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:

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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 > -1; i /= 2)

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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 first for loop is O(n).
The time complexity of second for loop is O(n/2), equivalent to O(n) in asymptotic analysis.
The time complexity of third for loop is O(logn).
The fourth for loop doesn’t terminate.

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