B+ Tree Leaf Nodes - Pages Organization - database

In a clustered index B+ tree, would doing a range scan require a disk I/O between every leaf node in that range? Furthermore, in the case that a leaf node consists of more than a single page (e.g. if a leaf node is 1MB in size and page size is 4KB), are all pages that comprise a leaf node organized sequentially on disk?

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How to handle b+ trees when the leaf nodes store content with variable size?

Some databases (like MySQL) use B+trees as a way to physically organize records. The primary index (also called clustering index) stores the keys as internal nodes and the records in the leaf level.
Since all pages have fixed size, I suppose that internal nodes and leaf nodes have different degrees: The degree of internal nodes is derived from the primary key size, and the degree of the leaf nodes is derived from the record size.
What if the record size is variable? How the degree of the leaf level is set?
Additionally, I always study b+trees under the assumption that keys have the same size. It enables a straightforward method for splitting and dividing the nodes. What about the leaf level? How to balance the nodes when the records to move have variable sizes?

Data entry handling for B+ tree

I have learned that there are three alternative ways for the data entry handling
storing full data record itself with key k
<key,rid>
<key,list>
But my question is why can't we apply method 3 to B+ tree?
I thought it was because the multiple mapping from the leaf node could occur but later on, since the B+ tree is compared with the key k (either left or right) having multiple rids mapped with a key shouldn't be a problem. But I am not sure why all of the examples for B+ tree show only method 2 which is one key and one rid mapping

Most efficient way of searching within a B-Tree node

What is the most efficient way to search for a key within a B-Tree node? For example, if I have a node with 100 sorted keys and I'm looking for key 23, what would be the fastest way of searching for that key within that node? What do most B-Tree implementations do?

why leaf nodes connected each other in clustered index?

As we know,when an clustered index is created,it is index key data is stored in a B-tree structure.The Bottom level of B-tree are the leaf nodes which contains the actual data rows for a table, and all leaf nodes point to the
next and previous leaf nodes.I want to know the purpose of using double linked list to connect leaf nodes.
I will be appreciate to any answer to my question
I want to know the purpose of using double linked list to connect leaf
nodes.
It is an efficient way to fetch the data ordered forward or backward when doing range queries.
Ex:
select ID
from YourTable
where ID between 10 and 20
order by ID desc
With an index on ID the above query can do an index seek on 20 and scan the index backwards to ID = 10 returning all rows found.

How does a database locate a record using clustered index?

In a non-clustered index, each entry is of fixed length and so the database may use binary search to locate the record address in O(nlogn) time.
Since the tables have variable length records, and clustered index uses the underlying table itself for search (or am I wrong?) , how does the database find a record for a specific key in O(nlogn) time?
each entry is of fixed length
Not true for real-world databases.
Rows are split into groups called pages. Pages have a fixed size (~8KB). They form a tree structure with the top levels linking to the physical location of the bottom level pages.
That allows the tree to be traversed top-to-bottom, entering the relevant branch at each step.
Clustered indexes typically have exactly the same physical structure as non-clustered indexes.

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