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/*
* $Id: btree.c,v 1.57 2025/01/26 14:47:08 tom Exp $
* Copyright 1997-2024,2025 by Thomas E. Dickey
*
* Maintains a balanced binary tree (aka AVL tree) of unspecified nodes. The
* algorithm is taken from "The Art of Computer Programming -- Volume 3 --
* Sorting and Searching", by Donald Knuth. Knuth presents the insertion and
* search algorithms in assembly language for MIX, and gives an overview of the
* deletion algorithm for the "interested reader".
*
* See 6.2.2 for deletion, as well as notes in 6.2.3 for rebalancing.
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <stdlib.h>
#include <stdio.h>
#include <string.h>
#include <ctype.h>
#if !defined(DEBUG_BTREE) && !defined(NDEBUG)
#define NDEBUG
#endif
#if defined(DEBUG_BTREE)
#if defined(OPT_TRACE) || defined(DOALLOC)
#include "trace.h"
#endif
#ifdef USE_DBMALLOC
#include <dbmalloc.h>
#endif
#ifdef USE_DMALLOC
#include <dmalloc.h>
#endif
#define castalloc(cast,nbytes) (cast *)malloc((size_t) nbytes)
#define for_ever for(;;)
#define beginDisplay() /* nothing */
#define endofDisplay() /* nothing */
#define NonNull(s) ((s == 0) ? "" : s)
#include <time.h>
#else
#include "estruct.h"
#include "edef.h"
#endif
#include <assert.h>
#include "btree.h"
/* definitions to make this simple, like Knuth */
#define LLINK(p) BI_LEFT(p)
#define RLINK(p) BI_RIGHT(p)
#define KEY(p) BI_KEY(p)
#define B(p) (p)->balance
#define COMPARE(a,b) btree_strcmp(a,b)
#define LINK(a,p) (p)->links[(a)>0]
#ifdef DEBUG_BTREE
# ifndef TRACE
# if DEBUG_BTREE > 1
# define TRACE(p) printf p ; fflush(stdout)
# endif
# endif
#elif 1
# undef TRACE
# undef OPT_TRACE
# define OPT_TRACE 0
# define DEBUG_BTREE -1
#else
# define DEBUG_BTREE -1
#endif
#if DEBUG_BTREE > 1
#define TRACE_TREE(s,p) TRACE((s)); btree_printf(p)
#endif
#if DEBUG_BTREE > 2
#define TRACE_SUBTREE(s,h,p) TRACE((s)); dump_nodes(h,p,0)
#endif
#ifndef TRACE
#define TRACE(p) /*nothing */
#endif
#ifndef TRACE_TREE
#define TRACE_TREE(s,p) /*nothing */
#endif
#ifndef TRACE_SUBTREE
#define TRACE_SUBTREE(s,h,p) /*nothing */
#endif
#if DEBUG_BTREE >= 0
static int btree_verify(BI_TREE * funcs, BI_NODE * p);
static void dump_nodes(BI_TREE * funcs, BI_NODE * p, int level);
#endif
/*
* FIXME - this should compare unsigned chars to be completely consistent.
*/
static int
btree_strcmp(const char *a, const char *b)
{
int cmp = strcmp(a, b);
if (cmp < 0)
cmp = -1;
else if (cmp > 0)
cmp = 1;
return cmp;
}
BI_DATA *
btree_insert(BI_TREE * funcs, BI_DATA * data)
{
/* (A1:Initialize) */
BI_NODE *t = &(funcs->head); /* 't' => to the father of 's' */
BI_NODE *s = RLINK(t); /* 's' => to rebalancing point */
BI_NODE *p = RLINK(t); /* 'p' => down the tree */
BI_NODE *q;
BI_NODE *r;
int a;
BI_DATA *value = NULL;
TRACE(("btree_insert(%p,%s)\n", funcs, data->bi_key));
if (p == NULL) {
if ((p = (*funcs->allocat) (data)) == NULL)
return NULL;
RLINK(t) = p;
funcs->depth += 1;
funcs->count += 1;
return &(p->value);
}
/* (A2:Compare) */
while ((a = COMPARE(data->bi_key, KEY(p))) != 0) {
/* (A3,A4: move left/right accordingly) */
if ((q = LINK(a, p)) != NULL) {
value = &(p->value);
if (B(q)) {
t = p;
s = q;
}
p = q;
/* ...continue comparing */
} else {
/* (A5:Insert) */
if ((q = (*funcs->allocat) (data)) == NULL)
return NULL;
LINK(a, p) = q;
funcs->count += 1;
value = &(q->value);
/* (A6:Adjust balance factors) */
/*
* Now the balance factors on nodes between 's' and 'q'
* need to be changed from zero to +/- 1.
*/
if (COMPARE(data->bi_key, KEY(s)) < 0)
r = p = LLINK(s);
else
r = p = RLINK(s);
while (p != q) {
if ((a = COMPARE(data->bi_key, KEY(p))) != 0) {
B(p) = (a < 0) ? -1 : 1;
p = LINK(a, p);
}
}
/* (A7:Balancing act) */
a = (COMPARE(data->bi_key, KEY(s)) < 0) ? -1 : 1;
if (B(s) == 0) {
/* ...the tree has grown higher */
B(s) = a;
funcs->depth += 1;
} else if (B(s) == -a) {
/* ...the tree has gotten more balanced */
B(s) = 0;
} else { /* (B(s) == a) */
assert(B(s) == a);
/* ...the tree has gotten out of balance */
TRACE(("...must rebalance\n"));
if (B(r) == a) {
TRACE(("(A8:Single rotation)\n"));
p = r;
LINK(a, s) = LINK(-a, r);
LINK(-a, r) = s;
B(s) = B(r) = 0;
} else { /* (B(r) == -a) */
assert(B(r) == -a);
TRACE(("(A9: Double rotation)\n"));
p = LINK(-a, r);
assert(p != 0);
if (p == NULL) {
TRACE(("(BUG: null pointer)\n"));
break;
}
LINK(-a, r) = LINK(a, p);
LINK(a, p) = r;
LINK(a, s) = LINK(-a, p);
LINK(-a, p) = s;
TRACE(("r=%s\n", KEY(r)));
TRACE(("s=%s\n", KEY(s)));
TRACE(("B(%s) = %d vs a = %d\n",
KEY(p), B(p), a));
if (B(p) == a) {
B(s) = -a;
B(r) = 0;
} else if (B(p) == 0) {
B(s) = 0;
B(r) = 0;
} else { /* if (B(p) == -a) */
B(s) = 0;
B(r) = a;
}
B(p) = 0;
}
/* A10:Finishing touch */
t->links[(s == RLINK(t))] = p;
}
break;
}
}
return (value);
}
#define MAXSTK 100
typedef struct {
BI_NODE *ptr;
int dir;
} STACKDATA;
static BI_NODE *
single_rotation(BI_NODE * item, int dir)
{
BI_NODE *temp = item->links[!dir];
item->links[!dir] = temp->links[dir];
temp->links[dir] = item;
return temp;
}
static BI_NODE *
double_rotation(BI_NODE * item, int dir)
{
BI_NODE *temp = item->links[!dir]->links[dir];
item->links[!dir]->links[dir] = temp->links[!dir];
temp->links[!dir] = item->links[!dir];
item->links[!dir] = temp;
temp = item->links[!dir];
item->links[!dir] = temp->links[dir];
temp->links[dir] = item;
return temp;
}
static void
readjust_balance(BI_NODE * item, int dir, int balance)
{
BI_NODE *next = item->links[dir];
BI_NODE *last = next->links[!dir];
if (last->balance == 0) {
item->balance = next->balance = 0;
} else if (last->balance == balance) {
item->balance = -balance;
next->balance = 0;
} else {
/* last->balance == -balance */
item->balance = 0;
next->balance = balance;
}
last->balance = 0;
}
static BI_NODE *
remove_balance(BI_NODE * item, int dir, int *done)
{
BI_NODE *next = item->links[!dir];
int balance = (dir == 0) ? -1 : 1;
if (next->balance == -balance) {
item->balance = next->balance = 0;
item = single_rotation(item, dir);
} else if (next->balance == balance) {
readjust_balance(item, !dir, -balance);
item = double_rotation(item, dir);
} else {
/* next->balance == 0 */
item->balance = -balance;
next->balance = balance;
item = single_rotation(item, dir);
*done = 1;
}
return item;
}
int
btree_delete(BI_TREE * funcs, const char *data)
{
TRACE(("btree_delete(%p,%s)\n", funcs, NonNull(data)));
if (funcs->count != 0) {
STACKDATA stack[MAXSTK + 1];
BI_NODE *item;
int top = 0;
int done = 0;
/* (A1:Initialize) */
item = &(funcs->head);
if (item == NULL
|| (item = LINK(1, item)) == NULL) {
TRACE(("...not found @%d\n", __LINE__));
return 0;
}
for (;;) {
/* (A2:Compare) */
if (item == NULL || KEY(item) == NULL) {
TRACE(("...not found @%d\n", __LINE__));
return 0;
} else {
if (COMPARE(KEY(item), data) == 0) {
break;
}
}
/* Push direction and node onto stack */
assert(top < (MAXSTK - 1));
if (top >= MAXSTK) {
TRACE(("(BUG: stack overflow)\n"));
return 0;
}
stack[top].dir = (COMPARE(KEY(item), data) < 0);
stack[top].ptr = item;
++top;
/* (A3,A4: move left/right accordingly) */
item = item->links[stack[top - 1].dir];
}
/* D1: Is RLINK null? */
/* D1.5: Is LLINK null? */
if (item->links[0] == NULL || item->links[1] == NULL) {
/* Which child is not null? */
int dir = item->links[0] == NULL;
/* Fix parent */
if (top != 0)
stack[top - 1].ptr->links[stack[top - 1].dir] = item->links[dir];
else
LINK(1, &(funcs->head)) = item->links[dir];
TRACE(("...freed %p @%d\n", BI_KEY(item), __LINE__));
(*funcs->dealloc) (item);
funcs->count -= 1;
} else {
/* D2: Find the inorder successor */
BI_NODE *child = item->links[1];
/* Save the path */
assert(top < (MAXSTK - 1));
if (top >= (MAXSTK - 1)) {
TRACE(("(BUG: stack overflow)\n"));
return 0;
}
stack[top].dir = 1;
stack[top].ptr = item;
++top;
/* D3: Find null LLINK */
while (child->links[0] != NULL) {
stack[top].dir = 0;
stack[top].ptr = child;
++top;
child = child->links[0];
}
/* Swap data */
(*funcs->exchang) (item, child);
/* Unlink successor and adjust parent */
stack[top - 1].ptr->links[stack[top - 1].ptr == item] =
child->links[1];
/* D4: Free the node */
TRACE(("...freed %p @%d\n", BI_KEY(child), __LINE__));
(*funcs->dealloc) (child);
funcs->count -= 1;
}
/* Walk back up the stack */
while (--top >= 0 && !done) {
/* Update balance factors */
stack[top].ptr->balance += (stack[top].dir != 0) ? -1 : +1;
/* Terminate, or rebalance as necessary */
if (abs(stack[top].ptr->balance) == 1) {
break;
} else if (abs(stack[top].ptr->balance) > 1) {
stack[top].ptr = remove_balance(stack[top].ptr,
stack[top].dir, &done);
/* Fix parent */
if (top != 0) {
stack[top - 1].ptr->links[stack[top - 1].dir] =
stack[top].ptr;
} else {
LINK(1, &(funcs->head)) = stack[0].ptr;
}
}
}
}
TRACE(("...found @%d\n", __LINE__));
return 1;
}
BI_DATA *
btree_search(BI_TREE * funcs, const char *data)
{
/* (A1:Initialize) */
BI_NODE *t = &(funcs->head); /* 't' => to the father of 's' */
BI_NODE *p = RLINK(t); /* 'p' => down the tree */
BI_NODE *q;
int a;
if (p == NULL) {
return NULL;
}
/* (A2:Compare) */
while ((a = COMPARE(data, KEY(p))) != 0) {
/* (A3,A4: move left/right accordingly) */
if ((q = LINK(a, p)) != NULL) {
p = q;
/* ...continue comparing */
} else {
break;
}
}
return a ? NULL : &(p->value);
}
/******************************************************************************/
#ifndef BTREE_VERIFY
#define BTREE_VERIFY 1
#endif
#ifndef BTREE_DRIVER
#define BTREE_DRIVER 1
#endif
#if DEBUG_BTREE >= BTREE_VERIFY
static int
btree_count(BI_NODE * p)
{
int count = 0;
if (p != 0) {
count = 1;
count += btree_count(LLINK(p));
count += btree_count(RLINK(p));
}
return count;
}
#endif
#if DEBUG_BTREE >= BTREE_VERIFY
static int
btree_depth(BI_NODE * p)
{
int depth = 0;
if (p != 0) {
int l, r;
assert(LLINK(p) != p);
assert(RLINK(p) != p);
l = btree_depth(LLINK(p));
r = btree_depth(RLINK(p));
depth = 1;
if (l > r)
depth += l;
else
depth += r;
}
return depth;
}
#endif
static void
dump_nodes(BI_TREE * funcs, BI_NODE * p, int level)
{
if (p) {
dump_nodes(funcs, LLINK(p), level + 1);
(*funcs->display) (p, level);
#if DEBUG_BTREE > 1
if (LLINK(p) != 0
&& COMPARE(KEY(LLINK(p)), KEY(p)) > 0)
TRACE((" OOPS:L"));
if (RLINK(p) != 0
&& COMPARE(KEY(RLINK(p)), KEY(p)) < 0)
TRACE((" OOPS:R"));
TRACE((" %d", btree_depth(p)));
#endif
#if DEBUG_BTREE >= BTREE_DRIVER
printf("\n");
#endif
dump_nodes(funcs, RLINK(p), level + 1);
}
}
/*
* Invoke display function for each node
*/
void
btree_printf(BI_TREE * funcs)
{
TRACE(("TREE, depth %d, count %d\n", funcs->depth, funcs->count));
dump_nodes(funcs, RLINK(&(funcs->head)), 0);
}
/******************************************************************************/
/*
* Find the the matching entry given a name in the tree. Match according to
* the 'mode' parameter:
*
* If it's FALSE then only the first len characters must match and this
* will return the parent of the subtree that contains these entries (so
* that an inorder walk can find the other matches).
*
* Use TRUE to force this to return the first of the ordered list of
* partial matches; we need this behavior for interactive name completion.
*/
BI_NODE *
btree_pmatch(BI_NODE * n, const int mode, const char *name)
{
BI_NODE *m = NULL;
size_t len = strlen(name);
while (n != NULL) {
int cmp;
cmp = strncmp(name, BI_KEY(n), len);
if (cmp == 0) {
if (mode
&& (m = btree_pmatch(BI_LEFT(n), mode, name)) != NULL)
n = m;
return n;
} else if (cmp < 0) {
n = BI_LEFT(n);
} else {
n = BI_RIGHT(n);
}
}
return NULL;
}
/*
* Find the size of the binary-subtree with the matching name.
*/
static int
btree_pcount(BI_NODE * node, char *matchname, size_t len)
{
int left = 0;
int right = 0;
int me = 0;
if (BI_LEFT(node) != NULL) {
left = btree_pcount(BI_LEFT(node), matchname, len);
}
if ((len == 0)
|| (strncmp(BI_KEY(node), matchname, len) == 0))
me = 1;
if (BI_RIGHT(node) != NULL) {
right = btree_pcount(BI_RIGHT(node), matchname, len);
}
return me + left + right;
}
static void
build_parray(BI_NODE * head, char *matchname, size_t len, const char **nptr, int *i)
{
if (BI_LEFT(head) != NULL) {
build_parray(BI_LEFT(head), matchname, len, nptr, i);
}
if ((len == 0)
|| (strncmp(BI_KEY(head), matchname, len) == 0)) {
nptr[*i] = BI_KEY(head);
(*i)++;
}
if (BI_RIGHT(head) != NULL) {
build_parray(BI_RIGHT(head), matchname, len, nptr, i);
}
}
/*
* Build an array of the keys that partially-match the given name to at least
* the given length 'len'.
*/
const char **
btree_parray(BI_TREE * tree, char *name, size_t len)
{
BI_NODE *top;
const char **nptr = NULL;
top = btree_pmatch(BI_RIGHT(&(tree->head)), 0, name);
if (top != NULL) {
int i = 0;
size_t cnt = (size_t) btree_pcount(top, name, len);
beginDisplay();
nptr = castalloc(const char *, sizeof(const char *) * (cnt + 1));
endofDisplay();
if (nptr != NULL) {
build_parray(top, name, len, nptr, &i);
nptr[i] = NULL;
}
}
return nptr;
}
int
btree_freeup(BI_TREE * funcs)
{
TRACE(("Deleting all nodes...\n"));
TRACE_TREE("INITIAL-", funcs);
while (RLINK(&(funcs->head))) {
TRACE(("Try to delete '%s'\n", KEY(RLINK(&(funcs->head)))));
if (!btree_delete(funcs, KEY(RLINK(&(funcs->head))))) {
TRACE(("Try-delete failed\n"));
return 0;
}
#if DEBUG_BTREE >= 0
TRACE_TREE("AFTER-DELETE, ", funcs);
if (!btree_verify(funcs, RLINK(&(funcs->head)))) {
TRACE(("Try-verify failed\n"));
return 0;
}
#endif
}
return 1;
}
/******************************************************************************/
#if DEBUG_BTREE >= 0
static int
btree_verify(BI_TREE * funcs, BI_NODE * p)
{
#if DEBUG_BTREE >= BTREE_VERIFY
int ok = 1;
if (p != 0) {
int root = (p == &(funcs->head));
BI_NODE *l = root ? 0 : LLINK(p);
BI_NODE *r = RLINK(p);
int balance = 0;
int compare = 0;
if (p == RLINK(&(funcs->head))) {
int count = btree_count(p);
if (count != funcs->count) {
ok = 0;
TRACE(("OOPS: Counted %d vs %d in header\n",
count, funcs->count));
}
}
/* verify the balance factor */
if ((balance = btree_depth(r) - btree_depth(l)) != 0) {
if (balance > 0) {
if (balance > 1) {
ok = 0;
TRACE(("OOPS: '%s' is unbalanced: %d\n", KEY(p), balance));
}
balance = 1;
} else {
if (balance < -1) {
ok = 0;
TRACE(("OOPS: '%s' is unbalanced: %d\n", KEY(p), balance));
}
balance = -1;
}
}
if (B(p) != balance) {
ok = 0;
TRACE(("OOPS: Balance '%s' have %d vs %d\n",
KEY(p), B(p), balance));
}
/* verify that the nodes are in correct order */
compare = COMPARE(
(l != 0) ? KEY(l) : "",
(r != 0) ? KEY(r) : "\377");
if (compare >= 0) {
ok = 0;
TRACE(("OOPS: Compare %s, have %d vs -1\n",
KEY(p), compare));
}
/* recur as needed */
ok &= btree_verify(funcs, l);
ok &= btree_verify(funcs, r);
}
return ok;
#else
return 1;
#endif
}
#if DEBUG_BTREE >= BTREE_DRIVER
/******************************************************************************/
#undef typecalloc
#define typecalloc(cast) (cast *)calloc((size_t) 1, sizeof(cast))
static BI_NODE *
new_node(BI_DATA * data)
{
BI_NODE *result = typecalloc(BI_NODE);
result->value = *data;
result->value.bi_key = strdup(data->bi_key); /* DEBUG-only */
return result;
}
static void
old_node(BI_NODE * node)
{
beginDisplay();
free(BI_KEY(node));
free(node);
endofDisplay();
}
static void
dpy_node(BI_NODE * a, int level)
{
while (level-- > 0)
printf(". ");
printf("%s (%d)", KEY(a), B(a));
fflush(stdout);
}
static void
xcg_node(BI_NODE * a, BI_NODE * b)
{
BI_DATA value = a->value;
a->value = b->value;
b->value = value;
}
static BI_TREE text_tree =
{
new_node,
old_node,
dpy_node,
xcg_node,
0,
0,
{
{0, 0}, 0,
{0, 0}
}
};
/******************************************************************************/
#define MAX_VEC 10000
static void
test_btree(FILE *fp)
{
BI_DATA temp;
BI_NODE *top;
int n, m;
int done = 0;
char buffer[BUFSIZ];
int vector[MAX_VEC];
const char **list;
memset(&temp, 0, sizeof(temp));
while (!done && fgets(buffer, sizeof(buffer), fp) != 0) {
char *t = buffer;
char *s = t + strlen(t);
if (s != buffer && *--s == '\n')
*s = 0;
if (isalpha(*buffer))
printf("%s\n", buffer);
switch (*t++) {
case '[':
case ']':
case '!':
case '#':
case '*':
break;
default:
printf("Commands are f(ind) i(nsert), d(elete), l(ist), p(rint), r(andom)\n");
break;
case 'f':
n = (btree_search(&text_tree, t) != 0);
printf("** find(%s) %d\n", t, n);
break;
case 'i':
temp.bi_key = t;
n = (btree_insert(&text_tree, &temp) != 0);
printf("** insert(%s) %d\n", t, n);
break;
case 'd':
n = btree_delete(&text_tree, t);
printf("** delete(%s) %d\n", t, n);
break;
case 'l':
if ((list = btree_parray(&text_tree, t, strlen(t))) != 0) {
printf("** list(%s)\n", t);
for (n = 0; list[n] != 0; n++)
printf("[%d] '%s'\n", n, list[n]);
free((char *) list);
} else
printf("** list(%s) fail\n", t);
break;
case 'L':
if ((top = btree_pmatch(RLINK(&text_tree.head), 1, t)) != 0)
printf("** List(%s) -> '%s'\n", t, KEY(top));
else
printf("** List(%s) fail\n", t);
break;
case 'p':
btree_printf(&text_tree);
break;
case 'r':
srand((unsigned) time(NULL));
for (n = 0; n < MAX_VEC; n++) {
vector[n] = rand();
sprintf(buffer, "%d", vector[n]);
temp.bi_key = buffer;
(void) btree_insert(&text_tree, &temp);
printf("** inserted(%s)\n", buffer);
}
for (m = 0; m < 2; m++)
for (n = 0; n < MAX_VEC; n++) {
unsigned delete = rand() & 1;
char *name = delete ? "delete" : "insert";
int ok;
sprintf(buffer, "%d", vector[n]);
printf("** random %s (%s)\n", name, buffer);
temp.bi_key = buffer;
if (delete)
ok = btree_delete(&text_tree, buffer);
else
ok = btree_insert(&text_tree, &temp) != 0;
if (!btree_verify(&text_tree, RLINK(&(text_tree.head)))) {
printf("OOPS: Random %s-verify '%s' failed\n", name, buffer);
btree_printf(&text_tree);
return;
}
printf("** result: %d\n", ok);
}
break;
case 'q':
done = 1;
break;
}
btree_verify(&text_tree, RLINK(&(text_tree.head)));
}
}
int
main(int argc, char *argv[])
{
if (argc > 1) {
int n;
for (n = 1; n < argc; ++n) {
FILE *fp = fopen(argv[n], "r");
if (fp != 0) {
printf("** read commands from \"%s\"\n", argv[n]);
test_btree(fp);
fclose(fp);
} else {
perror(argv[n]);
}
}
} else {
printf("** read commands from <stdin>\n");
test_btree(stdin);
}
btree_freeup(&text_tree);
return 0;
}
#endif /* DEBUG_BTREE >= BTREE_DRIVER */
#endif /* DEBUG_BTREE */
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