Question

Analyze the operation performed by the given piece of pseudocode and write a function that describes the number of steps required. Give the $\Theta$-class of the function

Assume that N is a power of 2.

1. $X \leftarrow 1$

2. $K \leftarrow N$

3. $WHILE (K \geq 1)$

a. $X \leftarrow 3X$

b. $K \leftarrow \left \lfloor K/2 \right \rfloor$

Answer 1

We are given that N is power of 2 and in while loop each time we are dividing K=K/2, in this way for any value of N while loop will be executed by Sqrt(N) +1 number of times. For example,

N = 16

1. After first iteration K = 16/2 = 8

2. After second iteration K = 8/2 = 4

3. After third iteration K = 4/2 =2

4. After fourth iteration k = 2/2 =1, now this will be the last iteration beacuse now K is 1.

So loop will be executed 5 times = 4 ( because 16 is 4th power of 2 ) +1

Running time = $\Theta (\sqrt{N})$