ref: fcf1d274c3f512e6f70cba71832e0ecc97b656d3
dir: /auxiliary/tree234-test.c/
/*
* 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 <assert.h>
#include <stdarg.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "puzzles.h"
#define TREE234_INTERNALS
#include "tree234.h"
/*
* Error reporting function.
*/
static void error(const char *fmt, ...) {
va_list ap;
printf("ERROR: ");
va_start(ap, fmt);
vfprintf(stdout, fmt, ap);
va_end(ap);
printf("\n");
}
/* The array representation of the data. */
static void **array;
static int arraylen, arraysize;
static cmpfn234 cmp;
/* The tree representation of the same data. */
static 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;
static int dispnode(node234 *n, int level, dispctx *ctx) {
if (level == 0) {
int xpos = strlen(ctx->levels[0]);
int len;
if (n->elems[2])
len = sprintf(ctx->levels[0]+xpos, " %s%s%s",
(char *)n->elems[0], (char *)n->elems[1],
(char *)n->elems[2]);
else if (n->elems[1])
len = sprintf(ctx->levels[0]+xpos, " %s%s",
(char *)n->elems[0], (char *)n->elems[1]);
else
len = sprintf(ctx->levels[0]+xpos, " %s",
(char *)n->elems[0]);
return xpos + 1 + (len-1) / 2;
} else {
int xpos[4], nkids;
int nodelen, mypos, myleft, x, i;
xpos[0] = dispnode(n->kids[0], level-3, ctx);
xpos[1] = dispnode(n->kids[1], level-3, ctx);
nkids = 2;
if (n->kids[2]) {
xpos[2] = dispnode(n->kids[2], level-3, ctx);
nkids = 3;
}
if (n->kids[3]) {
xpos[3] = dispnode(n->kids[3], level-3, ctx);
nkids = 4;
}
if (nkids == 4)
mypos = (xpos[1] + xpos[2]) / 2;
else if (nkids == 3)
mypos = xpos[1];
else
mypos = (xpos[0] + xpos[1]) / 2;
nodelen = nkids * 2 - 1;
myleft = mypos - ((nodelen-1)/2);
assert(myleft >= xpos[0]);
assert(myleft + nodelen-1 <= xpos[nkids-1]);
x = strlen(ctx->levels[level]);
while (x <= xpos[0] && x < myleft)
ctx->levels[level][x++] = ' ';
while (x < myleft)
ctx->levels[level][x++] = '_';
if (nkids==4)
x += sprintf(ctx->levels[level]+x, ".%s.%s.%s.",
(char *)n->elems[0], (char *)n->elems[1],
(char *)n->elems[2]);
else if (nkids==3)
x += sprintf(ctx->levels[level]+x, ".%s.%s.",
(char *)n->elems[0], (char *)n->elems[1]);
else
x += sprintf(ctx->levels[level]+x, ".%s.",
(char *)n->elems[0]);
while (x < xpos[nkids-1])
ctx->levels[level][x++] = '_';
ctx->levels[level][x] = '\0';
x = strlen(ctx->levels[level-1]);
for (i = 0; i < nkids; i++) {
int rpos, pos;
rpos = xpos[i];
if (i > 0 && i < nkids-1)
pos = myleft + 2*i;
else
pos = rpos;
if (rpos < pos)
rpos++;
while (x < pos && x < rpos)
ctx->levels[level-1][x++] = ' ';
if (x == pos)
ctx->levels[level-1][x++] = '|';
while (x < pos || x < rpos)
ctx->levels[level-1][x++] = '_';
if (x == pos)
ctx->levels[level-1][x++] = '|';
}
ctx->levels[level-1][x] = '\0';
x = strlen(ctx->levels[level-2]);
for (i = 0; i < nkids; i++) {
int rpos = xpos[i];
while (x < rpos)
ctx->levels[level-2][x++] = ' ';
ctx->levels[level-2][x++] = '|';
}
ctx->levels[level-2][x] = '\0';
return mypos;
}
}
static 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;
static 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;
}
static 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);
}
}
static void verify(void) { verifytree(tree, array, arraylen); }
static 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();
}
static 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);
}
static void addpostest(void *elem, int i) {
void *realret;
realret = addpos234(tree, elem, i);
internal_addtest(elem, i, realret);
}
static 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();
}
static 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.
*/
static int randomnumber(unsigned *seed) {
*seed *= 1103515245;
*seed += 12345;
return ((*seed) / 65536) % 32768;
}
static int mycmp(void *av, void *bv) {
char const *a = (char const *)av;
char const *b = (char const *)bv;
return strcmp(a, b);
}
static const char *const strings_init[] = {
"0", "2", "3", "I", "K", "d", "H", "J", "Q", "N", "n", "q", "j", "i",
"7", "G", "F", "D", "b", "x", "g", "B", "e", "v", "V", "T", "f", "E",
"S", "8", "A", "k", "X", "p", "C", "R", "a", "o", "r", "O", "Z", "u",
"6", "1", "w", "L", "P", "M", "c", "U", "h", "9", "t", "5", "W", "Y",
"m", "s", "l", "4",
#if 0
"a", "ab", "absque", "coram", "de",
"palam", "clam", "cum", "ex", "e",
"sine", "tenus", "pro", "prae",
"banana", "carrot", "cabbage", "broccoli", "onion", "zebra",
"penguin", "blancmange", "pangolin", "whale", "hedgehog",
"giraffe", "peanut", "bungee", "foo", "bar", "baz", "quux",
"murfl", "spoo", "breen", "flarn", "octothorpe",
"snail", "tiger", "elephant", "octopus", "warthog", "armadillo",
"aardvark", "wyvern", "dragon", "elf", "dwarf", "orc", "goblin",
"pixie", "basilisk", "warg", "ape", "lizard", "newt", "shopkeeper",
"wand", "ring", "amulet"
#endif
};
#define NSTR lenof(strings_init)
static char *strings[NSTR];
static 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);
}
}
static void splittest(tree234 *tree, void **array, int arraylen) {
int i;
tree234 *tree3, *tree4;
for (i = 0; i <= arraylen; i++) {
tree3 = copytree234(tree, NULL, NULL);
tree4 = splitpos234(tree3, i, false);
verifytree(tree3, array, i);
verifytree(tree4, array+i, arraylen-i);
join234(tree3, tree4);
freetree234(tree4); /* left empty by join */
verifytree(tree3, array, arraylen);
freetree234(tree3);
}
}
int main(void) {
int in[NSTR];
int i, j, k;
int tworoot, tmplen;
unsigned seed = 0;
tree234 *tree2, *tree3, *tree4;
setvbuf(stdout, NULL, _IOLBF, 0);
for (i = 0; i < (int)NSTR; i++)
strings[i] = dupstr(strings_init[i]);
for (i = 0; i < (int)NSTR; i++) in[i] = 0;
array = NULL;
arraylen = arraysize = 0;
tree = newtree234(mycmp);
cmp = mycmp;
verify();
for (i = 0; i < 10000; i++) {
j = randomnumber(&seed);
j %= NSTR;
printf("trial: %d\n", i);
if (in[j]) {
printf("deleting %s (%d)\n", strings[j], j);
deltest(strings[j]);
in[j] = 0;
} else {
printf("adding %s (%d)\n", strings[j], j);
addtest(strings[j]);
in[j] = 1;
}
disptree(tree);
findtest();
}
while (arraylen > 0) {
j = randomnumber(&seed);
j %= arraylen;
deltest(array[j]);
}
freetree234(tree);
/*
* Now try an unsorted tree. We don't really need to test
* delpos234 because we know del234 is based on it, so it's
* already been tested in the above sorted-tree code; but for
* completeness we'll use it to tear down our unsorted tree
* once we've built it.
*/
tree = newtree234(NULL);
cmp = NULL;
verify();
for (i = 0; i < 1000; i++) {
printf("trial: %d\n", i);
j = randomnumber(&seed);
j %= NSTR;
k = randomnumber(&seed);
k %= count234(tree)+1;
printf("adding string %s at index %d\n", strings[j], k);
addpostest(strings[j], k);
}
/*
* While we have this tree in its full form, we'll take a copy
* of it to use in split and join testing.
*/
tree2 = copytree234(tree, NULL, NULL);
verifytree(tree2, array, arraylen);/* check the copy is accurate */
/*
* Split tests. Split the tree at every possible point and
* check the resulting subtrees.
*/
tworoot = (!tree2->root->elems[1]);/* see if it has a 2-root */
splittest(tree2, array, arraylen);
/*
* Now do the split test again, but on a tree that has a 2-root
* (if the previous one didn't) or doesn't (if the previous one
* did).
*/
tmplen = arraylen;
while ((!tree2->root->elems[1]) == tworoot) {
delpos234(tree2, --tmplen);
}
printf("now trying splits on second tree\n");
splittest(tree2, array, tmplen);
freetree234(tree2);
/*
* Back to the main testing of uncounted trees.
*/
while (count234(tree) > 0) {
printf("cleanup: tree size %d\n", count234(tree));
j = randomnumber(&seed);
j %= count234(tree);
printf("deleting string %s from index %d\n", (char *)array[j], j);
delpostest(j);
}
freetree234(tree);
/*
* Finally, do some testing on split/join on _sorted_ trees. At
* the same time, we'll be testing split on very small trees.
*/
tree = newtree234(mycmp);
cmp = mycmp;
arraylen = 0;
for (i = 0; i < 17; i++) {
tree2 = copytree234(tree, NULL, NULL);
splittest(tree2, array, arraylen);
freetree234(tree2);
if (i < 16)
addtest(strings[i]);
}
freetree234(tree);
/*
* Test silly cases of join: join(emptytree, emptytree), and
* also ensure join correctly spots when sorted trees fail the
* ordering constraint.
*/
tree = newtree234(mycmp);
tree2 = newtree234(mycmp);
tree3 = newtree234(mycmp);
tree4 = newtree234(mycmp);
assert(mycmp(strings[0], strings[1]) < 0); /* just in case :-) */
add234(tree2, strings[1]);
add234(tree4, strings[0]);
array[0] = strings[0];
array[1] = strings[1];
verifytree(tree, array, 0);
verifytree(tree2, array+1, 1);
verifytree(tree3, array, 0);
verifytree(tree4, array, 1);
/*
* So:
* - join(tree,tree3) should leave both tree and tree3 unchanged.
* - joinr(tree,tree2) should leave both tree and tree2 unchanged.
* - join(tree4,tree3) should leave both tree3 and tree4 unchanged.
* - join(tree, tree2) should move the element from tree2 to tree.
* - joinr(tree4, tree3) should move the element from tree4 to tree3.
* - join(tree,tree3) should return NULL and leave both unchanged.
* - join(tree3,tree) should work and create a bigger tree in tree3.
*/
assert(tree == join234(tree, tree3));
verifytree(tree, array, 0);
verifytree(tree3, array, 0);
assert(tree2 == join234r(tree, tree2));
verifytree(tree, array, 0);
verifytree(tree2, array+1, 1);
assert(tree4 == join234(tree4, tree3));
verifytree(tree3, array, 0);
verifytree(tree4, array, 1);
assert(tree == join234(tree, tree2));
verifytree(tree, array+1, 1);
verifytree(tree2, array, 0);
assert(tree3 == join234r(tree4, tree3));
verifytree(tree3, array, 1);
verifytree(tree4, array, 0);
assert(NULL == join234(tree, tree3));
verifytree(tree, array+1, 1);
verifytree(tree3, array, 1);
assert(tree3 == join234(tree3, tree));
verifytree(tree3, array, 2);
verifytree(tree, array, 0);
return 0;
}