Question

(a, b) trees

Add the elements 6 , 4 , 2 , 5 , 3 , 1 in this order into an initial empty (2,3) tree. Then remove the elements 6 , 2 , 5 (in this order). Specify intermediate steps.

Answer 1

A (2-3) tree is a special case of B tree with maximum degree 3

Each node can have 1 element and two pointers to child left and right (here left<root<right)

Or 2 element and 3 pointers left, middle and right(for every element order being left<root<right)

Below is the step by step illustration of insertion and removal of elements in 2-3 tree

(The red border block shows an intermediate step)

INSERT 6

INSERT 4

INSERT 2

                     

INSERT 5

                                     

INSERT 3

                                    

INSERT 1

REMOVE 6

REMOVE 2

REMOVE 5