Editing 2–3 tree (section)

===Insertion===
Insertion maintains the balanced property of the tree.<ref name="A4">{{cite book|section=3.3 |title=Algorithms|edition=4|first1=Robert |last1=Sedgewick |first2=Kevin |last2=Wayne |date=2011 |publisher=Addison Wesley |isbn=978-0-321-57351-3}}</ref>

To insert into a 2-node, the new key is added to the 2-node in the appropriate order.

To insert into a 3-node, more work may be required depending on the location of the 3-node. If the tree consists only of a 3-node, the node is split into three 2-nodes with the appropriate keys and children.

[[File:2-3 insertion.svg|framed|none|Insertion of a number in a 2–3 tree for 3 possible cases]]

If the target node is a 3-node whose parent is a 2-node, the key is inserted into the 3-node to create a temporary 4-node. In the illustration, the key 10 is inserted into the 2-node with 6 and 9. The middle key is 9, and is promoted to the parent 2-node. This leaves a 3-node of 6 and 10, which is split to be two 2-nodes held as children of the parent 3-node.

If the target node is a 3-node and the parent is a 3-node, a temporary 4-node is created then split as above. This process continues up the tree to the root. If the root must be split, then the process of a single 3-node is followed: a temporary 4-node root is split into three 2-nodes, one of which is considered to be the root. This operation grows the height of the tree by one.