<P> Red--black trees, like all binary search trees, allow efficient in - order traversal (that is: in the order Left--Root--Right) of their elements . The search - time results from the traversal from root to leaf, and therefore a balanced tree of n nodes, having the least possible tree height, results in O (log n) search time . </P> <P> In addition to the requirements imposed on a binary search tree the following must be satisfied by a red--black tree: </P> <Ol> <Li> Each node is either red or black . </Li> <Li> The root is black . This rule is sometimes omitted . Since the root can always be changed from red to black, but not necessarily vice versa, this rule has little effect on analysis . </Li> <Li> All leaves (NIL) are black . </Li> <Li> If a node is red, then both its children are black . </Li> <Li> Every path from a given node to any of its descendant NIL nodes contains the same number of black nodes . Some definitions: the number of black nodes from the root to a node is the node's black depth; the uniform number of black nodes in all paths from root to the leaves is called the black - height of the red--black tree . </Li> </Ol> <Li> Each node is either red or black . </Li>

Properties of red black tree in data structure
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