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puzzles/tree234.c
Simon Tatham 5f5b284c0b Use C99 bool within source modules. 
This is the main bulk of this boolification work, but although it's
making the largest actual change, it should also be the least
disruptive to anyone interacting with this code base downstream of me,
because it doesn't modify any interface between modules: all the
inter-module APIs were updated one by one in the previous commits.
This just cleans up the code within each individual source file to use
bool in place of int where I think that makes things clearer.
2018-11-13 21:48:24 +00:00

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/*
* 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
#define LOG(x) (printf x)
#define smalloc malloc
#define srealloc realloc
#define sfree free
#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;
while (n) {
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];
}
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(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",
n->elems[0], n->elems[1], n->elems[2]);
else if (n->elems[1])
len = sprintf(ctx->levels[0]+xpos, " %s%s",
n->elems[0], n->elems[1]);
else
len = sprintf(ctx->levels[0]+xpos, " %s",
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.",
n->elems[0], n->elems[1], n->elems[2]);
else if (nkids==3)
x += sprintf(ctx->levels[level]+x, ".%s.%s.",
n->elems[0], n->elems[1]);
else
x += sprintf(ctx->levels[level]+x, ".%s.",
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);
}
char *strings[] = {
"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)
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;
int c;
setvbuf(stdout, NULL, _IOLBF, 0);
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
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