// delete removes a range from the range tree.
// Since this tree is not stored in memory but persisted through the ranges, in
// place deletion is not possible. Instead, we use the helper function
// swapNodes above.
func (tc *treeContext) delete(node *proto.RangeTreeNode) error {
	key := node.Key
	if node.LeftKey != nil && node.RightKey != nil {
		left, err := tc.getNode(node.LeftKey)
		if err != nil {
			return err
		}
		predecessor, err := tc.getMaxNode(left)
		if err != nil {
			return err
		}
		node, _, err = tc.swapNodes(node, predecessor)
		if err != nil {
			return err
		}
	}

	// Node will always have at most one child.
	var child *proto.RangeTreeNode
	var err error
	if node.LeftKey != nil {
		if child, err = tc.getNode(node.LeftKey); err != nil {
			return err
		}
	} else if node.RightKey != nil {
		if child, err = tc.getNode(node.RightKey); err != nil {
			return err
		}
	}
	if !isRed(node) {
		// Paint the node to the color of the child node.
		node.Black = !isRed(child)
		tc.setNode(node)
		if err := tc.deleteCase1(node); err != nil {
			return err
		}
	}
	if _, err := tc.replaceNode(node, child); err != nil {
		return err
	}

	// Always set the root back to black
	if node, err = tc.getNode(node.Key); err != nil {
		return err
	}
	if child != nil && node.ParentKey == nil {
		if child, err = tc.getNode(child.Key); err != nil {
			return err
		}
		child.Black = true
		tc.setNode(child)
	}

	tc.dropNode(key)
	return nil
}

// replaceNode cuts a node away form its parent, substituting a new node or
// nil. The updated new node is returned. Note that this does not in fact alter
// the old node in any way, but only the old node's parent and the new node.
func (tc *treeContext) replaceNode(oldNode, newNode *proto.RangeTreeNode) (*proto.RangeTreeNode, error) {
	if oldNode.ParentKey == nil {
		if newNode == nil {
			return nil, util.Error("cannot replace the root node with nil")
		}
		// Update the root key if this was the root.
		tc.setRootKey(newNode.Key)
	} else {
		oldParent, err := tc.getNode(oldNode.ParentKey)
		if err != nil {
			return nil, err
		}
		if oldParent.LeftKey != nil && oldNode.Key.Equal(oldParent.LeftKey) {
			if newNode == nil {
				oldParent.LeftKey = nil
			} else {
				oldParent.LeftKey = newNode.Key
			}
		} else {
			if newNode == nil {
				oldParent.RightKey = nil
			} else {
				oldParent.RightKey = newNode.Key
			}
		}
		tc.setNode(oldParent)
	}
	if newNode != nil {
		newNode.ParentKey = oldNode.ParentKey
		tc.setNode(newNode)
	}
	return newNode, nil
}

// rotateRight performs a right rotation around the node.
func (tc *treeContext) rotateRight(node *proto.RangeTreeNode) (*proto.RangeTreeNode, error) {
	left, err := tc.getNode(node.LeftKey)
	if err != nil {
		return nil, err
	}
	if left.Black {
		return nil, util.Error("rotating a black node")
	}
	node.LeftKey = left.RightKey
	left.RightKey = &node.Key
	left.Black = node.Black
	node.Black = false
	tc.setNode(node)
	tc.setNode(left)
	return left, nil
}

// rotateLeft performs a left rotation around the node.
func (tc *treeContext) rotateLeft(node *proto.RangeTreeNode) (*proto.RangeTreeNode, error) {
	right, err := tc.getNode(node.RightKey)
	if err != nil {
		return nil, err
	}
	if right.Black {
		return nil, util.Error("rotating a black node")
	}
	node.RightKey = right.LeftKey
	right.LeftKey = &node.Key
	right.Black = node.Black
	node.Black = false
	tc.setNode(node)
	tc.setNode(right)
	return right, nil
}

// insertCase1 handles the case when the inserted node is the root node.
func (tc *treeContext) insertCase1(node *proto.RangeTreeNode) error {
	if node.ParentKey == nil {
		node.Black = true
		tc.setNode(node)
		return nil
	}
	return tc.insertCase2(node)
}

// insert performs the insertion of a new range into the RangeTree. It will
// recursively call insert until it finds the correct location. It will not
// overwrite an already existing key, but that case should not occur.
func (tc *treeContext) insert(node *proto.RangeTreeNode, key proto.Key) (*proto.RangeTreeNode, error) {
	if node == nil {
		// Insert the new node here.
		node = &proto.RangeTreeNode{
			Key: key,
		}
		tc.setNode(node)
	} else if key.Less(node.Key) {
		// Walk down the tree to the left.
		left, err := tc.getNode(node.LeftKey)
		if err != nil {
			return nil, err
		}
		left, err = tc.insert(left, key)
		if err != nil {
			return nil, err
		}
		if node.LeftKey == nil || !(*node.LeftKey).Equal(left.Key) {
			node.LeftKey = &left.Key
			tc.setNode(node)
		}
	} else {
		// Walk down the tree to the right.
		right, err := tc.getNode(node.RightKey)
		if err != nil {
			return nil, err
		}
		right, err = tc.insert(right, key)
		if err != nil {
			return nil, err
		}
		if node.RightKey == nil || !(*node.RightKey).Equal(right.Key) {
			node.RightKey = &right.Key
			tc.setNode(node)
		}
	}
	return tc.walkUpRot23(node)
}

// rotateRight performs a right rotation around the node.
func (tc *treeContext) rotateRight(node *proto.RangeTreeNode) (*proto.RangeTreeNode, error) {
	left, err := tc.getNode(node.LeftKey)
	if err != nil {
		return nil, err
	}
	left, err = tc.replaceNode(node, left)
	if err != nil {
		return nil, err
	}
	node.LeftKey = left.RightKey
	if left.RightKey != nil {
		leftRight, err := tc.getNode(left.RightKey)
		if err != nil {
			return nil, err
		}
		leftRight.ParentKey = node.Key
		tc.setNode(leftRight)
	}
	left.RightKey = node.Key
	node.ParentKey = left.Key
	tc.setNode(left)
	tc.setNode(node)
	return left, nil
}

// rotateLeft performs a left rotation around the node.
func (tc *treeContext) rotateLeft(node *proto.RangeTreeNode) (*proto.RangeTreeNode, error) {
	right, err := tc.getNode(node.RightKey)
	if err != nil {
		return nil, err
	}
	right, err = tc.replaceNode(node, right)
	if err != nil {
		return nil, err
	}
	node.RightKey = right.LeftKey
	if right.LeftKey != nil {
		rightLeft, err := tc.getNode(right.LeftKey)
		if err != nil {
			return nil, err
		}
		rightLeft.ParentKey = node.Key
		tc.setNode(rightLeft)
	}
	right.LeftKey = node.Key
	node.ParentKey = right.Key
	tc.setNode(right)
	tc.setNode(node)
	return right, nil
}

// flip swaps the color of the node and both of its children. Both those
// children must exist.
func (tc *treeContext) flip(node *proto.RangeTreeNode) (*proto.RangeTreeNode, error) {
	left, err := tc.getNode(node.LeftKey)
	if err != nil {
		return nil, err
	}
	right, err := tc.getNode(node.RightKey)
	if err != nil {
		return nil, err
	}
	node.Black = !node.Black
	left.Black = !left.Black
	right.Black = !right.Black
	tc.setNode(node)
	tc.setNode(left)
	tc.setNode(right)
	return node, nil
}

// insert performs the insertion of a new node into the tree. It walks the tree
// until it finds the correct location. It will fail if the node already exists
// as that case should not occur. After inserting the node, it checks all insert
// cases to ensure the tree is balanced and adjusts it if needed.
func (tc *treeContext) insert(node *proto.RangeTreeNode) error {
	if tc.tree.RootKey == nil {
		tc.setRootKey(node.Key)
	} else {
		// Walk the tree to find the right place to insert the new node.
		currentKey := tc.tree.RootKey
		for {
			currentNode, err := tc.getNode(currentKey)
			if err != nil {
				return err
			}
			if node.Key.Equal(currentNode.Key) {
				return util.Errorf("key %s already exists in the range tree", node.Key)
			}
			if node.Key.Less(currentNode.Key) {
				if currentNode.LeftKey == nil {
					currentNode.LeftKey = node.Key
					tc.setNode(currentNode)
					break
				} else {
					currentKey = currentNode.LeftKey
				}
			} else {
				if currentNode.RightKey == nil {
					currentNode.RightKey = node.Key
					tc.setNode(currentNode)
					break
				} else {
					currentKey = currentNode.RightKey
				}
			}
		}
		node.ParentKey = currentKey
		tc.setNode(node)
	}
	return tc.insertCase1(node)
}