In a B-tree, when splitting a node due to an insertion that exceeds its capacity, where does the middle key go?

In a B-tree, when a node is split due to an insertion that exceeds its capacity, the middle key of the node is crucial. Here's how it works:

1. Node Splitting: When a B-tree node becomes full (having reached its maximum allowed keys), it needs to be split into two nodes. The process involves taking the keys and dividing them into two parts.

2. Middle Key Promotion: The key that resides in the middle position of the current set of keys in that full node is promoted to the parent node. This key becomes the new key that separates the two created nodes.

3. Creation of New Node: The keys to the left of the middle key will remain in the original node, while the keys to the right of the middle key will form a new node.

4. Parent Node Update: If the parent node is also full when the middle key is promoted, the same process will recursively apply, potentially causing further splits up the tree.

This operation is essential for maintaining the properties of the B-tree, ensuring that it remains balanced and can accommodate more keys while keeping operations efficient. This mechanism also ensures that the search, insertion, and deletion operations in a B-tree remain efficient.