Question

Consider the following recursive algorithm. Algorithm Mystery(n) if n=1 then Execute Task A; // Requires Θ(1)...

Consider the following recursive algorithm.

Algorithm Mystery(n)

if n=1 then

Execute Task A; // Requires Θ(1) operations

else

Mystery(n/3);

Mystery(n/3);

Mystery(n/3);

Execute Task B;  //Requires 2n operations

end if


Let C(n) be the complexity of Mystery(n). Use the method of backward substitution

to determine C(n) in three steps.


a) Write the recurrence relation for C(n) including the initial condition.

b) Write at least two substitution steps for C(n) and identify the pattern.

c) Determine the complexity class of the algorithm in terms of Θ(·).

Hand written working out helps me plenty if possible but all good if not !

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