Recurrence Relation for the following code?

Question

What is the recurrence relation of the above algorithm? a step-by-step walkthrough would be appreciated.

That's incomplete information to give a recurrence relation. What are x.c? — Mayur Kulkarni, Dec 18 '15 at 07:12
x.n = number of keys in node ; x.key = value of key ; x.leaf = boolean(true if leaf) ; x.c = child node ; — panther1, Dec 18 '15 at 07:20

score 0 · Accepted Answer · answered Dec 18 '15 at 07:42

Your algorithm comprise for following steps :

Initially it makes a linear search for the key, since it searches for all the elements it will add a complexity of -----> theta(n)
If it finds the key, it returns
Else, it recurses by passing it's child ------> T(child)

So, overall complexity : T(n) = T(n+1) + theta(n) ,

where T(n+1) will be the complexity for child node

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