Answer the following question.

How would the complexity change if all the three loops went to instead of , and ?

Computer Science20171 markShort answer

How would the complexity change if all the three loops went to $N$ instead of $a$, $b$ and $c$?

Show the code

for (int x = 1; x <= a; x++)
{
    statements;
}
for (int y = 1; y <= b; y++)
{
    for (int z = 1; z <= c; z++)
    {
        statements;
    }
}

Answer

$O(N^2)$ With all loops running to N the complexity becomes $O(N + N \times N) = O(N + N^2)$, and the dominant term $N^2$ gives $O(N^2)$.

Complexity and Big O notation