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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:
Q. If n is the size of input(positive), which function is most efficient(if the task to be performed is not an issue)?
  • 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)
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
In a competition, four different functions are observed. All the funct...
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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In a competition, four different functions are observed. All the funct...
Explanation:

The time complexity of a for loop depends upon the number of iterations it performs. In the given options, all the for loops perform the same set of statements, but differ in the number of iterations.

a) for(i = 0; i < n;="" />

This for loop will execute n times. The time complexity of this for loop is O(n).

b) for(i = 0; i < n;="" i="" />

This for loop will execute n/2 times. The time complexity of this for loop is O(n/2).

c) for(i = 1; i < n;="" i="" *="" />

This for loop will execute log2n times. The time complexity of this for loop is O(log n).

d) for(i = n; i > 1; i /= 2)

This for loop will execute log2n times. The time complexity of this for loop is O(log n).

Therefore, option 'c' is the most efficient option as it has the lowest time complexity.
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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:Q. Ifnis the size of input(positive), which function is most efficient(if the task to be performed is not an issue)?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)Correct answer is option 'C'. Can you explain this answer?
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