this and examine onethe treein tables and external storage howeverthe red-black tree is in most cases the most efficient balanced treeat least when data is stored in memory as opposed to external files our approach to the discussion we'll explain insertion into red-black trees little differently than we have explained insertion into other data structures red-black trees are not trivial to understand because of this and also because of multiplicity of symmetrical cases (for left or right childrenand inside or outside grandchildrenthe actual code is more lengthy and complex than one might expect it' therefore hard to learn about the algorithm by examining code conceptual for this reasonwe're going to concentrate on conceptual understanding rather than coding details in this we will be aided by the rbtree workshop applet we'll describe how you can work in partnership with the applet to insert new nodes into tree including human in the insertion routine certainly slows it downbut it also makes it easier for the human to understand how the process works searching works the same way in red-black tree as it does in an ordinary binary tree on the other handinsertion and deletionwhile based on the algorithms in an ordinary treeare extensively modified accordinglyin this we'll be concentrating on the insertion process top-down insertion in this the approach to insertion that we'll discuss is called top-down insertion this means that some structural changes may be made to the tree as the search routine descends the tree looking for the place to insert the node another approach is bottom-up insertion this involves finding the place to insert the node and then working back up through the tree making structural changes bottom-up insertion is less efficient because two passes must be made through the tree balanced and unbalanced trees before we begin our investigation of red-black treeslet' review how trees become unbalanced fire up the tree workshop applet from "binary trees,(not this rbtree appletuse the fill button to create tree with only one node then insert series of nodes whose keys are in either ascending or descending order the result will be something like that in figure figure items inserted in ascending order