Editing B-tree (section)

===Insertion and deletion===
To maintain the predefined range of child nodes, internal nodes may be joined or split.

Usually, the number of keys is chosen to vary between {{mvar|d}} and <math>2d</math>, where {{mvar|d}} is the minimum number of keys, and <math>d+1</math> is the minimum [[Outdegree#Indegree and outdegree|degree]] or [[branching factor]] of the tree. The factor of 2 will guarantee that nodes can be split or combined.

If an internal node has <math>2d</math> keys, then adding a key to that node can be accomplished by splitting the hypothetical <math>2d+1</math> key node into two {{mvar|d}} key nodes and moving the key that would have been in the middle to the parent node. Each split node has the required minimum number of keys. Similarly, if an internal node and its neighbor each have {{mvar|d}} keys, then a key may be deleted from the internal node by combining it with its neighbor. Deleting the key would make the internal node have <math>d-1</math> keys; joining the neighbor would add {{mvar|d}} keys plus one more key brought down from the neighbor's parent. The result is an entirely full node of <math>2d</math> keys.

A B-tree is kept balanced after insertion by splitting a would-be overfilled node, of <math>2d+1</math> keys, into two {{mvar|d}}-key siblings and inserting the mid-value key into the parent. Depth only increases when the root is split, maintaining balance. Similarly, a B-tree is kept balanced after deletion by merging or redistributing keys among siblings to maintain the {{mvar|d}}-key minimum for non-root nodes. A merger reduces the number of keys in the parent potentially forcing it to merge or redistribute keys with its siblings, and so on. The only change in depth occurs when the root has two children, of {{mvar|d}} and (transitionally) <math>d-1</math> keys, in which case the two siblings and parent are merged, reducing the depth by one.

This depth will increase slowly as elements are added to the tree, but an increase in the overall depth is infrequent, and results in all leaf nodes being one more node farther away from the root.