<s>
A	O
left-leaning	O
red	O
–	O
black	O
(	O
LLRB	B-Data_Structure
)	O
tree	O
is	O
a	O
type	O
of	O
self-balancing	B-Data_Structure
binary	I-Data_Structure
search	I-Data_Structure
tree	I-Data_Structure
.	O
</s>
<s>
All	O
of	O
the	O
red-black	O
tree	O
algorithms	O
that	O
have	O
been	O
proposed	O
are	O
characterized	O
by	O
a	O
worst-case	O
search	O
time	O
bounded	O
by	O
a	O
small	O
constant	O
multiple	O
of	O
in	O
a	O
tree	O
of	O
keys	O
,	O
and	O
the	O
behavior	O
observed	O
in	O
practice	O
is	O
typically	O
that	O
same	O
multiple	O
faster	O
than	O
the	O
worst-case	O
bound	O
,	O
close	O
to	O
the	O
optimal	O
nodes	O
examined	O
that	O
would	O
be	O
observed	O
in	O
a	O
perfectly	O
balanced	B-Data_Structure
tree	I-Data_Structure
.	O
</s>
<s>
Specifically	O
,	O
in	O
a	O
left-leaning	O
red-black	O
2	B-Data_Structure
–	I-Data_Structure
3	I-Data_Structure
tree	I-Data_Structure
built	O
from	O
random	O
keys	O
:	O
</s>
