## xEnOnn For big-O complexity equations, how is something like $$\frac{N(N-1)}{2}$$ simplifies to just $$O(N^2)$$? I know the constants can be ignored because they are not significant, but when expanded, For complexity equations, how is something like$\frac{N(N-1)}{2} = \frac{N^2-N)}{2}$ Only the $$2$$ is a constant, the other $$N$$ is not but why does it end up to only $$O(N^2)$$? one year ago one year ago
Look, we have : $\frac{ N^{2} - N }{ 2 } = \frac{ 1 }{ 2 } N^{2} - \frac{ 1 }{ 2 } N$ So when we talk about the complexity, we usually ignore N because it's very very small than $N^{2}$ Now we have Complexity equal : $\frac{ 1 }{ 2 } N^{2}$ So with the O notation, the complexity will be : $O(N^{2})$ Good luck.