ref: dc688b1f238fd7c343426b76d120e7ab40aa9668
dir: /tree234.c/
/* * tree234.c: reasonably generic counted 2-3-4 tree routines. * * This file is copyright 1999-2001 Simon Tatham. * * Permission is hereby granted, free of charge, to any person * obtaining a copy of this software and associated documentation * files (the "Software"), to deal in the Software without * restriction, including without limitation the rights to use, * copy, modify, merge, publish, distribute, sublicense, and/or * sell copies of the Software, and to permit persons to whom the * Software is furnished to do so, subject to the following * conditions: * * The above copyright notice and this permission notice shall be * included in all copies or substantial portions of the Software. * * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES * OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND * NONINFRINGEMENT. IN NO EVENT SHALL SIMON TATHAM BE LIABLE FOR * ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF * CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE * SOFTWARE. */ #include <stdio.h> #include <stdlib.h> #include <assert.h> #include "tree234.h" #include "puzzles.h" /* for smalloc/sfree */ #ifdef TEST #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. */ 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 <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, 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