Insertion: Let we create 2-3 tree by inserting elements: 20, 30, 40, 50, 60, 10, 15, 70, 80 Insert 20,30: Now we insert these two element in a single node as it can hold 2 elements so, Insert 40: Node is already full so split the node In splitting: We take two nodes left and right and a root node Left node contain smallest element Right node contain greatest element Root node contain middle element and take lest and ...
Rotation is required only in the nodes which are imbalance, imbalance means that | height of right sub-tree - height of left sub-tree | > 1. Balancing reduce the height of tree like a tree with node n have maximum height (n-1) but after rotation it will be about log(n).
Some properties: Multiway/M-way search tree Degree : 3 (maximum no. of children) All leaf at same level Every node must have at least ceil(n/2 here 3/2) children Also call B-Tree of degree 3 Can't have duplicate element Representation: l contain all the element smaller than k1 m contain all the element b/w k1 and k2 n contain all the element greater than n k1 < k2 for every node Applications: Used as example during study B-Tree and B+ Tree Used internally in DBMS
Comments
Post a Comment