find the worst-case

Question

for(i=0;i<N;i++){
  sequence of statements 
 }
for(j=0;j<M;j++){
  sequence of statements
 }

how would the complexity change if the second loop went to N instead of M?

Answer 1

tl;dr : O(N) .

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Instead of O(N + M) it would then be O(2 * N) which is the same complexity class as O(N) .

Of course under the assumption that "sequence of statements" run in constant time.

Answer 2

If the first loop runs N times and Second M times it would be o(N+M) , and if the second loop runs N then it would be o(N+N) or o(2N) which means o(N). (Independent loops run in constant time)