Find the time complexity of given loops

Question

for (int i = 1; i <=m; i += c)

{  ---do something ---}

for (int i = 1; i <=n; i += c)

{ ---do something ---  }

What will the the tiem complexity of given code pseudococde?

A. O (max(m,n))

B. O(min(m,n))

C. O( m+n)

D. O(mn)

Comments

first loop takes o(m) time .

and second one is o(n) time.

both are independent and are not nested loops,so whichever takes max time that is the overall execution time.

=O(max(m,n))

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Both A and C are right.

Answer 1

we generally give complexity according to the inputs given to that algorithm, here the inputs are both m,n ...so both m,n defines the complexity and they must be included in the complexity expression, as there is no relationship between m and n are mentioned in the ques ... so ans is C

http://www.geeksforgeeks.org/analysis-of-algorithms-set-4-analysis-of-loops/

Comments

option A is also correct.

---

@Vijaycs. Here the most appropriate is answer (C) which be tightest bound as compared to option (A).

Answer 2

option A is right

O(max(m,n))

Comments

O(m+n) = O(max(m,n)) isnt?