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Diffstat (limited to 'app/tools/halibut/tree234.c')
-rw-r--r-- | app/tools/halibut/tree234.c | 2197 |
1 files changed, 2197 insertions, 0 deletions
diff --git a/app/tools/halibut/tree234.c b/app/tools/halibut/tree234.c new file mode 100644 index 0000000..26d188e --- /dev/null +++ b/app/tools/halibut/tree234.c @@ -0,0 +1,2197 @@ +/* + * 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" + +#define smalloc malloc +#define sfree free + +#define snew(typ) ( (typ *) smalloc (sizeof (typ)) ) + +#ifdef TEST +#define LOG(x) (printf 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; + 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], *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. + */ + lparent = rparent = NULL; + 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])); + 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. + */ + int 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, int 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) { + int before; + int index; + + assert(rel != REL234_EQ); + + if (rel == REL234_GT || rel == REL234_GE) { + before = 1; + rel = (rel == REL234_GT ? REL234_LE : REL234_LT); + } else { + before = 0; + } + 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 <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); +} + +#define lenof(x) ( sizeof((x)) / sizeof(*(x)) ) + +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, 0); + 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 |