btree_class¶ ↑

Stanislaw Kolarzowski 2009

Implemention of B-tree

• create B-tree

• insert values

• delete values

• searching values

• upper iteration

• set order(n)

In computer science, a B-tree is a tree data structure that keeps data sorted and allows searches, insertions, and deletions in logarithmic amortized time. Unlike self-balancing binary search trees, it is optimized for systems that read and write large blocks of data. It is most commonly used in databases and filesystems. more: en.wikipedia.org/wiki/B-tree

B-tree of order n - n childern maximum, n/2 children minimum

Insert algorithm¶ ↑

1. Find leaf where insert value

2. If leaf is not full(contain less then maximum elements), insert value

3. If it is full:

• choose middle value

• make it parent, and make 2 subtrees(values less then middle value - left tree. greater then middle value - right tree)

• insert middle value to its parent node

Delete algorithm¶ ↑

1. Find element and delete it

2. If it was in leaf node and number of elements is now not less then minimum do nothing

3. If it was in leaf node and number of elements is now less then minimum do

a) If left or right brother(node) has number of elements grater then minimum

• insert parent’s value to actual node

• move smallest/biggest(for right/left) value from brother to parent

b) If left and right brother(node) has not number of elements grater then minimum

• move other values from node and parent’s value to brother node

• becouse we move value from parent node it could have less then minimum keys, so we must merge parent node with its brother

1. If it was not in leaf node

• Change value to next value in tree

• Delete next value from tree

Searching algorithm¶ ↑

Like in binary tree

• If searching value is less then key choose left subtree

• If searching value is greater then key check next key or choose right tree(if it is last element)

• Check tree recursive

Upper iteration algorithm¶ ↑

• In first leaf node select first value

• Choose next value or next subtree(if it exist) or if it is last value in node choose parent

Example:¶ ↑

Create new B-tree (3 order)

tree = BTree.new(:n => 3)

Add values to tree

tree.add_values( ([1, 2, 3, 4, 5, 6, 7])

Add 10 to tree

tree.insert_value(10)

Delete 10 from tree

tree.delete_value(10)

Finding

tree.find_value(1)          # Return true and node id where '1' is
tree.find_value(100)        # Return false and node id where '100' should be added

First value

tree.first_value            # Return 1

Next value after 4

tree.next(4)                # Return 5

Nodes

tree.nodes[4]               # Return node with id = 4
tree.nodes[4].keys          # Return keys(array) from node with id = 4
tree.nodes[4].sub_trees     # Return sub trees(array) from node with id = 4