Complexity Analysis MCQs

#1

I am not able to understand Q1, Q6, Q9 and Q13 of the pdf. please help me to understand the concept

#2

Hello @krikhi,

Ques 1:
You would understand this after studying graphs.

Ques 6:
the answer is O(n)

Ques 9:
the answer is O(log n)
int power(int 2, unsigned int n)
{
int temp;
if( n == 0)
return 1;
temp = power(2, n/2);
if (n%2 == 0)
return temp*temp;
else
return 2*temp*temp;
}

Ques 13:
You can use master’s theorem:
T(n) = aT(n/b) + f(n) where a >= 1 and b > 1
There are following three cases:

  • If f(n) = Θ(n^c) where c < Logb(a) then T(n) = Θ(nLogba)

  • If f(n) = Θ(n^c) where c = Logb(a) then T(n) = Θ((n^c)*(Log n))

  • If f(n) = Θ(n^c) where c > Logb(a) then T(n) = Θ(f(n))

using case 2:
The answer is Θ(nlogn)

Hope, this would help.
Give a like if you are satisfied.

#3

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#4

I am not able to understand the master theorem. please help me to get the concept.

#5

Hello @krikhi,

The master theorem is a technique to solve the recurrent equation.
Hence, a way to find the time complexity of the recursive approach.

You can refer to this video for better understanding.

Hope, this would help.