(10 points) To demonstrate your understanding of k-nearest neighbors, construct a labeled dataset where the dimensionality is 1 and the leave-one-out cross-validation accuracy for 1-nearest neighbor is always 0. As a reminder, leave-one-out uses all of the training data except one instance for learning the model and uses the held-out instance for testing, repeating the process for each possible holdout point and averaging the results. Therefore, this describes a situation where the classifier always gets the prediction wrong.

I know the concept on one dimensional dataset and what leave-on-out cross-validation is, but I'm not sure about how to come up with a dataset.