Which "for" loop has a better time complexity?

Question

    int i;
    for(i=0;i<n;i++)
    {
     if(i==number);
       break;
    }

OR

    for(i=0; ;i++)
    {
    if(i==number)
    break;
    }

Does removing the comparison part in the for loop effects the time complexity or not ?

it will terminate when i==number as there is a break statement. And its actually for an array which will have the "number" in it. — Alok Singh, Feb 01 '17 at 21:49
The first one will run at most `n` times. The second will run at most the maximum possible value of `number`. — Eugene Sh., Feb 01 '17 at 21:51
number is same in both the loops and are identical in everything except the comparison statement in for loop . Then they will have the same time complexity ? — Alok Singh, Feb 01 '17 at 21:54
`n` might be very small, while `number` is large. So it will be bounded by `n` and `number` wouldn't make any difference. But yeah, strictly speaking it should be `O(min(n, max(number))` — Eugene Sh., Feb 01 '17 at 21:59
But if we can assume `number` can be in the same range as `n`, the complexity will be just the same. — Eugene Sh., Feb 01 '17 at 22:02
The first one looks to be O(1), assuming C. Perhaps the semi-colon at the end of the if statement is a typo? — Paul Hankin, Feb 01 '17 at 22:49

Daniel · Answer 1 · 2017-02-02T02:01:57.800

1

You can't say which is faster precisely...

The time complexity for the first one is O(min(n, number)) and the second is O(number).

if n is bigger (or equal) than number, the first will be equal to the second.

first: O(number) (as number is smaller than n, min(n, number) = number
second:O(number)

if n is smaller than number, the first will be faster (as it also stops in n).

first: O(n) (as n is smaller than number, min(n, number) = n
second:O(number)

in an overall view, the first will be faster.

As you can see, removing the comparison inside the for look do make difference, what is quite obvious given the second case where their complexities become different.

edited Feb 02 '17 at 02:01

answered Feb 02 '17 at 01:56

Daniel

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Thanks Daniel, will the time also be same for both the loops ? Or some difference? – Alok Singh Feb 02 '17 at 07:29
as I explained, the time will be different if number is bigger than n, otherwise the time complexity is the same – Daniel Feb 02 '17 at 17:30

Which "for" loop has a better time complexity?

1 Answers1