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4 votes
4 votes

I think it would be 7..please check

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6 votes
@habibkhan.@prabhanjan_1

What I found was like this way..

insert 3,10,12,14.....and split on 10.So 10 goes up and 3 on Left child(min 1 key on a node) and 10,12,14 right child(max key on a node).So I am keeping Right child always full so that i get max no of spilts all the time.(Becoz inputs are in ascending order).

So from 14 onwards for all key input it is a split on leaf node.

Hence total no of split=7.(correct me if i m wrong)
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Hence number of splits required = 3 (at insertion of 14 , 45 and 68) in this case when we are following left biasing and splitting about right median(Here 2 medians since split is performed when we have no of elements = 4 and hence even.

Now let us consider the case when we take split across left median.

So we see here that considering this way no of times leaf node is splitted = 4

Hence maximum no of times the leaf node is splitted = 4 times

And if asked about no of splits simply then you have to consider both of the splits that is shown in the final step in the above figure

So no of splits in total in the 2nd case = 5

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