path from the root to the nearest leaf. The result is that the tree is height-balanced. Since operations such as inserting, deleting, and finding values require worst-case time proportional to the height of the tree, this upper bound on the height allows red–black trees to be efficient in the worst case, namely logarithmic in the number of entries, i.e. , which is not the case for ordinary binary search trees. For a mathematical proof see section Proof of bounds. Red–black trees, like all binary search trees, allow quite efficient sequential access (e.g. in-order traversal, that is: in the order Left–Root–Right) of their elements. But they support also asymptotically optimal direct access via a traversal from root to leaf, resulting in search time. Analogy to B-trees of order 4 A red–black tree is similar in structure to a B-tree of order 4, where each node can contain between 1 and 3 values and (accordingly) between 2 and 4 child pointers. In such a B-tree, each node will contain only one value matching the value in a black node of the red–black tree, with an optional value before and/or after it in the same node, both matching an equivalent red node of the red–black tree. One way to see this equivalence is to "move up" the red nodes in a graphical representation of the red–black tree, so that they align horizontally with their parent black node, by creating together a horizontal cluster. In the B-tree, or in the modified graphical representation of the red–black tree, all leaf nodes are at the same depth. The red–black tree is then structurally equivalent to a B-tree of order 4, with a minimum fill factor of 33% of values per cluster with a maximum capacity of 3 values. This B-tree type is still more general than a red–black tree though, as it allows ambiguity in a red–black tree conversion—multiple red–black trees can be produced from an equivalent B-tree of order 4 (see figure 3). If a B-tree cluster contains only 1 value, it is the minimum, black, and has two child pointers. If a cluster contains 3 values, then the central value will be black and each value stored on its sides will be red. If the cluster contains two values, however, either one can become the black node in the red–black tree (and the other one will be red). So the order-4 B-tree does not