B tree

B+ tree data structures are the data structures most commonly found in databases and filesystems implementation. B+ enables amortized constant inserts and deletes.
B+ idea is that an inner node can have a variable number of sons within some pre-defined range. This leads to the relativly rear re-balancing of the tree, on contrary with AVL? trees. The lower and upper watermarks are set ahead as for example, in B2-3 trees, where each node can have 2 or 3 sons.

Illegal state defined to be the state in which an inner node has illegal number of sons.

Inner node structures:
Each inner node has a separation values which divide between its sub-trees. For example, if some inner node has 3 sons (sub-trees) then it must have 2 separation values a1 and a2. All values less than a1 will be in the leftmost sub-tree, values between a1 and a2 will be found in the middle sub-tree, values greater than a2 will be in rightmost sub-tree.

Deletes:
If no inner node is in illegale state as a result of delete then finish.