Nested for loop complexity when number of elements differ

Question

Say I had a set containing n entries, and a set containing m entries, and the following nested for loop structure:

for 1 to n

  for 1 to n

    for 1 to m

What would the time complexity be? I want to say O(mn^2) but can this be simplified anymore so we just have a single variable?

Thanks.

Answer 1

Given your case,the answer seems obvious that the complexity would be O(mn^2)...

But,as you mentioned that n and m represent number of vertices and edges respectively,then also, there doesn't exist any direct relationship between no. of edges no. of edges and no. of vertices no. of vertices for a general graph.

So,then also,the complexity would be O(mn^2)...

Answer 2

如果n是图形中的顶点数，并且m是该图形中的边数，则m为O（ n ^ 2），因此您的算法将为O（ n ^ 4）。