Question

How many lines does his algorithm print? Write a recurrence and solve it.

function printaton(n: an integer power of 2) {

if n > 1 {

printaton(n/2)

printaton(n/2)

printaton(n/2)

for i = 1 to n ^ 4 do

printline("are we done yet?")

}

}

a. Use Master's theorem to obtain an asymptotic solution.

b. Derive an exact solution by expanding the recurrence.

Step 1

The given program splits into three subprograms with half of the input size each and then prints n^4 lines.

Hence, The recurrence is T(n) = 3T(n/2) + n^4 , T(1) = 1

- Using master theorem...

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