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-rw-r--r--src/zix/tree.c716
1 files changed, 716 insertions, 0 deletions
diff --git a/src/zix/tree.c b/src/zix/tree.c
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--- /dev/null
+++ b/src/zix/tree.c
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+/*
+ Copyright 2011-2014 David Robillard <http://drobilla.net>
+
+ Permission to use, copy, modify, and/or distribute this software for any
+ purpose with or without fee is hereby granted, provided that the above
+ copyright notice and this permission notice appear in all copies.
+
+ THIS SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
+ WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
+ MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
+ ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
+ WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
+ ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
+ OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
+*/
+
+#include <assert.h>
+#include <stdint.h>
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+#include "zix/common.h"
+#include "zix/tree.h"
+
+typedef struct ZixTreeNodeImpl ZixTreeNode;
+
+struct ZixTreeImpl {
+ ZixTreeNode* root;
+ ZixDestroyFunc destroy;
+ ZixComparator cmp;
+ void* cmp_data;
+ size_t size;
+ bool allow_duplicates;
+};
+
+struct ZixTreeNodeImpl {
+ void* data;
+ struct ZixTreeNodeImpl* left;
+ struct ZixTreeNodeImpl* right;
+ struct ZixTreeNodeImpl* parent;
+ int_fast8_t balance;
+};
+
+#define MIN(a, b) (((a) < (b)) ? (a) : (b))
+#define MAX(a, b) (((a) > (b)) ? (a) : (b))
+
+// Uncomment these for debugging features
+// #define ZIX_TREE_DUMP 1
+// #define ZIX_TREE_VERIFY 1
+// #define ZIX_TREE_HYPER_VERIFY 1
+
+#if defined(ZIX_TREE_VERIFY) || defined(ZIX_TREE_HYPER_VERIFY)
+# include "tree_debug.h"
+# define ASSERT_BALANCE(n) assert(verify_balance(n))
+#else
+# define ASSERT_BALANCE(n)
+#endif
+
+#ifdef ZIX_TREE_DUMP
+# include "tree_debug.h"
+# define DUMP(t) zix_tree_print(t->root, 0)
+# define DEBUG_PRINTF(fmt, ...) printf(fmt, __VA_ARGS__)
+#else
+# define DUMP(t)
+# define DEBUG_PRINTF(fmt, ...)
+#endif
+
+ZIX_API ZixTree*
+zix_tree_new(bool allow_duplicates,
+ ZixComparator cmp,
+ void* cmp_data,
+ ZixDestroyFunc destroy)
+{
+ ZixTree* t = (ZixTree*)malloc(sizeof(ZixTree));
+ t->root = NULL;
+ t->destroy = destroy;
+ t->cmp = cmp;
+ t->cmp_data = cmp_data;
+ t->size = 0;
+ t->allow_duplicates = allow_duplicates;
+ return t;
+}
+
+ZIX_PRIVATE void
+zix_tree_free_rec(ZixTree* t, ZixTreeNode* n)
+{
+ if (n) {
+ zix_tree_free_rec(t, n->left);
+ zix_tree_free_rec(t, n->right);
+ if (t->destroy) {
+ t->destroy(n->data);
+ }
+ free(n);
+ }
+}
+
+ZIX_API void
+zix_tree_free(ZixTree* t)
+{
+ if (t) {
+ zix_tree_free_rec(t, t->root);
+ free(t);
+ }
+}
+
+ZIX_API size_t
+zix_tree_size(const ZixTree* t)
+{
+ return t->size;
+}
+
+ZIX_PRIVATE void
+rotate(ZixTreeNode* p, ZixTreeNode* q)
+{
+ assert(q->parent == p);
+ assert(p->left == q || p->right == q);
+
+ q->parent = p->parent;
+ if (q->parent) {
+ if (q->parent->left == p) {
+ q->parent->left = q;
+ } else {
+ q->parent->right = q;
+ }
+ }
+
+ if (p->right == q) {
+ // Rotate left
+ p->right = q->left;
+ q->left = p;
+ if (p->right) {
+ p->right->parent = p;
+ }
+ } else {
+ // Rotate right
+ assert(p->left == q);
+ p->left = q->right;
+ q->right = p;
+ if (p->left) {
+ p->left->parent = p;
+ }
+ }
+
+ p->parent = q;
+}
+
+/**
+ * Rotate left about `p`.
+ *
+ * p q
+ * / \ / \
+ * A q => p C
+ * / \ / \
+ * B C A B
+ */
+ZIX_PRIVATE ZixTreeNode*
+rotate_left(ZixTreeNode* p, int* height_change)
+{
+ ZixTreeNode* const q = p->right;
+ *height_change = (q->balance == 0) ? 0 : -1;
+
+ DEBUG_PRINTF("LL %ld\n", (intptr_t)p->data);
+
+ assert(p->balance == 2);
+ assert(q->balance == 0 || q->balance == 1);
+
+ rotate(p, q);
+
+ // p->balance -= 1 + MAX(0, q->balance);
+ // q->balance -= 1 - MIN(0, p->balance);
+ --q->balance;
+ p->balance = -(q->balance);
+
+ ASSERT_BALANCE(p);
+ ASSERT_BALANCE(q);
+ return q;
+}
+
+/**
+ * Rotate right about `p`.
+ *
+ * p q
+ * / \ / \
+ * q C => A p
+ * / \ / \
+ * A B B C
+ *
+ */
+ZIX_PRIVATE ZixTreeNode*
+rotate_right(ZixTreeNode* p, int* height_change)
+{
+ ZixTreeNode* const q = p->left;
+ *height_change = (q->balance == 0) ? 0 : -1;
+
+ DEBUG_PRINTF("RR %ld\n", (intptr_t)p->data);
+
+ assert(p->balance == -2);
+ assert(q->balance == 0 || q->balance == -1);
+
+ rotate(p, q);
+
+ // p->balance += 1 - MIN(0, q->balance);
+ // q->balance += 1 + MAX(0, p->balance);
+ ++q->balance;
+ p->balance = -(q->balance);
+
+ ASSERT_BALANCE(p);
+ ASSERT_BALANCE(q);
+ return q;
+}
+
+/**
+ * Rotate left about `p->left` then right about `p`.
+ *
+ * p r
+ * / \ / \
+ * q D => q p
+ * / \ / \ / \
+ * A r A B C D
+ * / \
+ * B C
+ *
+ */
+ZIX_PRIVATE ZixTreeNode*
+rotate_left_right(ZixTreeNode* p, int* height_change)
+{
+ ZixTreeNode* const q = p->left;
+ ZixTreeNode* const r = q->right;
+
+ assert(p->balance == -2);
+ assert(q->balance == 1);
+ assert(r->balance == -1 || r->balance == 0 || r->balance == 1);
+
+ DEBUG_PRINTF("LR %ld P: %2d Q: %2d R: %2d\n",
+ (intptr_t)p->data, p->balance, q->balance, r->balance);
+
+ rotate(q, r);
+ rotate(p, r);
+
+ q->balance -= 1 + MAX(0, r->balance);
+ p->balance += 1 - MIN(MIN(0, r->balance) - 1, r->balance + q->balance);
+ // r->balance += MAX(0, p->balance) + MIN(0, q->balance);
+
+ // p->balance = (p->left && p->right) ? -MIN(r->balance, 0) : 0;
+ // q->balance = - MAX(r->balance, 0);
+ r->balance = 0;
+
+ *height_change = -1;
+
+ ASSERT_BALANCE(p);
+ ASSERT_BALANCE(q);
+ ASSERT_BALANCE(r);
+ return r;
+}
+
+/**
+ * Rotate right about `p->right` then right about `p`.
+ *
+ * p r
+ * / \ / \
+ * A q => p q
+ * / \ / \ / \
+ * r D A B C D
+ * / \
+ * B C
+ *
+ */
+ZIX_PRIVATE ZixTreeNode*
+rotate_right_left(ZixTreeNode* p, int* height_change)
+{
+ ZixTreeNode* const q = p->right;
+ ZixTreeNode* const r = q->left;
+
+ assert(p->balance == 2);
+ assert(q->balance == -1);
+ assert(r->balance == -1 || r->balance == 0 || r->balance == 1);
+
+ DEBUG_PRINTF("RL %ld P: %2d Q: %2d R: %2d\n",
+ (intptr_t)p->data, p->balance, q->balance, r->balance);
+
+ rotate(q, r);
+ rotate(p, r);
+
+ q->balance += 1 - MIN(0, r->balance);
+ p->balance -= 1 + MAX(MAX(0, r->balance) + 1, r->balance + q->balance);
+ // r->balance += MAX(0, q->balance) + MIN(0, p->balance);
+
+ // p->balance = (p->left && p->right) ? -MAX(r->balance, 0) : 0;
+ // q->balance = - MIN(r->balance, 0);
+ r->balance = 0;
+ // assert(r->balance == 0);
+
+ *height_change = -1;
+
+ ASSERT_BALANCE(p);
+ ASSERT_BALANCE(q);
+ ASSERT_BALANCE(r);
+ return r;
+}
+
+ZIX_PRIVATE ZixTreeNode*
+zix_tree_rebalance(ZixTree* t, ZixTreeNode* node, int* height_change)
+{
+#ifdef ZIX_TREE_HYPER_VERIFY
+ const size_t old_height = height(node);
+#endif
+ DEBUG_PRINTF("REBALANCE %ld (%d)\n", (intptr_t)node->data, node->balance);
+ *height_change = 0;
+ const bool is_root = !node->parent;
+ assert((is_root && t->root == node) || (!is_root && t->root != node));
+ ZixTreeNode* replacement = node;
+ if (node->balance == -2) {
+ assert(node->left);
+ if (node->left->balance == 1) {
+ replacement = rotate_left_right(node, height_change);
+ } else {
+ replacement = rotate_right(node, height_change);
+ }
+ } else if (node->balance == 2) {
+ assert(node->right);
+ if (node->right->balance == -1) {
+ replacement = rotate_right_left(node, height_change);
+ } else {
+ replacement = rotate_left(node, height_change);
+ }
+ }
+ if (is_root) {
+ assert(!replacement->parent);
+ t->root = replacement;
+ }
+ DUMP(t);
+#ifdef ZIX_TREE_HYPER_VERIFY
+ assert(old_height + *height_change == height(replacement));
+#endif
+ return replacement;
+}
+
+ZIX_API ZixStatus
+zix_tree_insert(ZixTree* t, void* e, ZixTreeIter** ti)
+{
+ DEBUG_PRINTF("**** INSERT %ld\n", (intptr_t)e);
+ int cmp = 0;
+ ZixTreeNode* n = t->root;
+ ZixTreeNode* p = NULL;
+
+ // Find the parent p of e
+ while (n) {
+ p = n;
+ cmp = t->cmp(e, n->data, t->cmp_data);
+ if (cmp < 0) {
+ n = n->left;
+ } else if (cmp > 0) {
+ n = n->right;
+ } else if (t->allow_duplicates) {
+ n = n->right;
+ } else {
+ if (ti) {
+ *ti = n;
+ }
+ DEBUG_PRINTF("%ld EXISTS!\n", (intptr_t)e);
+ return ZIX_STATUS_EXISTS;
+ }
+ }
+
+ // Allocate a new node n
+ if (!(n = (ZixTreeNode*)malloc(sizeof(ZixTreeNode)))) {
+ return ZIX_STATUS_NO_MEM;
+ }
+ memset(n, '\0', sizeof(ZixTreeNode));
+ n->data = e;
+ n->balance = 0;
+ if (ti) {
+ *ti = n;
+ }
+
+ bool p_height_increased = false;
+
+ // Make p the parent of n
+ n->parent = p;
+ if (!p) {
+ t->root = n;
+ } else {
+ if (cmp < 0) {
+ assert(!p->left);
+ assert(p->balance == 0 || p->balance == 1);
+ p->left = n;
+ --p->balance;
+ p_height_increased = !p->right;
+ } else {
+ assert(!p->right);
+ assert(p->balance == 0 || p->balance == -1);
+ p->right = n;
+ ++p->balance;
+ p_height_increased = !p->left;
+ }
+ }
+
+ DUMP(t);
+
+ // Rebalance if necessary (at most 1 rotation)
+ assert(!p || p->balance == -1 || p->balance == 0 || p->balance == 1);
+ if (p && p_height_increased) {
+ int height_change = 0;
+ for (ZixTreeNode* i = p; i && i->parent; i = i->parent) {
+ if (i == i->parent->left) {
+ if (--i->parent->balance == -2) {
+ zix_tree_rebalance(t, i->parent, &height_change);
+ break;
+ }
+ } else {
+ assert(i == i->parent->right);
+ if (++i->parent->balance == 2) {
+ zix_tree_rebalance(t, i->parent, &height_change);
+ break;
+ }
+ }
+
+ if (i->parent->balance == 0) {
+ break;
+ }
+ }
+ }
+
+ DUMP(t);
+
+ ++t->size;
+
+#ifdef ZIX_TREE_VERIFY
+ if (!verify(t, t->root)) {
+ return ZIX_STATUS_ERROR;
+ }
+#endif
+
+ return ZIX_STATUS_SUCCESS;
+}
+
+ZIX_API ZixStatus
+zix_tree_remove(ZixTree* t, ZixTreeIter* ti)
+{
+ ZixTreeNode* const n = ti;
+ ZixTreeNode** pp = NULL; // parent pointer
+ ZixTreeNode* to_balance = n->parent; // lowest node to balance
+ int8_t d_balance = 0; // delta(balance) for n->parent
+
+ DEBUG_PRINTF("*** REMOVE %ld\n", (intptr_t)n->data);
+
+ if ((n == t->root) && !n->left && !n->right) {
+ t->root = NULL;
+ if (t->destroy) {
+ t->destroy(n->data);
+ }
+ free(n);
+ --t->size;
+ assert(t->size == 0);
+ return ZIX_STATUS_SUCCESS;
+ }
+
+ // Set pp to the parent pointer to n, if applicable
+ if (n->parent) {
+ assert(n->parent->left == n || n->parent->right == n);
+ if (n->parent->left == n) { // n is left child
+ pp = &n->parent->left;
+ d_balance = 1;
+ } else { // n is right child
+ assert(n->parent->right == n);
+ pp = &n->parent->right;
+ d_balance = -1;
+ }
+ }
+
+ assert(!pp || *pp == n);
+
+ int height_change = 0;
+ if (!n->left && !n->right) {
+ // n is a leaf, just remove it
+ if (pp) {
+ *pp = NULL;
+ to_balance = n->parent;
+ height_change = (!n->parent->left && !n->parent->right) ? -1 : 0;
+ }
+ } else if (!n->left) {
+ // Replace n with right (only) child
+ if (pp) {
+ *pp = n->right;
+ to_balance = n->parent;
+ } else {
+ t->root = n->right;
+ }
+ n->right->parent = n->parent;
+ height_change = -1;
+ } else if (!n->right) {
+ // Replace n with left (only) child
+ if (pp) {
+ *pp = n->left;
+ to_balance = n->parent;
+ } else {
+ t->root = n->left;
+ }
+ n->left->parent = n->parent;
+ height_change = -1;
+ } else {
+ // Replace n with in-order successor (leftmost child of right subtree)
+ ZixTreeNode* replace = n->right;
+ while (replace->left) {
+ assert(replace->left->parent == replace);
+ replace = replace->left;
+ }
+
+ // Remove replace from parent (replace_p)
+ if (replace->parent->left == replace) {
+ height_change = replace->parent->right ? 0 : -1;
+ d_balance = 1;
+ to_balance = replace->parent;
+ replace->parent->left = replace->right;
+ } else {
+ assert(replace->parent == n);
+ height_change = replace->parent->left ? 0 : -1;
+ d_balance = -1;
+ to_balance = replace->parent;
+ replace->parent->right = replace->right;
+ }
+
+ if (to_balance == n) {
+ to_balance = replace;
+ }
+
+ if (replace->right) {
+ replace->right->parent = replace->parent;
+ }
+
+ replace->balance = n->balance;
+
+ // Swap node to delete with replace
+ if (pp) {
+ *pp = replace;
+ } else {
+ assert(t->root == n);
+ t->root = replace;
+ }
+ replace->parent = n->parent;
+ replace->left = n->left;
+ n->left->parent = replace;
+ replace->right = n->right;
+ if (n->right) {
+ n->right->parent = replace;
+ }
+
+ assert(!replace->parent
+ || replace->parent->left == replace
+ || replace->parent->right == replace);
+ }
+
+ // Rebalance starting at to_balance upwards.
+ for (ZixTreeNode* i = to_balance; i; i = i->parent) {
+ i->balance += d_balance;
+ if (d_balance == 0 || i->balance == -1 || i->balance == 1) {
+ break;
+ }
+
+ assert(i != n);
+ i = zix_tree_rebalance(t, i, &height_change);
+ if (i->balance == 0) {
+ height_change = -1;
+ }
+
+ if (i->parent) {
+ if (i == i->parent->left) {
+ d_balance = height_change * -1;
+ } else {
+ assert(i == i->parent->right);
+ d_balance = height_change;
+ }
+ }
+ }
+
+ DUMP(t);
+
+ if (t->destroy) {
+ t->destroy(n->data);
+ }
+ free(n);
+
+ --t->size;
+
+#ifdef ZIX_TREE_VERIFY
+ if (!verify(t, t->root)) {
+ return ZIX_STATUS_ERROR;
+ }
+#endif
+
+ return ZIX_STATUS_SUCCESS;
+}
+
+ZIX_API ZixStatus
+zix_tree_find(const ZixTree* t, const void* e, ZixTreeIter** ti)
+{
+ ZixTreeNode* n = t->root;
+ while (n) {
+ const int cmp = t->cmp(e, n->data, t->cmp_data);
+ if (cmp == 0) {
+ break;
+ } else if (cmp < 0) {
+ n = n->left;
+ } else {
+ n = n->right;
+ }
+ }
+
+ *ti = n;
+ return (n) ? ZIX_STATUS_SUCCESS : ZIX_STATUS_NOT_FOUND;
+}
+
+ZIX_API void*
+zix_tree_get(const ZixTreeIter* ti)
+{
+ return ti ? ti->data : NULL;
+}
+
+ZIX_API ZixTreeIter*
+zix_tree_begin(ZixTree* t)
+{
+ if (!t->root) {
+ return NULL;
+ }
+
+ ZixTreeNode* n = t->root;
+ while (n->left) {
+ n = n->left;
+ }
+ return n;
+}
+
+ZIX_API ZixTreeIter*
+zix_tree_end(ZixTree* t)
+{
+ return NULL;
+}
+
+ZIX_API ZixTreeIter*
+zix_tree_rbegin(ZixTree* t)
+{
+ if (!t->root) {
+ return NULL;
+ }
+
+ ZixTreeNode* n = t->root;
+ while (n->right) {
+ n = n->right;
+ }
+ return n;
+}
+
+ZIX_API ZixTreeIter*
+zix_tree_rend(ZixTree* t)
+{
+ return NULL;
+}
+
+ZIX_API bool
+zix_tree_iter_is_end(const ZixTreeIter* i)
+{
+ return !i;
+}
+
+ZIX_API bool
+zix_tree_iter_is_rend(const ZixTreeIter* i)
+{
+ return !i;
+}
+
+ZIX_API ZixTreeIter*
+zix_tree_iter_next(ZixTreeIter* i)
+{
+ if (!i) {
+ return NULL;
+ }
+
+ if (i->right) {
+ i = i->right;
+ while (i->left) {
+ i = i->left;
+ }
+ } else {
+ while (i->parent && i->parent->right == i) { // i is a right child
+ i = i->parent;
+ }
+
+ i = i->parent;
+ }
+
+ return i;
+}
+
+ZIX_API ZixTreeIter*
+zix_tree_iter_prev(ZixTreeIter* i)
+{
+ if (!i) {
+ return NULL;
+ }
+
+ if (i->left) {
+ i = i->left;
+ while (i->right) {
+ i = i->right;
+ }
+ } else {
+ while (i->parent && i->parent->left == i) { // i is a left child
+ i = i->parent;
+ }
+
+ i = i->parent;
+ }
+
+ return i;
+}
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