Algorithms | Analysis of Algorithms | Question 9

In a competition, four different functions are observed. All the functions use a single for loop and within the for loop, same set of statements are executed. Consider the following for loops: 

C

A) for(i = 0; i < n; i++)

B) for(i = 0; i < n; i += 2)

C) for(i = 1; i < n; i *= 2)

D) for(i = n; i <= n; i /= 2)

If n is the size of input(positive), which function is most efficient(if the task to be performed is not an issue)?

(A)

A

(B)

B

(C)

C

(D)

D

Answer: (C)

Explanation:

The time complexity of the first for loop is O(n).

The time complexity of the second for loop is O(n/2), equivalent to O(n) in asymptotic analysis.

The time complexity of the third for loop is O(log(n)).

The fourth for loop doesn’t terminate.

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