innobase/ut/ut0rbt.cc

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/** Red-Black tree implementation

 (c) 2007 Oracle/Innobase Oy

 Created 2007-03-20 Sunny Bains
 ***********************************************************************/

#include "ut0rbt.h"
#include "univ.i"
#include "ut0new.h"

/** Definition of a red-black tree
 ==============================

 A red-black tree is a binary search tree which has the following
 red-black properties:

    1. Every node is either red or black.
    2. Every leaf (NULL - in our case tree->nil) is black.
    3. If a node is red, then both its children are black.
    4. Every simple path from a node to a descendant leaf contains the
       same number of black nodes.

    from (3) above, the implication is that on any path from the root
    to a leaf, red nodes must not be adjacent.

    However, any number of black nodes may appear in a sequence.
  */

#if defined(IB_RBT_TESTING)
#warning "Testing enabled!"
#endif

#define ROOT(t) (t->root->left)
#define SIZEOF_NODE(t) ((sizeof(ib_rbt_node_t) + t->sizeof_value) - 1)

#if defined UNIV_DEBUG || defined IB_RBT_TESTING
/** Verify that the keys are in order.
 @return true of OK. false if not ordered */
static ibool rbt_check_ordering(
    const ib_rbt_t *tree) /*!< in: tree to verfify */
{
  const ib_rbt_node_t *node;
  const ib_rbt_node_t *prev = nullptr;

  /* Iterate over all the nodes, comparing each node with the prev */
  for (node = rbt_first(tree); node; node = rbt_next(tree, prev)) {
    if (prev) {
      int result;

      if (tree->cmp_arg) {
        result =
            tree->compare_with_arg(tree->cmp_arg, prev->value, node->value);
      } else {
        result = tree->compare(prev->value, node->value);
      }

      if (result >= 0) {
        return (FALSE);
      }
    }

    prev = node;
  }

  return (TRUE);
}

/** Check that every path from the root to the leaves has the same count.
 Count is expressed in the number of black nodes.
 @return 0 on failure else black height of the subtree */
static ibool rbt_count_black_nodes(
    const ib_rbt_t *tree,      /*!< in: tree to verify */
    const ib_rbt_node_t *node) /*!< in: start of sub-tree */
{
  ulint result;

  if (node != tree->nil) {
    ulint left_height = rbt_count_black_nodes(tree, node->left);

    ulint right_height = rbt_count_black_nodes(tree, node->right);

    if (left_height == 0 || right_height == 0 || left_height != right_height) {
      result = 0;
    } else if (node->color == IB_RBT_RED) {
      /* Case 3 */
      if (node->left->color != IB_RBT_BLACK ||
          node->right->color != IB_RBT_BLACK) {
        result = 0;
      } else {
        result = left_height;
      }
      /* Check if it's anything other than RED or BLACK. */
    } else if (node->color != IB_RBT_BLACK) {
      result = 0;
    } else {
      result = right_height + 1;
    }
  } else {
    result = 1;
  }

  return (result);
}
#endif /* UNIV_DEBUG || IB_RBT_TESTING */

/** Turn the node's right child's left sub-tree into node's right sub-tree.
 This will also make node's right child it's parent. */
static void rbt_rotate_left(
    const ib_rbt_node_t *nil, /*!< in: nil node of the tree */
    ib_rbt_node_t *node)      /*!< in: node to rotate */
{
  ib_rbt_node_t *right = node->right;

  node->right = right->left;

  if (right->left != nil) {
    right->left->parent = node;
  }

  /* Right's new parent was node's parent. */
  right->parent = node->parent;

  /* Since root's parent is tree->nil and root->parent->left points
  back to root, we can avoid the check. */
  if (node == node->parent->left) {
    /* Node was on the left of its parent. */
    node->parent->left = right;
  } else {
    /* Node must have been on the right. */
    node->parent->right = right;
  }

  /* Finally, put node on right's left. */
  right->left = node;
  node->parent = right;
}

/** Turn the node's left child's right sub-tree into node's left sub-tree.
 This also make node's left child it's parent. */
static void rbt_rotate_right(
    const ib_rbt_node_t *nil, /*!< in: nil node of tree */
    ib_rbt_node_t *node)      /*!< in: node to rotate */
{
  ib_rbt_node_t *left = node->left;

  node->left = left->right;

  if (left->right != nil) {
    left->right->parent = node;
  }

  /* Left's new parent was node's parent. */
  left->parent = node->parent;

  /* Since root's parent is tree->nil and root->parent->left points
  back to root, we can avoid the check. */
  if (node == node->parent->right) {
    /* Node was on the left of its parent. */
    node->parent->right = left;
  } else {
    /* Node must have been on the left. */
    node->parent->left = left;
  }

  /* Finally, put node on left's right. */
  left->right = node;
  node->parent = left;
}

/** Append a node to the tree. */
static ib_rbt_node_t *rbt_tree_add_child(const ib_rbt_t *tree,
                                         ib_rbt_bound_t *parent,
                                         ib_rbt_node_t *node) {
  /* Cast away the const. */
  ib_rbt_node_t *last = (ib_rbt_node_t *)parent->last;

  if (last == tree->root || parent->result < 0) {
    last->left = node;
  } else {
    /* FIXME: We don't handle duplicates (yet)! */
    ut_a(parent->result != 0);

    last->right = node;
  }

  node->parent = last;

  return (node);
}

/** Generic binary tree insert */
static ib_rbt_node_t *rbt_tree_insert(ib_rbt_t *tree, const void *key,
                                      ib_rbt_node_t *node) {
  ib_rbt_bound_t parent;
  ib_rbt_node_t *current = ROOT(tree);

  parent.result = 0;
  parent.last = tree->root;

  /* Regular binary search. */
  while (current != tree->nil) {
    parent.last = current;

    if (tree->cmp_arg) {
      parent.result =
          tree->compare_with_arg(tree->cmp_arg, key, current->value);
    } else {
      parent.result = tree->compare(key, current->value);
    }

    if (parent.result < 0) {
      current = current->left;
    } else {
      current = current->right;
    }
  }

  ut_a(current == tree->nil);

  rbt_tree_add_child(tree, &parent, node);

  return (node);
}

/** Balance a tree after inserting a node. */
static void rbt_balance_tree(
    const ib_rbt_t *tree, /*!< in: tree to balance */
    ib_rbt_node_t *node)  /*!< in: node that was inserted */
{
  const ib_rbt_node_t *nil = tree->nil;
  ib_rbt_node_t *parent = node->parent;

  /* Restore the red-black property. */
  node->color = IB_RBT_RED;

  while (node != ROOT(tree) && parent->color == IB_RBT_RED) {
    ib_rbt_node_t *grand_parent = parent->parent;

    if (parent == grand_parent->left) {
      ib_rbt_node_t *uncle = grand_parent->right;

      if (uncle->color == IB_RBT_RED) {
        /* Case 1 - change the colors. */
        uncle->color = IB_RBT_BLACK;
        parent->color = IB_RBT_BLACK;
        grand_parent->color = IB_RBT_RED;

        /* Move node up the tree. */
        node = grand_parent;

      } else {
        if (node == parent->right) {
          /* Right is a black node and node is
          to the right, case 2 - move node
          up and rotate. */
          node = parent;
          rbt_rotate_left(nil, node);
        }

        grand_parent = node->parent->parent;

        /* Case 3. */
        node->parent->color = IB_RBT_BLACK;
        grand_parent->color = IB_RBT_RED;

        rbt_rotate_right(nil, grand_parent);
      }

    } else {
      ib_rbt_node_t *uncle = grand_parent->left;

      if (uncle->color == IB_RBT_RED) {
        /* Case 1 - change the colors. */
        uncle->color = IB_RBT_BLACK;
        parent->color = IB_RBT_BLACK;
        grand_parent->color = IB_RBT_RED;

        /* Move node up the tree. */
        node = grand_parent;

      } else {
        if (node == parent->left) {
          /* Left is a black node and node is to
          the right, case 2 - move node up and
          rotate. */
          node = parent;
          rbt_rotate_right(nil, node);
        }

        grand_parent = node->parent->parent;

        /* Case 3. */
        node->parent->color = IB_RBT_BLACK;
        grand_parent->color = IB_RBT_RED;

        rbt_rotate_left(nil, grand_parent);
      }
    }

    parent = node->parent;
  }

  /* Color the root black. */
  ROOT(tree)->color = IB_RBT_BLACK;
}

/** Find the given node's successor.
 @return successor node or NULL if no successor */
static ib_rbt_node_t *rbt_find_successor(
    const ib_rbt_t *tree,         /*!< in: rb tree */
    const ib_rbt_node_t *current) /*!< in: this is declared const
                                  because it can be called via
                                  rbt_next() */
{
  const ib_rbt_node_t *nil = tree->nil;
  ib_rbt_node_t *next = current->right;

  /* Is there a sub-tree to the right that we can follow. */
  if (next != nil) {
    /* Follow the left most links of the current right child. */
    while (next->left != nil) {
      next = next->left;
    }

  } else { /* We will have to go up the tree to find the successor. */
    ib_rbt_node_t *parent = current->parent;

    /* Cast away the const. */
    next = (ib_rbt_node_t *)current;

    while (parent != tree->root && next == parent->right) {
      next = parent;
      parent = next->parent;
    }

    next = (parent == tree->root) ? nullptr : parent;
  }

  return (next);
}

/** Find the given node's precedecessor.
 @return predecessor node or NULL if no predecesor */
static ib_rbt_node_t *rbt_find_predecessor(
    const ib_rbt_t *tree,         /*!< in: rb tree */
    const ib_rbt_node_t *current) /*!< in: this is declared const
                                  because it can be called via
                                  rbt_prev() */
{
  const ib_rbt_node_t *nil = tree->nil;
  ib_rbt_node_t *prev = current->left;

  /* Is there a sub-tree to the left that we can follow. */
  if (prev != nil) {
    /* Follow the right most links of the current left child. */
    while (prev->right != nil) {
      prev = prev->right;
    }

  } else { /* We will have to go up the tree to find the precedecessor. */
    ib_rbt_node_t *parent = current->parent;

    /* Cast away the const. */
    prev = (ib_rbt_node_t *)current;

    while (parent != tree->root && prev == parent->left) {
      prev = parent;
      parent = prev->parent;
    }

    prev = (parent == tree->root) ? nullptr : parent;
  }

  return (prev);
}

/** Replace node with child. After applying transformations eject becomes
 an orphan. */
static void rbt_eject_node(ib_rbt_node_t *eject, /*!< in: node to eject */
                           ib_rbt_node_t *node) /*!< in: node to replace with */
{
  /* Update the to be ejected node's parent's child pointers. */
  if (eject->parent->left == eject) {
    eject->parent->left = node;
  } else if (eject->parent->right == eject) {
    eject->parent->right = node;
  } else {
    ut_a(0);
  }
  /* eject is now an orphan but otherwise its pointers
  and color are left intact. */

  node->parent = eject->parent;
}

/** Replace a node with another node. */
static void rbt_replace_node(
    ib_rbt_node_t *replace, /*!< in: node to replace */
    ib_rbt_node_t *node)    /*!< in: node to replace with */
{
  ib_rbt_color_t color = node->color;

  /* Update the node pointers. */
  node->left = replace->left;
  node->right = replace->right;

  /* Update the child node pointers. */
  node->left->parent = node;
  node->right->parent = node;

  /* Make the parent of replace point to node. */
  rbt_eject_node(replace, node);

  /* Swap the colors. */
  node->color = replace->color;
  replace->color = color;
}

/** Detach node from the tree replacing it with one of it's children.
 @return the child node that now occupies the position of the detached node */
static ib_rbt_node_t *rbt_detach_node(
    const ib_rbt_t *tree, /*!< in: rb tree */
    ib_rbt_node_t *node)  /*!< in: node to detach */
{
  ib_rbt_node_t *child;
  const ib_rbt_node_t *nil = tree->nil;

  if (node->left != nil && node->right != nil) {
    /* Case where the node to be deleted has two children. */
    ib_rbt_node_t *successor = rbt_find_successor(tree, node);

    ut_a(successor != nil);
    ut_a(successor->parent != nil);
    ut_a(successor->left == nil);

    child = successor->right;

    /* Remove the successor node and replace with its child. */
    rbt_eject_node(successor, child);

    /* Replace the node to delete with its successor node. */
    rbt_replace_node(node, successor);
  } else {
    ut_a(node->left == nil || node->right == nil);

    child = (node->left != nil) ? node->left : node->right;

    /* Replace the node to delete with one of it's children. */
    rbt_eject_node(node, child);
  }

  /* Reset the node links. */
  node->parent = node->right = node->left = tree->nil;

  return (child);
}

/** Rebalance the right sub-tree after deletion.
 @return node to rebalance if more rebalancing required else NULL */
static ib_rbt_node_t *rbt_balance_right(
    const ib_rbt_node_t *nil, /*!< in: rb tree nil node */
    ib_rbt_node_t *parent,    /*!< in: parent node */
    ib_rbt_node_t *sibling)   /*!< in: sibling node */
{
  ib_rbt_node_t *node = nullptr;

  ut_a(sibling != nil);

  /* Case 3. */
  if (sibling->color == IB_RBT_RED) {
    parent->color = IB_RBT_RED;
    sibling->color = IB_RBT_BLACK;

    rbt_rotate_left(nil, parent);

    sibling = parent->right;

    ut_a(sibling != nil);
  }

  /* Since this will violate case 3 because of the change above. */
  if (sibling->left->color == IB_RBT_BLACK &&
      sibling->right->color == IB_RBT_BLACK) {
    node = parent; /* Parent needs to be rebalanced too. */
    sibling->color = IB_RBT_RED;

  } else {
    if (sibling->right->color == IB_RBT_BLACK) {
      ut_a(sibling->left->color == IB_RBT_RED);

      sibling->color = IB_RBT_RED;
      sibling->left->color = IB_RBT_BLACK;

      rbt_rotate_right(nil, sibling);

      sibling = parent->right;
      ut_a(sibling != nil);
    }

    sibling->color = parent->color;
    sibling->right->color = IB_RBT_BLACK;

    parent->color = IB_RBT_BLACK;

    rbt_rotate_left(nil, parent);
  }

  return (node);
}

/** Rebalance the left sub-tree after deletion.
 @return node to rebalance if more rebalancing required else NULL */
static ib_rbt_node_t *rbt_balance_left(
    const ib_rbt_node_t *nil, /*!< in: rb tree nil node */
    ib_rbt_node_t *parent,    /*!< in: parent node */
    ib_rbt_node_t *sibling)   /*!< in: sibling node */
{
  ib_rbt_node_t *node = nullptr;

  ut_a(sibling != nil);

  /* Case 3. */
  if (sibling->color == IB_RBT_RED) {
    parent->color = IB_RBT_RED;
    sibling->color = IB_RBT_BLACK;

    rbt_rotate_right(nil, parent);
    sibling = parent->left;

    ut_a(sibling != nil);
  }

  /* Since this will violate case 3 because of the change above. */
  if (sibling->right->color == IB_RBT_BLACK &&
      sibling->left->color == IB_RBT_BLACK) {
    node = parent; /* Parent needs to be rebalanced too. */
    sibling->color = IB_RBT_RED;

  } else {
    if (sibling->left->color == IB_RBT_BLACK) {
      ut_a(sibling->right->color == IB_RBT_RED);

      sibling->color = IB_RBT_RED;
      sibling->right->color = IB_RBT_BLACK;

      rbt_rotate_left(nil, sibling);

      sibling = parent->left;

      ut_a(sibling != nil);
    }

    sibling->color = parent->color;
    sibling->left->color = IB_RBT_BLACK;

    parent->color = IB_RBT_BLACK;

    rbt_rotate_right(nil, parent);
  }

  return (node);
}

/** Delete the node and rebalance the tree if necessary */
static void rbt_remove_node_and_rebalance(
    ib_rbt_t *tree,      /*!< in: rb tree */
    ib_rbt_node_t *node) /*!< in: node to remove */
{
  /* Detach node and get the node that will be used
  as rebalance start. */
  ib_rbt_node_t *child = rbt_detach_node(tree, node);

  if (node->color == IB_RBT_BLACK) {
    ib_rbt_node_t *last = child;

    ROOT(tree)->color = IB_RBT_RED;

    while (child && child->color == IB_RBT_BLACK) {
      ib_rbt_node_t *parent = child->parent;

      /* Did the deletion cause an imbalance in the
      parents left sub-tree. */
      if (parent->left == child) {
        child = rbt_balance_right(tree->nil, parent, parent->right);

      } else if (parent->right == child) {
        child = rbt_balance_left(tree->nil, parent, parent->left);

      } else {
        ut_error;
      }

      if (child) {
        last = child;
      }
    }

    ut_a(last);

    last->color = IB_RBT_BLACK;
    ROOT(tree)->color = IB_RBT_BLACK;
  }

  /* Note that we have removed a node from the tree. */
  --tree->n_nodes;
}

/** Recursively free the nodes. */
static void rbt_free_node(ib_rbt_node_t *node, /*!< in: node to free */
                          ib_rbt_node_t *nil)  /*!< in: rb tree nil node */
{
  if (node != nil) {
    rbt_free_node(node->left, nil);
    rbt_free_node(node->right, nil);

    ut_free(node);
  }
}

/** Free all the nodes and free the tree. */
void rbt_free(ib_rbt_t *tree) /*!< in: rb tree to free */
{
  rbt_free_node(tree->root, tree->nil);
  ut_free(tree->nil);
  ut_free(tree);
}

/** Create an instance of a red black tree, whose comparison function takes
 an argument
 @return an empty rb tree */
ib_rbt_t *rbt_create_arg_cmp(
    size_t sizeof_value,        /*!< in: sizeof data item */
    ib_rbt_arg_compare compare, /*!< in: fn to compare items */
    void *cmp_arg)              /*!< in: compare fn arg */
{
  ib_rbt_t *tree;

  ut_a(cmp_arg);

  tree = rbt_create(sizeof_value, nullptr);
  tree->cmp_arg = cmp_arg;
  tree->compare_with_arg = compare;

  return (tree);
}

/** Create an instance of a red black tree.
 @return an empty rb tree */
ib_rbt_t *rbt_create(size_t sizeof_value,    /*!< in: sizeof data item */
                     ib_rbt_compare compare) /*!< in: fn to compare items */
{
  ib_rbt_t *tree;
  ib_rbt_node_t *node;

  tree = (ib_rbt_t *)ut_zalloc_nokey(sizeof(*tree));

  tree->sizeof_value = sizeof_value;

  /* Create the sentinel (NIL) node. */
  node = tree->nil = (ib_rbt_node_t *)ut_zalloc_nokey(sizeof(*node));

  node->color = IB_RBT_BLACK;
  node->parent = node->left = node->right = node;

  /* Create the "fake" root, the real root node will be the
  left child of this node. */
  node = tree->root = (ib_rbt_node_t *)ut_zalloc_nokey(sizeof(*node));

  node->color = IB_RBT_BLACK;
  node->parent = node->left = node->right = tree->nil;

  tree->compare = compare;

  return (tree);
}

/** Generic insert of a value in the rb tree.
 @return inserted node */
const ib_rbt_node_t *rbt_insert(
    ib_rbt_t *tree,    /*!< in: rb tree */
    const void *key,   /*!< in: key for ordering */
    const void *value) /*!< in: value of key, this value
                       is copied to the node */
{
  ib_rbt_node_t *node;

  /* Create the node that will hold the value data. */
  node = (ib_rbt_node_t *)ut_malloc_nokey(SIZEOF_NODE(tree));

  memcpy(node->value, value, tree->sizeof_value);
  node->parent = node->left = node->right = tree->nil;

  /* Insert in the tree in the usual way. */
  rbt_tree_insert(tree, key, node);
  rbt_balance_tree(tree, node);

  ++tree->n_nodes;

  return (node);
}

/** Add a new node to the tree, useful for data that is pre-sorted.
 @return appended node */
const ib_rbt_node_t *rbt_add_node(ib_rbt_t *tree,         /*!< in: rb tree */
                                  ib_rbt_bound_t *parent, /*!< in: bounds */
                                  const void *value)      /*!< in: this value is
                                                          copied      to the node */
{
  ib_rbt_node_t *node;

  /* Create the node that will hold the value data */
  node = (ib_rbt_node_t *)ut_malloc_nokey(SIZEOF_NODE(tree));

  memcpy(node->value, value, tree->sizeof_value);
  node->parent = node->left = node->right = tree->nil;

  /* If tree is empty */
  if (parent->last == nullptr) {
    parent->last = tree->root;
  }

  /* Append the node, the hope here is that the caller knows
  what s/he is doing. */
  rbt_tree_add_child(tree, parent, node);
  rbt_balance_tree(tree, node);

  ++tree->n_nodes;

#if (defined IB_RBT_TESTING)
  ut_a(rbt_validate(tree));
#endif
  return (node);
}

/** Find a matching node in the rb tree.
 @return NULL if not found else the node where key was found */
static const ib_rbt_node_t *rbt_lookup(
    const ib_rbt_t *tree, /*!< in: rb tree */
    const void *key)      /*!< in: key to use for search */
{
  const ib_rbt_node_t *current = ROOT(tree);

  /* Regular binary search. */
  while (current != tree->nil) {
    int result;

    if (tree->cmp_arg) {
      result = tree->compare_with_arg(tree->cmp_arg, key, current->value);
    } else {
      result = tree->compare(key, current->value);
    }

    if (result < 0) {
      current = current->left;
    } else if (result > 0) {
      current = current->right;
    } else {
      break;
    }
  }

  return (current != tree->nil ? current : nullptr);
}

/** Delete a node indentified by key.
 @return true if success false if not found */
ibool rbt_delete(ib_rbt_t *tree,  /*!< in: rb tree */
                 const void *key) /*!< in: key to delete */
{
  ibool deleted = FALSE;
  ib_rbt_node_t *node = (ib_rbt_node_t *)rbt_lookup(tree, key);

  if (node) {
    rbt_remove_node_and_rebalance(tree, node);

    ut_free(node);
    deleted = TRUE;
  }

  return (deleted);
}

/** Remove a node from the rb tree, the node is not free'd, that is the
 callers responsibility.
 @return deleted node but without the const */
ib_rbt_node_t *rbt_remove_node(
    ib_rbt_t *tree,                  /*!< in: rb tree */
    const ib_rbt_node_t *const_node) /*!< in: node to delete, this
                                     is a fudge and declared const
                                     because the caller can access
                                     only const nodes */
{
  /* Cast away the const. */
  rbt_remove_node_and_rebalance(tree, (ib_rbt_node_t *)const_node);

  /* This is to make it easier to do something like this:
          ut_free(rbt_remove_node(node));
  */

  return ((ib_rbt_node_t *)const_node);
}

/**********************************************************************/ /**
 Find the node that has the lowest key that is >= key.
 @return node satisfying the lower bound constraint or NULL */
const ib_rbt_node_t *rbt_lower_bound(
    /*============*/
    const ib_rbt_t *tree, /*!< in: rb tree */
    const void *key)      /*!< in: key to search */
{
  ib_rbt_node_t *lb_node = NULL;
  ib_rbt_node_t *current = ROOT(tree);

  while (current != tree->nil) {
    int result;

    if (tree->cmp_arg) {
      result = tree->compare_with_arg(tree->cmp_arg, key, current->value);
    } else {
      result = tree->compare(key, current->value);
    }

    if (result > 0) {
      current = current->right;

    } else if (result < 0) {
      lb_node = current;
      current = current->left;

    } else {
      lb_node = current;
      break;
    }
  }

  return (lb_node);
}

/**********************************************************************/ /**
 Find the node that has the greatest key that is <= key.
 @return node satisfying the upper bound constraint or NULL */
const ib_rbt_node_t *rbt_upper_bound(
    /*============*/
    const ib_rbt_t *tree, /*!< in: rb tree */
    const void *key)      /*!< in: key to search */
{
  ib_rbt_node_t *ub_node = NULL;
  ib_rbt_node_t *current = ROOT(tree);

  while (current != tree->nil) {
    int result;

    if (tree->cmp_arg) {
      result = tree->compare_with_arg(tree->cmp_arg, key, current->value);
    } else {
      result = tree->compare(key, current->value);
    }

    if (result > 0) {
      ub_node = current;
      current = current->right;

    } else if (result < 0) {
      current = current->left;

    } else {
      ub_node = current;
      break;
    }
  }

  return (ub_node);
}

/** Find the node that has the greatest key that is <= key.
 @return value of result */
int rbt_search(const ib_rbt_t *tree,   /*!< in: rb tree */
               ib_rbt_bound_t *parent, /*!< in: search bounds */
               const void *key)        /*!< in: key to search */
{
  ib_rbt_node_t *current = ROOT(tree);

  /* Every thing is greater than the NULL root. */
  parent->result = 1;
  parent->last = nullptr;

  while (current != tree->nil) {
    parent->last = current;

    if (tree->cmp_arg) {
      parent->result =
          tree->compare_with_arg(tree->cmp_arg, key, current->value);
    } else {
      parent->result = tree->compare(key, current->value);
    }

    if (parent->result > 0) {
      current = current->right;
    } else if (parent->result < 0) {
      current = current->left;
    } else {
      break;
    }
  }

  return (parent->result);
}

/** Find the node that has the greatest key that is <= key. But use the
 supplied comparison function.
 @return value of result */
int rbt_search_cmp(const ib_rbt_t *tree,   /*!< in: rb tree */
                   ib_rbt_bound_t *parent, /*!< in: search bounds */
                   const void *key,        /*!< in: key to search */
                   ib_rbt_compare compare, /*!< in: fn to compare items */
                   ib_rbt_arg_compare arg_compare) /*!< in: fn to compare items
                                                   with argument */
{
  ib_rbt_node_t *current = ROOT(tree);

  /* Every thing is greater than the NULL root. */
  parent->result = 1;
  parent->last = nullptr;

  while (current != tree->nil) {
    parent->last = current;

    if (arg_compare) {
      ut_ad(tree->cmp_arg);
      parent->result = arg_compare(tree->cmp_arg, key, current->value);
    } else {
      parent->result = compare(key, current->value);
    }

    if (parent->result > 0) {
      current = current->right;
    } else if (parent->result < 0) {
      current = current->left;
    } else {
      break;
    }
  }

  return (parent->result);
}

/** Return the left most node in the tree. */
const ib_rbt_node_t *rbt_first(
    /* out leftmost node or NULL */
    const ib_rbt_t *tree) /* in: rb tree */
{
  ib_rbt_node_t *first = nullptr;
  ib_rbt_node_t *current = ROOT(tree);

  while (current != tree->nil) {
    first = current;
    current = current->left;
  }

  return (first);
}

/** Return the right most node in the tree.
 @return the rightmost node or NULL */
const ib_rbt_node_t *rbt_last(const ib_rbt_t *tree) /*!< in: rb tree */
{
  ib_rbt_node_t *last = nullptr;
  ib_rbt_node_t *current = ROOT(tree);

  while (current != tree->nil) {
    last = current;
    current = current->right;
  }

  return (last);
}

/** Return the next node.
 @return node next from current */
const ib_rbt_node_t *rbt_next(
    const ib_rbt_t *tree,         /*!< in: rb tree */
    const ib_rbt_node_t *current) /*!< in: current node */
{
  return (current ? rbt_find_successor(tree, current) : nullptr);
}

/** Return the previous node.
 @return node prev from current */
const ib_rbt_node_t *rbt_prev(
    const ib_rbt_t *tree,         /*!< in: rb tree */
    const ib_rbt_node_t *current) /*!< in: current node */
{
  return (current ? rbt_find_predecessor(tree, current) : nullptr);
}

/** Merge the node from dst into src. Return the number of nodes merged.
 @return no. of recs merged */
ulint rbt_merge_uniq(ib_rbt_t *dst,       /*!< in: dst rb tree */
                     const ib_rbt_t *src) /*!< in: src rb tree */
{
  ib_rbt_bound_t parent;
  ulint n_merged = 0;
  const ib_rbt_node_t *src_node = rbt_first(src);

  if (rbt_empty(src) || dst == src) {
    return (0);
  }

  for (/* No op */; src_node; src_node = rbt_next(src, src_node)) {
    if (rbt_search(dst, &parent, src_node->value) != 0) {
      rbt_add_node(dst, &parent, src_node->value);
      ++n_merged;
    }
  }

  return (n_merged);
}

#if defined UNIV_DEBUG || defined IB_RBT_TESTING
/** Check that every path from the root to the leaves has the same count and
 the tree nodes are in order.
 @return true if OK false otherwise */
ibool rbt_validate(const ib_rbt_t *tree) /*!< in: RB tree to validate */
{
  if (rbt_count_black_nodes(tree, ROOT(tree)) > 0) {
    return (rbt_check_ordering(tree));
  }

  return (FALSE);
}
#endif /* UNIV_DEBUG || IB_RBT_TESTING */