GATE CSE 2004 | Complexity Analysis and Asymptotic Notations Question 42 | Algorithms

GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

Let A[1,...,n] be an array storing a bit (1 or 0) at each location, and f(m) is a function whose time complexity is O(m). Consider the following program fragment written in a C like language:

counter = 0;
for(i = 1; i <= n; i++){
 if(A[i]==1){
   counter++;
 }else{
   f(counter); counter = 0;
 }
}

The complexity of this program fragment is

$$\Omega ({n^2})$$

$$\Omega (n\,\log n)\,and\,O({n^2})$$

$$\theta (n)$$

$$O(n)$$

GATE CSE 2004

MCQ (Single Correct Answer)

-0.6

What does the following algorithm approximate?
(Assume m > 1, $$ \in > 0$$)

x = m;
y = 1;
while(x - y > ε){
 x = (x + y) / 2;
 y = m/x;
}
print(x);

log m

m²

m^1/2

m^1/3

GATE CSE 2003

MCQ (Single Correct Answer)

-0.6

The cube root of a natural number n is defined as the largest natural number m such that $${m^3} \le n$$. The complexity of computing the cube root of n (n is represented in binary notation) is

O(n) but not O(n^0.5)

O(n^0.5) but not O((log n)^k) for any constant k > 0

O((log n)^k) for some constant k > 0, but not O((log log n)^m) for any constant m > 0

O((log log n)^k) for some constant k > 0.5, but not O((log log n)^0.5)

GATE CSE 2002

MCQ (Single Correct Answer)

-0.6

The running time of the following algorithm Procedure A(n)
If n<=2 return (1) else return (A([$$\sqrt n $$])); is best described by

O(n)

O(log n)

O(log log n)

O(1)