Which of the following are true for k$-$nearest neighbor classification?

A$.$

In very high dimensions, exhaustively checking every training point is often faster than any widely used competing exact k$-$NN query algorithm

B$.$

In the k$-$Nearest Neighbors algorithm, a data point is classified or predicted based on the majority class or average value of its k nearest neighbors in the feature space.

C$.$

It is more likely to over fit with k$=1(1-$NN$)$ than with k$=1,000(1,000-$NN$)$

D$.$

If you have enough training points drawn from the same distribution as the test points, k$-$NN can achieve accuracy almost as good as the Bayes decision rule

E$.$

The optimal running time to classify a point with k$-$NN grows linearly with k