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In a B+ tree, both the internal nodes and the leaves have keys.

Question

In a B+ tree, both the internal nodes and the leaves have keys.

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Solution

Yes, in a B+ tree, both the internal nodes and the leaves have keys. The keys act as a separation value which divides its subtrees. For example, if an internal node has a value of 'n', then all the values in the left subtree of 'n' are less than 'n' and all the values in the right subtree are greater than 'n'.

The leaves in a B+ tree are linked together to provide ordered access to the records which makes it suitable for range queries. The keys in the leaf nodes are a copy of the keys in the internal nodes and these keys point to the actual records in the database.

Here are the steps to understand how keys work in a B+ tree:

  1. Each internal node of a B+ tree contains a number of keys and pointers. The keys act as separation values which divide its subtrees.

  2. The pointers correspond to the disk block addresses which contain the child nodes.

  3. The keys in the internal nodes are a copy of the maximum or minimum key in their child nodes.

  4. The leaf nodes contain a set of keys and pointers. The keys are a copy of the keys in the database and the pointers point to the actual records in the database.

  5. The leaf nodes of a B+ tree are linked together to provide ordered access to the records.

  6. When a search is performed, the B+ tree is traversed from the root to the leaf node to find the desired key. The key in the internal nodes guides the search.

  7. When a new key is inserted, if the leaf node is full, it is split into two and the middle key is moved up to the parent node. If the parent node is full, it is also split and the process continues until a parent is found that can accommodate the new key or the root is split.

  8. When a key is deleted, if the leaf node becomes less than half full, keys and pointers are borrowed from a neighbor node or nodes are merged to keep the tree balanced.

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