n->counts[2]) {
ki = 2;
} else {
index -= n->counts[2]+1;
ki = 3;
}
LOG((" splitting at subtree %d\n", ki));
sub = n->kids[ki];
LOG((" splitting at child index %d\n", ki));
/*
* Split the node, put halves[0] on the right of the left
* one and halves[1] on the left of the right one, put the
* new node pointers in halves[0] and halves[1], and go up
* a level.
*/
sib = snew(node234);
for (i = 0; i < 3; i++) {
if (i+ki < 3 && n->elems[i+ki]) {
sib->elems[i] = n->elems[i+ki];
sib->kids[i+1] = n->kids[i+ki+1];
if (sib->kids[i+1]) sib->kids[i+1]->parent = sib;
sib->counts[i+1] = n->counts[i+ki+1];
n->elems[i+ki] = NULL;
n->kids[i+ki+1] = NULL;
n->counts[i+ki+1] = 0;
} else {
sib->elems[i] = NULL;
sib->kids[i+1] = NULL;
sib->counts[i+1] = 0;
}
}
if (lparent) {
lparent->kids[pki] = n;
lparent->counts[pki] = lcount;
n->parent = lparent;
rparent->kids[0] = sib;
rparent->counts[0] = rcount;
sib->parent = rparent;
} else {
halves[0] = n;
n->parent = NULL;
halves[1] = sib;
sib->parent = NULL;
}
lparent = n;
rparent = sib;
pki = ki;
LOG((" left node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
LOG((" right node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
sib,
sib->kids[0], sib->counts[0], sib->elems[0],
sib->kids[1], sib->counts[1], sib->elems[1],
sib->kids[2], sib->counts[2], sib->elems[2],
sib->kids[3], sib->counts[3]));
n = sub;
}
/*
* We've come off the bottom here, so we've successfully split
* the tree into two equally high subtrees. The only problem is
* that some of the nodes down the fault line will be smaller
* than the minimum permitted size. (Since this is a 2-3-4
* tree, that means they'll be zero-element one-child nodes.)
*/
LOG((" fell off bottom, lroot is %p, rroot is %p\n",
halves[0], halves[1]));
assert(halves[0] != NULL);
assert(halves[1] != NULL);
lparent->counts[pki] = rparent->counts[0] = 0;
lparent->kids[pki] = rparent->kids[0] = NULL;
/*
* So now we go back down the tree from each of the two roots,
* fixing up undersize nodes.
*/
for (half = 0; half < 2; half++) {
/*
* Remove the root if it's undersize (it will contain only
* one child pointer, so just throw it away and replace it
* with its child). This might happen several times.
*/
while (halves[half] && !halves[half]->elems[0]) {
LOG((" root %p is undersize, throwing away\n", halves[half]));
halves[half] = halves[half]->kids[0];
sfree(halves[half]->parent);
halves[half]->parent = NULL;
LOG((" new root is %p\n", halves[half]));
}
n = halves[half];
while (n) {
void (*toward)(node234 *n, int ki, int *k, int *index);
int ni, merge;
/*
* Now we have a potentially undersize node on the
* right (if half==0) or left (if half==1). Sort it
* out, by merging with a neighbour or by transferring
* subtrees over. At this time we must also ensure that
* nodes are bigger than minimum, in case we need an
* element to merge two nodes below.
*/
LOG((" node %p: %p/%d \"%s\" %p/%d \"%s\" %p/%d \"%s\" %p/%d\n",
n,
n->kids[0], n->counts[0], n->elems[0],
n->kids[1], n->counts[1], n->elems[1],
n->kids[2], n->counts[2], n->elems[2],
n->kids[3], n->counts[3]));
if (half == 1) {
ki = 0; /* the kid we're interested in */
ni = 1; /* the neighbour */
merge = 0; /* for merge: leftmost of the two */
toward = trans234_subtree_left;
} else {
ki = (n->kids[3] ? 3 : n->kids[2] ? 2 : 1);
ni = ki-1;
merge = ni;
toward = trans234_subtree_right;
}
sub = n->kids[ki];
if (sub && !sub->elems[1]) {
/*
* This node is undersized or minimum-size. If we
* can merge it with its neighbour, we do so;
* otherwise we must be able to transfer subtrees
* over to it until it is greater than minimum
* size.
*/
bool undersized = (!sub->elems[0]);
LOG((" child %d is %ssize\n", ki,
undersized ? "under" : "minimum-"));
LOG((" neighbour is %s\n",
n->kids[ni]->elems[2] ? "large" :
n->kids[ni]->elems[1] ? "medium" : "small"));
if (!n->kids[ni]->elems[1] ||
(undersized && !n->kids[ni]->elems[2])) {
/*
* Neighbour is small, or possibly neighbour is
* medium and we are undersize.
*/
trans234_subtree_merge(n, merge, NULL, NULL);
sub = n->kids[merge];
if (!n->elems[0]) {
/*
* n is empty, and hence must have been the
* root and needs to be removed.
*/
assert(!n->parent);
LOG((" shifting root!\n"));
halves[half] = sub;
halves[half]->parent = NULL;
sfree(n);
}
} else {
/* Neighbour is big enough to move trees over. */
toward(n, ni, NULL, NULL);
if (undersized)
toward(n, ni, NULL, NULL);
}
}
n = sub;
}
}
t->root = halves[1];
return halves[0];
}
tree234 *splitpos234(tree234 *t, int index, bool before) {
tree234 *ret;
node234 *n;
int count;
count = countnode234(t->root);
if (index < 0 || index > count)
return NULL; /* error */
ret = newtree234(t->cmp);
n = split234_internal(t, index);
if (before) {
/* We want to return the ones before the index. */
ret->root = n;
} else {
/*
* We want to keep the ones before the index and return the
* ones after.
*/
ret->root = t->root;
t->root = n;
}
return ret;
}
tree234 *split234(tree234 *t, void *e, cmpfn234 cmp, int rel) {
bool before;
int index;
assert(rel != REL234_EQ);
if (rel == REL234_GT || rel == REL234_GE) {
before = true;
rel = (rel == REL234_GT ? REL234_LE : REL234_LT);
} else {
before = false;
}
if (!findrelpos234(t, e, cmp, rel, &index))
index = 0;
return splitpos234(t, index+1, before);
}
static node234 *copynode234(node234 *n, copyfn234 copyfn, void *copyfnstate) {
int i;
node234 *n2 = snew(node234);
for (i = 0; i < 3; i++) {
if (n->elems[i] && copyfn)
n2->elems[i] = copyfn(copyfnstate, n->elems[i]);
else
n2->elems[i] = n->elems[i];
}
for (i = 0; i < 4; i++) {
if (n->kids[i]) {
n2->kids[i] = copynode234(n->kids[i], copyfn, copyfnstate);
n2->kids[i]->parent = n2;
} else {
n2->kids[i] = NULL;
}
n2->counts[i] = n->counts[i];
}
return n2;
}
tree234 *copytree234(tree234 *t, copyfn234 copyfn, void *copyfnstate) {
tree234 *t2;
t2 = newtree234(t->cmp);
if (t->root) {
t2->root = copynode234(t->root, copyfn, copyfnstate);
t2->root->parent = NULL;
} else
t2->root = NULL;
return t2;
}
#ifdef TEST
/*
* Test code for the 2-3-4 tree. This code maintains an alternative
* representation of the data in the tree, in an array (using the
* obvious and slow insert and delete functions). After each tree
* operation, the verify() function is called, which ensures all
* the tree properties are preserved:
* - node->child->parent always equals node
* - tree->root->parent always equals NULL
* - number of kids == 0 or number of elements + 1;
* - tree has the same depth everywhere
* - every node has at least one element
* - subtree element counts are accurate
* - any NULL kid pointer is accompanied by a zero count
* - in a sorted tree: ordering property between elements of a
* node and elements of its children is preserved
* and also ensures the list represented by the tree is the same
* list it should be. (This last check also doubly verifies the
* ordering properties, because the `same list it should be' is by
* definition correctly ordered. It also ensures all nodes are
* distinct, because the enum functions would get caught in a loop
* if not.)
*/
#include <string.h>
#include <stdarg.h>
#define srealloc realloc
/*
* Error reporting function.
*/
void error(const char *fmt, ...) {
va_list ap;
printf("ERROR: ");
va_start(ap, fmt);
vfprintf(stdout, fmt, ap);
va_end(ap);
printf("\n");
}
/* The array representation of the data. */
void **array;
int arraylen, arraysize;
cmpfn234 cmp;
/* The tree representation of the same data. */
tree234 *tree;
/*
* Routines to provide a diagnostic printout of a tree. Currently
* relies on every element in the tree being a one-character string
* :-)
*/
typedef struct {
char **levels;
} dispctx;
int dispnode(node234 *n, int level, dispctx *ctx) {
if (level == 0) {
int xpos = strlen(ctx->levels[0]);
int len;
if (n->elems[2])
len = sprintf(ctx->levels[0]+xpos, " %s%s%s",
(char *)n->elems[0], (char *)n->elems[1],
(char *)n->elems[2]);
else if (n->elems[1])
len = sprintf(ctx->levels[0]+xpos, " %s%s",
(char *)n->elems[0], (char *)n->elems[1]);
else
len = sprintf(ctx->levels[0]+xpos, " %s",
(char *)n->elems[0]);
return xpos + 1 + (len-1) / 2;
} else {
int xpos[4], nkids;
int nodelen, mypos, myleft, x, i;
xpos[0] = dispnode(n->kids[0], level-3, ctx);
xpos[1] = dispnode(n->kids[1], level-3, ctx);
nkids = 2;
if (n->kids[2]) {
xpos[2] = dispnode(n->kids[2], level-3, ctx);
nkids = 3;
}
if (n->kids[3]) {
xpos[3] = dispnode(n->kids[3], level-3, ctx);
nkids = 4;
}
if (nkids == 4)
mypos = (xpos[1] + xpos[2]) / 2;
else if (nkids == 3)
mypos = xpos[1];
else
mypos = (xpos[0] + xpos[1]) / 2;
nodelen = nkids * 2 - 1;
myleft = mypos - ((nodelen-1)/2);
assert(myleft >= xpos[0]);
assert(myleft + nodelen-1 <= xpos[nkids-1]);
x = strlen(ctx->levels[level]);
while (x <= xpos[0] && x < myleft)
ctx->levels[level][x++] = ' ';
while (x < myleft)
ctx->levels[level][x++] = '_';
if (nkids==4)
x += sprintf(ctx->levels[level]+x, ".%s.%s.%s.",
(char *)n->elems[0], (char *)n->elems[1],
(char *)n->elems[2]);
else if (nkids==3)
x += sprintf(ctx->levels[level]+x, ".%s.%s.",
(char *)n->elems[0], (char *)n->elems[1]);
else
x += sprintf(ctx->levels[level]+x, ".%s.",
(char *)n->elems[0]);
while (x < xpos[nkids-1])
ctx->levels[level][x++] = '_';
ctx->levels[level][x] = '\0';
x = strlen(ctx->levels[level-1]);
for (i = 0; i < nkids; i++) {
int rpos, pos;
rpos = xpos[i];
if (i > 0 && i < nkids-1)
pos = myleft + 2*i;
else
pos = rpos;
if (rpos < pos)
rpos++;
while (x < pos && x < rpos)
ctx->levels[level-1][x++] = ' ';
if (x == pos)
ctx->levels[level-1][x++] = '|';
while (x < pos || x < rpos)
ctx->levels[level-1][x++] = '_';
if (x == pos)
ctx->levels[level-1][x++] = '|';
}
ctx->levels[level-1][x] = '\0';
x = strlen(ctx->levels[level-2]);
for (i = 0; i < nkids; i++) {
int rpos = xpos[i];
while (x < rpos)
ctx->levels[level-2][x++] = ' ';
ctx->levels[level-2][x++] = '|';
}
ctx->levels[level-2][x] = '\0';
return mypos;
}
}
void disptree(tree234 *t) {
dispctx ctx;
char *leveldata;
int width = count234(t);
int ht = height234(t) * 3 - 2;
int i;
if (!t->root) {
printf("[empty tree]\n");
}
leveldata = smalloc(ht * (width+2));
ctx.levels = smalloc(ht * sizeof(char *));
for (i = 0; i < ht; i++) {
ctx.levels[i] = leveldata + i * (width+2);
ctx.levels[i][0] = '\0';
}
(void) dispnode(t->root, ht-1, &ctx);
for (i = ht; i-- ;)
printf("%s\n", ctx.levels[i]);
sfree(ctx.levels);
sfree(leveldata);
}
typedef struct {
int treedepth;
int elemcount;
} chkctx;
int chknode(chkctx *ctx, int level, node234 *node,
void *lowbound, void *highbound) {
int nkids, nelems;
int i;
int count;
/* Count the non-NULL kids. */
for (nkids = 0; nkids < 4 && node->kids[nkids]; nkids++);
/* Ensure no kids beyond the first NULL are non-NULL. */
for (i = nkids; i < 4; i++)
if (node->kids[i]) {
error("node %p: nkids=%d but kids[%d] non-NULL",
node, nkids, i);
} else if (node->counts[i]) {
error("node %p: kids[%d] NULL but count[%d]=%d nonzero",
node, i, i, node->counts[i]);
}
/* Count the non-NULL elements. */
for (nelems = 0; nelems < 3 && node->elems[nelems]; nelems++);
/* Ensure no elements beyond the first NULL are non-NULL. */
for (i = nelems; i < 3; i++)
if (node->elems[i]) {
error("node %p: nelems=%d but elems[%d] non-NULL",
node, nelems, i);
}
if (nkids == 0) {
/*
* If nkids==0, this is a leaf node; verify that the tree
* depth is the same everywhere.
*/
if (ctx->treedepth < 0)
ctx->treedepth = level; /* we didn't know the depth yet */
else if (ctx->treedepth != level)
error("node %p: leaf at depth %d, previously seen depth %d",
node, level, ctx->treedepth);
} else {
/*
* If nkids != 0, then it should be nelems+1, unless nelems
* is 0 in which case nkids should also be 0 (and so we
* shouldn't be in this condition at all).
*/
int shouldkids = (nelems ? nelems+1 : 0);
if (nkids != shouldkids) {
error("node %p: %d elems should mean %d kids but has %d",
node, nelems, shouldkids, nkids);
}
}
/*
* nelems should be at least 1.
*/
if (nelems == 0) {
error("node %p: no elems", node, nkids);
}
/*
* Add nelems to the running element count of the whole tree.
*/
ctx->elemcount += nelems;
/*
* Check ordering property: all elements should be strictly >
* lowbound, strictly < highbound, and strictly < each other in
* sequence. (lowbound and highbound are NULL at edges of tree
* - both NULL at root node - and NULL is considered to be <
* everything and > everything. IYSWIM.)
*/
if (cmp) {
for (i = -1; i < nelems; i++) {
void *lower = (i == -1 ? lowbound : node->elems[i]);
void *higher = (i+1 == nelems ? highbound : node->elems[i+1]);
if (lower && higher && cmp(lower, higher) >= 0) {
error("node %p: kid comparison [%d=%s,%d=%s] failed",
node, i, lower, i+1, higher);
}
}
}
/*
* Check parent pointers: all non-NULL kids should have a
* parent pointer coming back to this node.
*/
for (i = 0; i < nkids; i++)
if (node->kids[i]->parent != node) {
error("node %p kid %d: parent ptr is %p not %p",
node, i, node->kids[i]->parent, node);
}
/*
* Now (finally!) recurse into subtrees.
*/
count = nelems;
for (i = 0; i < nkids; i++) {
void *lower = (i == 0 ? lowbound : node->elems[i-1]);
void *higher = (i >= nelems ? highbound : node->elems[i]);
int subcount = chknode(ctx, level+1, node->kids[i], lower, higher);
if (node->counts[i] != subcount) {
error("node %p kid %d: count says %d, subtree really has %d",
node, i, node->counts[i], subcount);
}
count += subcount;
}
return count;
}
void verifytree(tree234 *tree, void **array, int arraylen) {
chkctx ctx;
int i;
void *p;
ctx.treedepth = -1; /* depth unknown yet */
ctx.elemcount = 0; /* no elements seen yet */
/*
* Verify validity of tree properties.
*/
if (tree->root) {
if (tree->root->parent != NULL)
error("root->parent is %p should be null", tree->root->parent);
chknode(&ctx, 0, tree->root, NULL, NULL);
}
printf("tree depth: %d\n", ctx.treedepth);
/*
* Enumerate the tree and ensure it matches up to the array.
*/
for (i = 0; NULL != (p = index234(tree, i)); i++) {
if (i >= arraylen)
error("tree contains more than %d elements", arraylen);
if (array[i] != p)
error("enum at position %d: array says %s, tree says %s",
i, array[i], p);
}
if (ctx.elemcount != i) {
error("tree really contains %d elements, enum gave %d",
ctx.elemcount, i);
}
if (i < arraylen) {
error("enum gave only %d elements, array has %d", i, arraylen);
}
i = count234(tree);
if (ctx.elemcount != i) {
error("tree really contains %d elements, count234 gave %d",
ctx.elemcount, i);
}
}
void verify(void) { verifytree(tree, array, arraylen); }
void internal_addtest(void *elem, int index, void *realret) {
int i, j;
void *retval;
if (arraysize < arraylen+1) {
arraysize = arraylen+1+256;
array = (array == NULL ? smalloc(arraysize*sizeof(*array)) :
srealloc(array, arraysize*sizeof(*array)));
}
i = index;
/* now i points to the first element >= elem */
retval = elem; /* expect elem returned (success) */
for (j = arraylen; j > i; j--)
array[j] = array[j-1];
array[i] = elem; /* add elem to array */
arraylen++;
if (realret != retval) {
error("add: retval was %p expected %p", realret, retval);
}
verify();
}
void addtest(void *elem) {
int i;
void *realret;
realret = add234(tree, elem);
i = 0;
while (i < arraylen && cmp(elem, array[i]) > 0)
i++;
if (i < arraylen && !cmp(elem, array[i])) {
void *retval = array[i]; /* expect that returned not elem */
if (realret != retval) {
error("add: retval was %p expected %p", realret, retval);
}
} else
internal_addtest(elem, i, realret);
}
void addpostest(void *elem, int i) {
void *realret;
realret = addpos234(tree, elem, i);
internal_addtest(elem, i, realret);
}
void delpostest(int i) {
int index = i;
void *elem = array[i], *ret;
/* i points to the right element */
while (i < arraylen-1) {
array[i] = array[i+1];
i++;
}
arraylen--; /* delete elem from array */
if (tree->cmp)
ret = del234(tree, elem);
else
ret = delpos234(tree, index);
if (ret != elem) {
error("del returned %p, expected %p", ret, elem);
}
verify();
}
void deltest(void *elem) {
int i;
i = 0;
while (i < arraylen && cmp(elem, array[i]) > 0)
i++;
if (i >= arraylen || cmp(elem, array[i]) != 0)
return; /* don't do it! */
delpostest(i);
}
/* A sample data set and test utility. Designed for pseudo-randomness,
* and yet repeatability. */
/*
* This random number generator uses the `portable implementation'
* given in ANSI C99 draft N869. It assumes `unsigned' is 32 bits;
* change it if not.
*/
int randomnumber(unsigned *seed) {
*seed *= 1103515245;
*seed += 12345;
return ((*seed) / 65536) % 32768;
}
int mycmp(void *av, void *bv) {
char const *a = (char const *)av;
char const *b = (char const *)bv;
return strcmp(a, b);
}
const char *const strings_init[] = {
"0", "2", "3", "I", "K", "d", "H", "J", "Q", "N", "n", "q", "j", "i",
"7", "G", "F", "D", "b", "x", "g", "B", "e", "v", "V", "T", "f", "E",
"S", "8", "A", "k", "X", "p", "C", "R", "a", "o", "r", "O", "Z", "u",
"6", "1", "w", "L", "P", "M", "c", "U", "h", "9", "t", "5", "W", "Y",
"m", "s", "l", "4",
#if 0
"a", "ab", "absque", "coram", "de",
"palam", "clam", "cum", "ex", "e",
"sine", "tenus", "pro", "prae",
"banana", "carrot", "cabbage", "broccoli", "onion", "zebra",
"penguin", "blancmange", "pangolin", "whale", "hedgehog",
"giraffe", "peanut", "bungee", "foo", "bar", "baz", "quux",
"murfl", "spoo", "breen", "flarn", "octothorpe",
"snail", "tiger", "elephant", "octopus", "warthog", "armadillo",
"aardvark", "wyvern", "dragon", "elf", "dwarf", "orc", "goblin",
"pixie", "basilisk", "warg", "ape", "lizard", "newt", "shopkeeper",
"wand", "ring", "amulet"
#endif
};
#define NSTR lenof(strings_init)
char *strings[NSTR];
void findtest(void) {
static const int rels[] = {
REL234_EQ, REL234_GE, REL234_LE, REL234_LT, REL234_GT
};
static const char *const relnames[] = {
"EQ", "GE", "LE", "LT", "GT"
};
int i, j, rel, index;
char *p, *ret, *realret, *realret2;
int lo, hi, mid, c;
for (i = 0; i < (int)NSTR; i++) {
p = strings[i];
for (j = 0; j < (int)(sizeof(rels)/sizeof(*rels)); j++) {
rel = rels[j];
lo = 0; hi = arraylen-1;
while (lo <= hi) {
mid = (lo + hi) / 2;
c = strcmp(p, array[mid]);
if (c < 0)
hi = mid-1;
else if (c > 0)
lo = mid+1;
else
break;
}
if (c == 0) {
if (rel == REL234_LT)
ret = (mid > 0 ? array[--mid] : NULL);
else if (rel == REL234_GT)
ret = (mid < arraylen-1 ? array[++mid] : NULL);
else
ret = array[mid];
} else {
assert(lo == hi+1);
if (rel == REL234_LT || rel == REL234_LE) {
mid = hi;
ret = (hi >= 0 ? array[hi] : NULL);
} else if (rel == REL234_GT || rel == REL234_GE) {
mid = lo;
ret = (lo < arraylen ? array[lo] : NULL);
} else
ret = NULL;
}
realret = findrelpos234(tree, p, NULL, rel, &index);
if (realret != ret) {
error("find(\"%s\",%s) gave %s should be %s",
p, relnames[j], realret, ret);
}
if (realret && index != mid) {
error("find(\"%s\",%s) gave %d should be %d",
p, relnames[j], index, mid);
}
if (realret && rel == REL234_EQ) {
realret2 = index234(tree, index);
if (realret2 != realret) {
error("find(\"%s\",%s) gave %s(%d) but %d -> %s",
p, relnames[j], realret, index, index, realret2);
}
}
#if 0
printf("find(\"%s\",%s) gave %s(%d)\n", p, relnames[j],
realret, index);
#endif
}
}
realret = findrelpos234(tree, NULL, NULL, REL234_GT, &index);
if (arraylen && (realret != array[0] || index != 0)) {
error("find(NULL,GT) gave %s(%d) should be %s(0)",
realret, index, array[0]);
} else if (!arraylen && (realret != NULL)) {
error("find(NULL,GT) gave %s(%d) should be NULL",
realret, index);
}
realret = findrelpos234(tree, NULL, NULL, REL234_LT, &index);
if (arraylen && (realret != array[arraylen-1] || index != arraylen-1)) {
error("find(NULL,LT) gave %s(%d) should be %s(0)",
realret, index, array[arraylen-1]);
} else if (!arraylen && (realret != NULL)) {
error("find(NULL,LT) gave %s(%d) should be NULL",
realret, index);
}
}
void splittest(tree234 *tree, void **array, int arraylen) {
int i;
tree234 *tree3, *tree4;
for (i = 0; i <= arraylen; i++) {
tree3 = copytree234(tree, NULL, NULL);
tree4 = splitpos234(tree3, i, false);
verifytree(tree3, array, i);
verifytree(tree4, array+i, arraylen-i);
join234(tree3, tree4);
freetree234(tree4); /* left empty by join */
verifytree(tree3, array, arraylen);
freetree234(tree3);
}
}
int main(void) {
int in[NSTR];
int i, j, k;
int tworoot, tmplen;
unsigned seed = 0;
tree234 *tree2, *tree3, *tree4;
setvbuf(stdout, NULL, _IOLBF, 0);
for (i = 0; i < (int)NSTR; i++)
strings[i] = dupstr(strings_init[i]);
for (i = 0; i < (int)NSTR; i++) in[i] = 0;
array = NULL;
arraylen = arraysize = 0;
tree = newtree234(mycmp);
cmp = mycmp;
verify();
for (i = 0; i < 10000; i++) {
j = randomnumber(&seed);
j %= NSTR;
printf("trial: %d\n", i);
if (in[j]) {
printf("deleting %s (%d)\n", strings[j], j);
deltest(strings[j]);
in[j] = 0;
} else {
printf("adding %s (%d)\n", strings[j], j);
addtest(strings[j]);
in[j] = 1;
}
disptree(tree);
findtest();
}
while (arraylen > 0) {
j = randomnumber(&seed);
j %= arraylen;
deltest(array[j]);
}
freetree234(tree);
/*
* Now try an unsorted tree. We don't really need to test
* delpos234 because we know del234 is based on it, so it's
* already been tested in the above sorted-tree code; but for
* completeness we'll use it to tear down our unsorted tree
* once we've built it.
*/
tree = newtree234(NULL);
cmp = NULL;
verify();
for (i = 0; i < 1000; i++) {
printf("trial: %d\n", i);
j = randomnumber(&seed);
j %= NSTR;
k = randomnumber(&seed);
k %= count234(tree)+1;
printf("adding string %s at index %d\n", strings[j], k);
addpostest(strings[j], k);
}
/*
* While we have this tree in its full form, we'll take a copy
* of it to use in split and join testing.
*/
tree2 = copytree234(tree, NULL, NULL);
verifytree(tree2, array, arraylen);/* check the copy is accurate */
/*
* Split tests. Split the tree at every possible point and
* check the resulting subtrees.
*/
tworoot = (!tree2->root->elems[1]);/* see if it has a 2-root */
splittest(tree2, array, arraylen);
/*
* Now do the split test again, but on a tree that has a 2-root
* (if the previous one didn't) or doesn't (if the previous one
* did).
*/
tmplen = arraylen;
while ((!tree2->root->elems[1]) == tworoot) {
delpos234(tree2, --tmplen);
}
printf("now trying splits on second tree\n");
splittest(tree2, array, tmplen);
freetree234(tree2);
/*
* Back to the main testing of uncounted trees.
*/
while (count234(tree) > 0) {
printf("cleanup: tree size %d\n", count234(tree));
j = randomnumber(&seed);
j %= count234(tree);
printf("deleting string %s from index %d\n", (char *)array[j], j);
delpostest(j);
}
freetree234(tree);
/*
* Finally, do some testing on split/join on _sorted_ trees. At
* the same time, we'll be testing split on very small trees.
*/
tree = newtree234(mycmp);
cmp = mycmp;
arraylen = 0;
for (i = 0; i < 17; i++) {
tree2 = copytree234(tree, NULL, NULL);
splittest(tree2, array, arraylen);
freetree234(tree2);
if (i < 16)
addtest(strings[i]);
}
freetree234(tree);
/*
* Test silly cases of join: join(emptytree, emptytree), and
* also ensure join correctly spots when sorted trees fail the
* ordering constraint.
*/
tree = newtree234(mycmp);
tree2 = newtree234(mycmp);
tree3 = newtree234(mycmp);
tree4 = newtree234(mycmp);
assert(mycmp(strings[0], strings[1]) < 0); /* just in case :-) */
add234(tree2, strings[1]);
add234(tree4, strings[0]);
array[0] = strings[0];
array[1] = strings[1];
verifytree(tree, array, 0);
verifytree(tree2, array+1, 1);
verifytree(tree3, array, 0);
verifytree(tree4, array, 1);
/*
* So:
* - join(tree,tree3) should leave both tree and tree3 unchanged.
* - joinr(tree,tree2) should leave both tree and tree2 unchanged.
* - join(tree4,tree3) should leave both tree3 and tree4 unchanged.
* - join(tree, tree2) should move the element from tree2 to tree.
* - joinr(tree4, tree3) should move the element from tree4 to tree3.
* - join(tree,tree3) should return NULL and leave both unchanged.
* - join(tree3,tree) should work and create a bigger tree in tree3.
*/
assert(tree == join234(tree, tree3));
verifytree(tree, array, 0);
verifytree(tree3, array, 0);
assert(tree2 == join234r(tree, tree2));
verifytree(tree, array, 0);
verifytree(tree2, array+1, 1);
assert(tree4 == join234(tree4, tree3));
verifytree(tree3, array, 0);
verifytree(tree4, array, 1);
assert(tree == join234(tree, tree2));
verifytree(tree, array+1, 1);
verifytree(tree2, array, 0);
assert(tree3 == join234r(tree4, tree3));
verifytree(tree3, array, 1);
verifytree(tree4, array, 0);
assert(NULL == join234(tree, tree3));
verifytree(tree, array+1, 1);
verifytree(tree3, array, 1);
assert(tree3 == join234(tree3, tree));
verifytree(tree3, array, 2);
verifytree(tree, array, 0);
return 0;
}
#endif
#if 0 /* sorted list of strings might be useful */
{
"0", "1", "2", "3", "4", "5", "6", "7", "8", "9", "A", "B", "C", "D", "E", "F", "G", "H", "I", "J", "K", "L", "M", "N", "O", "P", "Q", "R", "S", "T", "U", "V", "W", "X", "Y", "Z", "a", "b", "c", "d", "e", "f", "g", "h", "i", "j", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x",
}
#endif