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+/*
+ * GLIB - Library of useful routines for C programming
+ * Copyright (C) 1995-1997  Peter Mattis, Spencer Kimball and Josh MacDonald
+ *
+ * SPDX-License-Identifier: LGPL-2.1-or-later
+ *
+ * This library is free software; you can redistribute it and/or
+ * modify it under the terms of the GNU Lesser General Public
+ * License as published by the Free Software Foundation; either
+ * version 2.1 of the License, or (at your option) any later version.
+ *
+ * This library is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+ * Lesser General Public License for more details.
+ *
+ * You should have received a copy of the GNU Lesser General Public
+ * License along with this library; if not, see <http://www.gnu.org/licenses/>.
+ */
+
+/*
+ * Modified by the GLib Team and others 1997-2000.  See the AUTHORS
+ * file for a list of people on the GLib Team.  See the ChangeLog
+ * files for a list of changes.  These files are distributed with
+ * GLib at ftp://ftp.gtk.org/pub/gtk/.
+ */
+
+/*
+ * MT safe
+ */
+
+#include "qemu/osdep.h"
+#include "qemu/qtree.h"
+
+/**
+ * SECTION:trees-binary
+ * @title: Balanced Binary Trees
+ * @short_description: a sorted collection of key/value pairs optimized
+ *                     for searching and traversing in order
+ *
+ * The #QTree structure and its associated functions provide a sorted
+ * collection of key/value pairs optimized for searching and traversing
+ * in order. This means that most of the operations  (access, search,
+ * insertion, deletion, ...) on #QTree are O(log(n)) in average and O(n)
+ * in worst case for time complexity. But, note that maintaining a
+ * balanced sorted #QTree of n elements is done in time O(n log(n)).
+ *
+ * To create a new #QTree use q_tree_new().
+ *
+ * To insert a key/value pair into a #QTree use q_tree_insert()
+ * (O(n log(n))).
+ *
+ * To remove a key/value pair use q_tree_remove() (O(n log(n))).
+ *
+ * To look up the value corresponding to a given key, use
+ * q_tree_lookup() and q_tree_lookup_extended().
+ *
+ * To find out the number of nodes in a #QTree, use q_tree_nnodes(). To
+ * get the height of a #QTree, use q_tree_height().
+ *
+ * To traverse a #QTree, calling a function for each node visited in
+ * the traversal, use q_tree_foreach().
+ *
+ * To destroy a #QTree, use q_tree_destroy().
+ **/
+
+#define MAX_GTREE_HEIGHT 40
+
+/**
+ * QTree:
+ *
+ * The QTree struct is an opaque data structure representing a
+ * [balanced binary tree][glib-Balanced-Binary-Trees]. It should be
+ * accessed only by using the following functions.
+ */
+struct _QTree {
+    QTreeNode        *root;
+    GCompareDataFunc  key_compare;
+    GDestroyNotify    key_destroy_func;
+    GDestroyNotify    value_destroy_func;
+    gpointer          key_compare_data;
+    guint             nnodes;
+    gint              ref_count;
+};
+
+struct _QTreeNode {
+    gpointer   key;         /* key for this node */
+    gpointer   value;       /* value stored at this node */
+    QTreeNode *left;        /* left subtree */
+    QTreeNode *right;       /* right subtree */
+    gint8      balance;     /* height (right) - height (left) */
+    guint8     left_child;
+    guint8     right_child;
+};
+
+
+static QTreeNode *q_tree_node_new(gpointer       key,
+                                  gpointer       value);
+static QTreeNode *q_tree_insert_internal(QTree *tree,
+                                         gpointer key,
+                                         gpointer value,
+                                         gboolean replace);
+static gboolean   q_tree_remove_internal(QTree         *tree,
+                                         gconstpointer  key,
+                                         gboolean       steal);
+static QTreeNode *q_tree_node_balance(QTreeNode     *node);
+static QTreeNode *q_tree_find_node(QTree         *tree,
+                                   gconstpointer  key);
+static QTreeNode *q_tree_node_search(QTreeNode *node,
+                                     GCompareFunc search_func,
+                                     gconstpointer data);
+static QTreeNode *q_tree_node_rotate_left(QTreeNode     *node);
+static QTreeNode *q_tree_node_rotate_right(QTreeNode     *node);
+#ifdef Q_TREE_DEBUG
+static void       q_tree_node_check(QTreeNode     *node);
+#endif
+
+static QTreeNode*
+q_tree_node_new(gpointer key,
+                gpointer value)
+{
+    QTreeNode *node = g_new(QTreeNode, 1);
+
+    node->balance = 0;
+    node->left = NULL;
+    node->right = NULL;
+    node->left_child = FALSE;
+    node->right_child = FALSE;
+    node->key = key;
+    node->value = value;
+
+    return node;
+}
+
+/**
+ * q_tree_new:
+ * @key_compare_func: the function used to order the nodes in the #QTree.
+ *   It should return values similar to the standard strcmp() function -
+ *   0 if the two arguments are equal, a negative value if the first argument
+ *   comes before the second, or a positive value if the first argument comes
+ *   after the second.
+ *
+ * Creates a new #QTree.
+ *
+ * Returns: a newly allocated #QTree
+ */
+QTree *
+q_tree_new(GCompareFunc key_compare_func)
+{
+    g_return_val_if_fail(key_compare_func != NULL, NULL);
+
+    return q_tree_new_full((GCompareDataFunc) key_compare_func, NULL,
+                           NULL, NULL);
+}
+
+/**
+ * q_tree_new_with_data:
+ * @key_compare_func: qsort()-style comparison function
+ * @key_compare_data: data to pass to comparison function
+ *
+ * Creates a new #QTree with a comparison function that accepts user data.
+ * See q_tree_new() for more details.
+ *
+ * Returns: a newly allocated #QTree
+ */
+QTree *
+q_tree_new_with_data(GCompareDataFunc key_compare_func,
+                     gpointer         key_compare_data)
+{
+    g_return_val_if_fail(key_compare_func != NULL, NULL);
+
+    return q_tree_new_full(key_compare_func, key_compare_data,
+                           NULL, NULL);
+}
+
+/**
+ * q_tree_new_full:
+ * @key_compare_func: qsort()-style comparison function
+ * @key_compare_data: data to pass to comparison function
+ * @key_destroy_func: a function to free the memory allocated for the key
+ *   used when removing the entry from the #QTree or %NULL if you don't
+ *   want to supply such a function
+ * @value_destroy_func: a function to free the memory allocated for the
+ *   value used when removing the entry from the #QTree or %NULL if you
+ *   don't want to supply such a function
+ *
+ * Creates a new #QTree like q_tree_new() and allows to specify functions
+ * to free the memory allocated for the key and value that get called when
+ * removing the entry from the #QTree.
+ *
+ * Returns: a newly allocated #QTree
+ */
+QTree *
+q_tree_new_full(GCompareDataFunc key_compare_func,
+                gpointer         key_compare_data,
+                GDestroyNotify   key_destroy_func,
+                GDestroyNotify   value_destroy_func)
+{
+    QTree *tree;
+
+    g_return_val_if_fail(key_compare_func != NULL, NULL);
+
+    tree = g_new(QTree, 1);
+    tree->root               = NULL;
+    tree->key_compare        = key_compare_func;
+    tree->key_destroy_func   = key_destroy_func;
+    tree->value_destroy_func = value_destroy_func;
+    tree->key_compare_data   = key_compare_data;
+    tree->nnodes             = 0;
+    tree->ref_count          = 1;
+
+    return tree;
+}
+
+/**
+ * q_tree_node_first:
+ * @tree: a #QTree
+ *
+ * Returns the first in-order node of the tree, or %NULL
+ * for an empty tree.
+ *
+ * Returns: (nullable) (transfer none): the first node in the tree
+ *
+ * Since: 2.68 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static QTreeNode *
+q_tree_node_first(QTree *tree)
+{
+    QTreeNode *tmp;
+
+    g_return_val_if_fail(tree != NULL, NULL);
+
+    if (!tree->root) {
+        return NULL;
+    }
+
+    tmp = tree->root;
+
+    while (tmp->left_child) {
+        tmp = tmp->left;
+    }
+
+    return tmp;
+}
+
+/**
+ * q_tree_node_previous
+ * @node: a #QTree node
+ *
+ * Returns the previous in-order node of the tree, or %NULL
+ * if the passed node was already the first one.
+ *
+ * Returns: (nullable) (transfer none): the previous node in the tree
+ *
+ * Since: 2.68 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static QTreeNode *
+q_tree_node_previous(QTreeNode *node)
+{
+    QTreeNode *tmp;
+
+    g_return_val_if_fail(node != NULL, NULL);
+
+    tmp = node->left;
+
+    if (node->left_child) {
+        while (tmp->right_child) {
+            tmp = tmp->right;
+        }
+    }
+
+    return tmp;
+}
+
+/**
+ * q_tree_node_next
+ * @node: a #QTree node
+ *
+ * Returns the next in-order node of the tree, or %NULL
+ * if the passed node was already the last one.
+ *
+ * Returns: (nullable) (transfer none): the next node in the tree
+ *
+ * Since: 2.68 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static QTreeNode *
+q_tree_node_next(QTreeNode *node)
+{
+    QTreeNode *tmp;
+
+    g_return_val_if_fail(node != NULL, NULL);
+
+    tmp = node->right;
+
+    if (node->right_child) {
+        while (tmp->left_child) {
+            tmp = tmp->left;
+        }
+    }
+
+    return tmp;
+}
+
+/**
+ * q_tree_remove_all:
+ * @tree: a #QTree
+ *
+ * Removes all nodes from a #QTree and destroys their keys and values,
+ * then resets the #QTree’s root to %NULL.
+ *
+ * Since: 2.70 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static void
+q_tree_remove_all(QTree *tree)
+{
+    QTreeNode *node;
+    QTreeNode *next;
+
+    g_return_if_fail(tree != NULL);
+
+    node = q_tree_node_first(tree);
+
+    while (node) {
+        next = q_tree_node_next(node);
+
+        if (tree->key_destroy_func) {
+            tree->key_destroy_func(node->key);
+        }
+        if (tree->value_destroy_func) {
+            tree->value_destroy_func(node->value);
+        }
+        g_free(node);
+
+#ifdef Q_TREE_DEBUG
+        g_assert(tree->nnodes > 0);
+        tree->nnodes--;
+#endif
+
+        node = next;
+    }
+
+#ifdef Q_TREE_DEBUG
+    g_assert(tree->nnodes == 0);
+#endif
+
+    tree->root = NULL;
+#ifndef Q_TREE_DEBUG
+    tree->nnodes = 0;
+#endif
+}
+
+/**
+ * q_tree_ref:
+ * @tree: a #QTree
+ *
+ * Increments the reference count of @tree by one.
+ *
+ * It is safe to call this function from any thread.
+ *
+ * Returns: the passed in #QTree
+ *
+ * Since: 2.22
+ */
+QTree *
+q_tree_ref(QTree *tree)
+{
+    g_return_val_if_fail(tree != NULL, NULL);
+
+    g_atomic_int_inc(&tree->ref_count);
+
+    return tree;
+}
+
+/**
+ * q_tree_unref:
+ * @tree: a #QTree
+ *
+ * Decrements the reference count of @tree by one.
+ * If the reference count drops to 0, all keys and values will
+ * be destroyed (if destroy functions were specified) and all
+ * memory allocated by @tree will be released.
+ *
+ * It is safe to call this function from any thread.
+ *
+ * Since: 2.22
+ */
+void
+q_tree_unref(QTree *tree)
+{
+    g_return_if_fail(tree != NULL);
+
+    if (g_atomic_int_dec_and_test(&tree->ref_count)) {
+        q_tree_remove_all(tree);
+        g_free(tree);
+    }
+}
+
+/**
+ * q_tree_destroy:
+ * @tree: a #QTree
+ *
+ * Removes all keys and values from the #QTree and decreases its
+ * reference count by one. If keys and/or values are dynamically
+ * allocated, you should either free them first or create the #QTree
+ * using q_tree_new_full(). In the latter case the destroy functions
+ * you supplied will be called on all keys and values before destroying
+ * the #QTree.
+ */
+void
+q_tree_destroy(QTree *tree)
+{
+    g_return_if_fail(tree != NULL);
+
+    q_tree_remove_all(tree);
+    q_tree_unref(tree);
+}
+
+/**
+ * q_tree_insert_node:
+ * @tree: a #QTree
+ * @key: the key to insert
+ * @value: the value corresponding to the key
+ *
+ * Inserts a key/value pair into a #QTree.
+ *
+ * If the given key already exists in the #QTree its corresponding value
+ * is set to the new value. If you supplied a @value_destroy_func when
+ * creating the #QTree, the old value is freed using that function. If
+ * you supplied a @key_destroy_func when creating the #QTree, the passed
+ * key is freed using that function.
+ *
+ * The tree is automatically 'balanced' as new key/value pairs are added,
+ * so that the distance from the root to every leaf is as small as possible.
+ * The cost of maintaining a balanced tree while inserting new key/value
+ * result in a O(n log(n)) operation where most of the other operations
+ * are O(log(n)).
+ *
+ * Returns: (transfer none): the inserted (or set) node.
+ *
+ * Since: 2.68 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static QTreeNode *
+q_tree_insert_node(QTree    *tree,
+                   gpointer  key,
+                   gpointer  value)
+{
+    QTreeNode *node;
+
+    g_return_val_if_fail(tree != NULL, NULL);
+
+    node = q_tree_insert_internal(tree, key, value, FALSE);
+
+#ifdef Q_TREE_DEBUG
+    q_tree_node_check(tree->root);
+#endif
+
+    return node;
+}
+
+/**
+ * q_tree_insert:
+ * @tree: a #QTree
+ * @key: the key to insert
+ * @value: the value corresponding to the key
+ *
+ * Inserts a key/value pair into a #QTree.
+ *
+ * Inserts a new key and value into a #QTree as q_tree_insert_node() does,
+ * only this function does not return the inserted or set node.
+ */
+void
+q_tree_insert(QTree    *tree,
+              gpointer  key,
+              gpointer  value)
+{
+    q_tree_insert_node(tree, key, value);
+}
+
+/**
+ * q_tree_replace_node:
+ * @tree: a #QTree
+ * @key: the key to insert
+ * @value: the value corresponding to the key
+ *
+ * Inserts a new key and value into a #QTree similar to q_tree_insert_node().
+ * The difference is that if the key already exists in the #QTree, it gets
+ * replaced by the new key. If you supplied a @value_destroy_func when
+ * creating the #QTree, the old value is freed using that function. If you
+ * supplied a @key_destroy_func when creating the #QTree, the old key is
+ * freed using that function.
+ *
+ * The tree is automatically 'balanced' as new key/value pairs are added,
+ * so that the distance from the root to every leaf is as small as possible.
+ *
+ * Returns: (transfer none): the inserted (or set) node.
+ *
+ * Since: 2.68 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static QTreeNode *
+q_tree_replace_node(QTree    *tree,
+                    gpointer  key,
+                    gpointer  value)
+{
+    QTreeNode *node;
+
+    g_return_val_if_fail(tree != NULL, NULL);
+
+    node = q_tree_insert_internal(tree, key, value, TRUE);
+
+#ifdef Q_TREE_DEBUG
+    q_tree_node_check(tree->root);
+#endif
+
+    return node;
+}
+
+/**
+ * q_tree_replace:
+ * @tree: a #QTree
+ * @key: the key to insert
+ * @value: the value corresponding to the key
+ *
+ * Inserts a new key and value into a #QTree as q_tree_replace_node() does,
+ * only this function does not return the inserted or set node.
+ */
+void
+q_tree_replace(QTree    *tree,
+               gpointer  key,
+               gpointer  value)
+{
+    q_tree_replace_node(tree, key, value);
+}
+
+/* internal insert routine */
+static QTreeNode *
+q_tree_insert_internal(QTree    *tree,
+                       gpointer  key,
+                       gpointer  value,
+                       gboolean  replace)
+{
+    QTreeNode *node, *retnode;
+    QTreeNode *path[MAX_GTREE_HEIGHT];
+    int idx;
+
+    g_return_val_if_fail(tree != NULL, NULL);
+
+    if (!tree->root) {
+        tree->root = q_tree_node_new(key, value);
+        tree->nnodes++;
+        return tree->root;
+    }
+
+    idx = 0;
+    path[idx++] = NULL;
+    node = tree->root;
+
+    while (1) {
+        int cmp = tree->key_compare(key, node->key, tree->key_compare_data);
+
+        if (cmp == 0) {
+            if (tree->value_destroy_func) {
+                tree->value_destroy_func(node->value);
+            }
+
+            node->value = value;
+
+            if (replace) {
+                if (tree->key_destroy_func) {
+                    tree->key_destroy_func(node->key);
+                }
+
+                node->key = key;
+            } else {
+                /* free the passed key */
+                if (tree->key_destroy_func) {
+                    tree->key_destroy_func(key);
+                }
+            }
+
+            return node;
+        } else if (cmp < 0) {
+            if (node->left_child) {
+                path[idx++] = node;
+                node = node->left;
+            } else {
+                QTreeNode *child = q_tree_node_new(key, value);
+
+                child->left = node->left;
+                child->right = node;
+                node->left = child;
+                node->left_child = TRUE;
+                node->balance -= 1;
+
+                tree->nnodes++;
+
+                retnode = child;
+                break;
+            }
+        } else {
+            if (node->right_child) {
+                path[idx++] = node;
+                node = node->right;
+            } else {
+                QTreeNode *child = q_tree_node_new(key, value);
+
+                child->right = node->right;
+                child->left = node;
+                node->right = child;
+                node->right_child = TRUE;
+                node->balance += 1;
+
+                tree->nnodes++;
+
+                retnode = child;
+                break;
+            }
+        }
+    }
+
+    /*
+     * Restore balance. This is the goodness of a non-recursive
+     * implementation, when we are done with balancing we 'break'
+     * the loop and we are done.
+     */
+    while (1) {
+        QTreeNode *bparent = path[--idx];
+        gboolean left_node = (bparent && node == bparent->left);
+        g_assert(!bparent || bparent->left == node || bparent->right == node);
+
+        if (node->balance < -1 || node->balance > 1) {
+            node = q_tree_node_balance(node);
+            if (bparent == NULL) {
+                tree->root = node;
+            } else if (left_node) {
+                bparent->left = node;
+            } else {
+                bparent->right = node;
+            }
+        }
+
+        if (node->balance == 0 || bparent == NULL) {
+            break;
+        }
+
+        if (left_node) {
+            bparent->balance -= 1;
+        } else {
+            bparent->balance += 1;
+        }
+
+        node = bparent;
+    }
+
+    return retnode;
+}
+
+/**
+ * q_tree_remove:
+ * @tree: a #QTree
+ * @key: the key to remove
+ *
+ * Removes a key/value pair from a #QTree.
+ *
+ * If the #QTree was created using q_tree_new_full(), the key and value
+ * are freed using the supplied destroy functions, otherwise you have to
+ * make sure that any dynamically allocated values are freed yourself.
+ * If the key does not exist in the #QTree, the function does nothing.
+ *
+ * The cost of maintaining a balanced tree while removing a key/value
+ * result in a O(n log(n)) operation where most of the other operations
+ * are O(log(n)).
+ *
+ * Returns: %TRUE if the key was found (prior to 2.8, this function
+ *     returned nothing)
+ */
+gboolean
+q_tree_remove(QTree         *tree,
+              gconstpointer  key)
+{
+    gboolean removed;
+
+    g_return_val_if_fail(tree != NULL, FALSE);
+
+    removed = q_tree_remove_internal(tree, key, FALSE);
+
+#ifdef Q_TREE_DEBUG
+    q_tree_node_check(tree->root);
+#endif
+
+    return removed;
+}
+
+/**
+ * q_tree_steal:
+ * @tree: a #QTree
+ * @key: the key to remove
+ *
+ * Removes a key and its associated value from a #QTree without calling
+ * the key and value destroy functions.
+ *
+ * If the key does not exist in the #QTree, the function does nothing.
+ *
+ * Returns: %TRUE if the key was found (prior to 2.8, this function
+ *     returned nothing)
+ */
+gboolean
+q_tree_steal(QTree         *tree,
+             gconstpointer  key)
+{
+    gboolean removed;
+
+    g_return_val_if_fail(tree != NULL, FALSE);
+
+    removed = q_tree_remove_internal(tree, key, TRUE);
+
+#ifdef Q_TREE_DEBUG
+    q_tree_node_check(tree->root);
+#endif
+
+    return removed;
+}
+
+/* internal remove routine */
+static gboolean
+q_tree_remove_internal(QTree         *tree,
+                       gconstpointer  key,
+                       gboolean       steal)
+{
+    QTreeNode *node, *parent, *balance;
+    QTreeNode *path[MAX_GTREE_HEIGHT];
+    int idx;
+    gboolean left_node;
+
+    g_return_val_if_fail(tree != NULL, FALSE);
+
+    if (!tree->root) {
+        return FALSE;
+    }
+
+    idx = 0;
+    path[idx++] = NULL;
+    node = tree->root;
+
+    while (1) {
+        int cmp = tree->key_compare(key, node->key, tree->key_compare_data);
+
+        if (cmp == 0) {
+            break;
+        } else if (cmp < 0) {
+            if (!node->left_child) {
+                return FALSE;
+            }
+
+            path[idx++] = node;
+            node = node->left;
+        } else {
+            if (!node->right_child) {
+                return FALSE;
+            }
+
+            path[idx++] = node;
+            node = node->right;
+        }
+    }
+
+    /*
+     * The following code is almost equal to q_tree_remove_node,
+     * except that we do not have to call q_tree_node_parent.
+     */
+    balance = parent = path[--idx];
+    g_assert(!parent || parent->left == node || parent->right == node);
+    left_node = (parent && node == parent->left);
+
+    if (!node->left_child) {
+        if (!node->right_child) {
+            if (!parent) {
+                tree->root = NULL;
+            } else if (left_node) {
+                parent->left_child = FALSE;
+                parent->left = node->left;
+                parent->balance += 1;
+            } else {
+                parent->right_child = FALSE;
+                parent->right = node->right;
+                parent->balance -= 1;
+            }
+        } else {
+            /* node has a right child */
+            QTreeNode *tmp = q_tree_node_next(node);
+            tmp->left = node->left;
+
+            if (!parent) {
+                tree->root = node->right;
+            } else if (left_node) {
+                parent->left = node->right;
+                parent->balance += 1;
+            } else {
+                parent->right = node->right;
+                parent->balance -= 1;
+            }
+        }
+    } else {
+        /* node has a left child */
+        if (!node->right_child) {
+            QTreeNode *tmp = q_tree_node_previous(node);
+            tmp->right = node->right;
+
+            if (parent == NULL) {
+                tree->root = node->left;
+            } else if (left_node) {
+                parent->left = node->left;
+                parent->balance += 1;
+            } else {
+                parent->right = node->left;
+                parent->balance -= 1;
+            }
+        } else {
+            /* node has a both children (pant, pant!) */
+            QTreeNode *prev = node->left;
+            QTreeNode *next = node->right;
+            QTreeNode *nextp = node;
+            int old_idx = idx + 1;
+            idx++;
+
+            /* path[idx] == parent */
+            /* find the immediately next node (and its parent) */
+            while (next->left_child) {
+                path[++idx] = nextp = next;
+                next = next->left;
+            }
+
+            path[old_idx] = next;
+            balance = path[idx];
+
+            /* remove 'next' from the tree */
+            if (nextp != node) {
+                if (next->right_child) {
+                    nextp->left = next->right;
+                } else {
+                    nextp->left_child = FALSE;
+                }
+                nextp->balance += 1;
+
+                next->right_child = TRUE;
+                next->right = node->right;
+            } else {
+                node->balance -= 1;
+            }
+
+            /* set the prev to point to the right place */
+            while (prev->right_child) {
+                prev = prev->right;
+            }
+            prev->right = next;
+
+            /* prepare 'next' to replace 'node' */
+            next->left_child = TRUE;
+            next->left = node->left;
+            next->balance = node->balance;
+
+            if (!parent) {
+                tree->root = next;
+            } else if (left_node) {
+                parent->left = next;
+            } else {
+                parent->right = next;
+            }
+        }
+    }
+
+    /* restore balance */
+    if (balance) {
+        while (1) {
+            QTreeNode *bparent = path[--idx];
+            g_assert(!bparent ||
+                     bparent->left == balance ||
+                     bparent->right == balance);
+            left_node = (bparent && balance == bparent->left);
+
+            if (balance->balance < -1 || balance->balance > 1) {
+                balance = q_tree_node_balance(balance);
+                if (!bparent) {
+                    tree->root = balance;
+                } else if (left_node) {
+                    bparent->left = balance;
+                } else {
+                    bparent->right = balance;
+                }
+            }
+
+            if (balance->balance != 0 || !bparent) {
+                break;
+            }
+
+            if (left_node) {
+                bparent->balance += 1;
+            } else {
+                bparent->balance -= 1;
+            }
+
+            balance = bparent;
+        }
+    }
+
+    if (!steal) {
+        if (tree->key_destroy_func) {
+            tree->key_destroy_func(node->key);
+        }
+        if (tree->value_destroy_func) {
+            tree->value_destroy_func(node->value);
+        }
+    }
+
+    g_free(node);
+
+    tree->nnodes--;
+
+    return TRUE;
+}
+
+/**
+ * q_tree_lookup_node:
+ * @tree: a #QTree
+ * @key: the key to look up
+ *
+ * Gets the tree node corresponding to the given key. Since a #QTree is
+ * automatically balanced as key/value pairs are added, key lookup
+ * is O(log n) (where n is the number of key/value pairs in the tree).
+ *
+ * Returns: (nullable) (transfer none): the tree node corresponding to
+ *          the key, or %NULL if the key was not found
+ *
+ * Since: 2.68 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static QTreeNode *
+q_tree_lookup_node(QTree         *tree,
+                   gconstpointer  key)
+{
+    g_return_val_if_fail(tree != NULL, NULL);
+
+    return q_tree_find_node(tree, key);
+}
+
+/**
+ * q_tree_lookup:
+ * @tree: a #QTree
+ * @key: the key to look up
+ *
+ * Gets the value corresponding to the given key. Since a #QTree is
+ * automatically balanced as key/value pairs are added, key lookup
+ * is O(log n) (where n is the number of key/value pairs in the tree).
+ *
+ * Returns: the value corresponding to the key, or %NULL
+ *     if the key was not found
+ */
+gpointer
+q_tree_lookup(QTree         *tree,
+              gconstpointer  key)
+{
+    QTreeNode *node;
+
+    node = q_tree_lookup_node(tree, key);
+
+    return node ? node->value : NULL;
+}
+
+/**
+ * q_tree_lookup_extended:
+ * @tree: a #QTree
+ * @lookup_key: the key to look up
+ * @orig_key: (out) (optional) (nullable): returns the original key
+ * @value: (out) (optional) (nullable): returns the value associated with
+ *         the key
+ *
+ * Looks up a key in the #QTree, returning the original key and the
+ * associated value. This is useful if you need to free the memory
+ * allocated for the original key, for example before calling
+ * q_tree_remove().
+ *
+ * Returns: %TRUE if the key was found in the #QTree
+ */
+gboolean
+q_tree_lookup_extended(QTree         *tree,
+                       gconstpointer  lookup_key,
+                       gpointer      *orig_key,
+                       gpointer      *value)
+{
+    QTreeNode *node;
+
+    g_return_val_if_fail(tree != NULL, FALSE);
+
+    node = q_tree_find_node(tree, lookup_key);
+
+    if (node) {
+        if (orig_key) {
+            *orig_key = node->key;
+        }
+        if (value) {
+            *value = node->value;
+        }
+        return TRUE;
+    } else {
+        return FALSE;
+    }
+}
+
+/**
+ * q_tree_foreach:
+ * @tree: a #QTree
+ * @func: the function to call for each node visited.
+ *     If this function returns %TRUE, the traversal is stopped.
+ * @user_data: user data to pass to the function
+ *
+ * Calls the given function for each of the key/value pairs in the #QTree.
+ * The function is passed the key and value of each pair, and the given
+ * @data parameter. The tree is traversed in sorted order.
+ *
+ * The tree may not be modified while iterating over it (you can't
+ * add/remove items). To remove all items matching a predicate, you need
+ * to add each item to a list in your #GTraverseFunc as you walk over
+ * the tree, then walk the list and remove each item.
+ */
+void
+q_tree_foreach(QTree         *tree,
+               GTraverseFunc  func,
+               gpointer       user_data)
+{
+    QTreeNode *node;
+
+    g_return_if_fail(tree != NULL);
+
+    if (!tree->root) {
+        return;
+    }
+
+    node = q_tree_node_first(tree);
+
+    while (node) {
+        if ((*func)(node->key, node->value, user_data)) {
+            break;
+        }
+
+        node = q_tree_node_next(node);
+    }
+}
+
+/**
+ * q_tree_search_node:
+ * @tree: a #QTree
+ * @search_func: a function used to search the #QTree
+ * @user_data: the data passed as the second argument to @search_func
+ *
+ * Searches a #QTree using @search_func.
+ *
+ * The @search_func is called with a pointer to the key of a key/value
+ * pair in the tree, and the passed in @user_data. If @search_func returns
+ * 0 for a key/value pair, then the corresponding node is returned as
+ * the result of q_tree_search(). If @search_func returns -1, searching
+ * will proceed among the key/value pairs that have a smaller key; if
+ * @search_func returns 1, searching will proceed among the key/value
+ * pairs that have a larger key.
+ *
+ * Returns: (nullable) (transfer none): the node corresponding to the
+ *          found key, or %NULL if the key was not found
+ *
+ * Since: 2.68 in GLib. Internal in Qtree, i.e. not in the public API.
+ */
+static QTreeNode *
+q_tree_search_node(QTree         *tree,
+                   GCompareFunc   search_func,
+                   gconstpointer  user_data)
+{
+    g_return_val_if_fail(tree != NULL, NULL);
+
+    if (!tree->root) {
+        return NULL;
+    }
+
+    return q_tree_node_search(tree->root, search_func, user_data);
+}
+
+/**
+ * q_tree_search:
+ * @tree: a #QTree
+ * @search_func: a function used to search the #QTree
+ * @user_data: the data passed as the second argument to @search_func
+ *
+ * Searches a #QTree using @search_func.
+ *
+ * The @search_func is called with a pointer to the key of a key/value
+ * pair in the tree, and the passed in @user_data. If @search_func returns
+ * 0 for a key/value pair, then the corresponding value is returned as
+ * the result of q_tree_search(). If @search_func returns -1, searching
+ * will proceed among the key/value pairs that have a smaller key; if
+ * @search_func returns 1, searching will proceed among the key/value
+ * pairs that have a larger key.
+ *
+ * Returns: the value corresponding to the found key, or %NULL
+ *     if the key was not found
+ */
+gpointer
+q_tree_search(QTree         *tree,
+              GCompareFunc   search_func,
+              gconstpointer  user_data)
+{
+    QTreeNode *node;
+
+    node = q_tree_search_node(tree, search_func, user_data);
+
+    return node ? node->value : NULL;
+}
+
+/**
+ * q_tree_height:
+ * @tree: a #QTree
+ *
+ * Gets the height of a #QTree.
+ *
+ * If the #QTree contains no nodes, the height is 0.
+ * If the #QTree contains only one root node the height is 1.
+ * If the root node has children the height is 2, etc.
+ *
+ * Returns: the height of @tree
+ */
+gint
+q_tree_height(QTree *tree)
+{
+    QTreeNode *node;
+    gint height;
+
+    g_return_val_if_fail(tree != NULL, 0);
+
+    if (!tree->root) {
+        return 0;
+    }
+
+    height = 0;
+    node = tree->root;
+
+    while (1) {
+        height += 1 + MAX(node->balance, 0);
+
+        if (!node->left_child) {
+            return height;
+        }
+
+        node = node->left;
+    }
+}
+
+/**
+ * q_tree_nnodes:
+ * @tree: a #QTree
+ *
+ * Gets the number of nodes in a #QTree.
+ *
+ * Returns: the number of nodes in @tree
+ */
+gint
+q_tree_nnodes(QTree *tree)
+{
+    g_return_val_if_fail(tree != NULL, 0);
+
+    return tree->nnodes;
+}
+
+static QTreeNode *
+q_tree_node_balance(QTreeNode *node)
+{
+    if (node->balance < -1) {
+        if (node->left->balance > 0) {
+            node->left = q_tree_node_rotate_left(node->left);
+        }
+        node = q_tree_node_rotate_right(node);
+    } else if (node->balance > 1) {
+        if (node->right->balance < 0) {
+            node->right = q_tree_node_rotate_right(node->right);
+        }
+        node = q_tree_node_rotate_left(node);
+    }
+
+    return node;
+}
+
+static QTreeNode *
+q_tree_find_node(QTree        *tree,
+                 gconstpointer key)
+{
+    QTreeNode *node;
+    gint cmp;
+
+    node = tree->root;
+    if (!node) {
+        return NULL;
+    }
+
+    while (1) {
+        cmp = tree->key_compare(key, node->key, tree->key_compare_data);
+        if (cmp == 0) {
+            return node;
+        } else if (cmp < 0) {
+            if (!node->left_child) {
+                return NULL;
+            }
+
+            node = node->left;
+        } else {
+            if (!node->right_child) {
+                return NULL;
+            }
+
+            node = node->right;
+        }
+    }
+}
+
+static QTreeNode *
+q_tree_node_search(QTreeNode     *node,
+                   GCompareFunc   search_func,
+                   gconstpointer  data)
+{
+    gint dir;
+
+    if (!node) {
+        return NULL;
+    }
+
+    while (1) {
+        dir = (*search_func)(node->key, data);
+        if (dir == 0) {
+            return node;
+        } else if (dir < 0) {
+            if (!node->left_child) {
+                return NULL;
+            }
+
+            node = node->left;
+        } else {
+            if (!node->right_child) {
+                return NULL;
+            }
+
+            node = node->right;
+        }
+    }
+}
+
+static QTreeNode *
+q_tree_node_rotate_left(QTreeNode *node)
+{
+    QTreeNode *right;
+    gint a_bal;
+    gint b_bal;
+
+    right = node->right;
+
+    if (right->left_child) {
+        node->right = right->left;
+    } else {
+        node->right_child = FALSE;
+        right->left_child = TRUE;
+    }
+    right->left = node;
+
+    a_bal = node->balance;
+    b_bal = right->balance;
+
+    if (b_bal <= 0) {
+        if (a_bal >= 1) {
+            right->balance = b_bal - 1;
+        } else {
+            right->balance = a_bal + b_bal - 2;
+        }
+        node->balance = a_bal - 1;
+    } else {
+        if (a_bal <= b_bal) {
+            right->balance = a_bal - 2;
+        } else {
+            right->balance = b_bal - 1;
+        }
+        node->balance = a_bal - b_bal - 1;
+    }
+
+    return right;
+}
+
+static QTreeNode *
+q_tree_node_rotate_right(QTreeNode *node)
+{
+    QTreeNode *left;
+    gint a_bal;
+    gint b_bal;
+
+    left = node->left;
+
+    if (left->right_child) {
+        node->left = left->right;
+    } else {
+        node->left_child = FALSE;
+        left->right_child = TRUE;
+    }
+    left->right = node;
+
+    a_bal = node->balance;
+    b_bal = left->balance;
+
+    if (b_bal <= 0) {
+        if (b_bal > a_bal) {
+            left->balance = b_bal + 1;
+        } else {
+            left->balance = a_bal + 2;
+        }
+        node->balance = a_bal - b_bal + 1;
+    } else {
+        if (a_bal <= -1) {
+            left->balance = b_bal + 1;
+        } else {
+            left->balance = a_bal + b_bal + 2;
+        }
+        node->balance = a_bal + 1;
+    }
+
+    return left;
+}
+
+#ifdef Q_TREE_DEBUG
+static gint
+q_tree_node_height(QTreeNode *node)
+{
+    gint left_height;
+    gint right_height;
+
+    if (node) {
+        left_height = 0;
+        right_height = 0;
+
+        if (node->left_child) {
+            left_height = q_tree_node_height(node->left);
+        }
+
+        if (node->right_child) {
+            right_height = q_tree_node_height(node->right);
+        }
+
+        return MAX(left_height, right_height) + 1;
+    }
+
+    return 0;
+}
+
+static void q_tree_node_check(QTreeNode *node)
+{
+    gint left_height;
+    gint right_height;
+    gint balance;
+    QTreeNode *tmp;
+
+    if (node) {
+        if (node->left_child) {
+            tmp = q_tree_node_previous(node);
+            g_assert(tmp->right == node);
+        }
+
+        if (node->right_child) {
+            tmp = q_tree_node_next(node);
+            g_assert(tmp->left == node);
+        }
+
+        left_height = 0;
+        right_height = 0;
+
+        if (node->left_child) {
+            left_height = q_tree_node_height(node->left);
+        }
+        if (node->right_child) {
+            right_height = q_tree_node_height(node->right);
+        }
+
+        balance = right_height - left_height;
+        g_assert(balance == node->balance);
+
+        if (node->left_child) {
+            q_tree_node_check(node->left);
+        }
+        if (node->right_child) {
+            q_tree_node_check(node->right);
+        }
+    }
+}
+#endif