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: 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)If n is the size of input(positive), which function is the most efficient? In other words, which loop completes the fastest.
Question
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: 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)If n is the size of input(positive), which function is the most efficient? In other words, which loop completes the fastest.
Solution
The most efficient function in this case would be C) for(i = 1; i < n; i *= 2).
Here's why:
A) for(i = 0; i < n; i++) - This loop runs n times, so its time complexity is O(n).
B) for(i = 0; i < n; i += 2) - This loop runs n/2 times, so its time complexity is O(n).
C) for(i = 1; i < n; i *= 2) - This loop runs log(n) times, so its time complexity is O(log n).
D) for(i = n; i > -1; i /= 2) - This loop runs log(n) times, so its time complexity is O(log n).
Among these, O(log n) is the best time complexity because it increases the slowest as n increases. Therefore, loops C and D are the most efficient. However, loop D has a potential issue: if n is not an exact power of 2, the condition i > -1 will never be false because i, being an integer, will never exactly reach -1. Therefore, loop C is the most efficient and reliable.
Similar Questions
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