BTree- predetermined size?

I read this on wikipedia:

In B-trees, internal (non-leaf) nodes can have a variable number of child nodes within some pre-defined range. When data is inserted or removed from a node, its number of child nodes changes. In order to maintain the pre-defined range, internal nodes may be joined or split. Because a range of child nodes is permitted, B-trees do not need re-balancing as frequently as other self-balancing search trees, but may waste some space, since nodes are not entirely full.

We have to specify this range for B trees. Even when I looked up CLRS (Intro to Algorithms), it seemed to make to use of arrays for keys and children. My question is- is there any way to reduce this wastage in space by defining the keys and开发者_JAVA百科 children as lists instead of predetermined arrays? Is this too much of a hassle?

Also, for the life of me I'm not able to get a decent psedocode on btreeDeleteNode. Any help here is appreciated too.

When you say "lists", do you mean linked lists?

An array of some kind of element takes up one element's worth of memory per slot, whether that slot is filled or not. A linked list only takes up memory for elements it actually contains, but for each one, it takes up one element's worth of memory, plus the size of one pointer (two if it's a doubly-linked list, unless you can use the xor trick to overlap them).

If you are storing pointers, and using a singly-linked list, then each list link is twice the size of each array slot. That means that unless the list is less than half full, a linked list will use more memory, not less.

If you're using a language whose runtime has per-object overhead (like Java, and like C unless you are handling memory allocation yourself), then you will also have to pay for that overhead on each list link, but only once on an array, and the ratio is even worse.

I would suggest that your balancing algorithm should keep tree nodes at least half full. If you split a node when it is full, you will create two half-full nodes. You then need to merge adjacent nodes when they are less than half full. You can then use an array, safe in the knowledge that it is more efficient than a linked list.

No idea about the details of deletion, sorry!

B-Tree node has an important characteristic, all keys in the node is sorted. When finding a specific key, binary search is used to find the right position. Using binary search keeps the complexity of search algorithm in B-Tree O(logn).

If you replace the preallocated array with some kind of linked list, you lost the ordering. Unless you use some complex data structures, like skip list, to keep the search algorithm with O(logn). But it's totally unnecessary, skip list itself is better.