In the following questions you will consider a k$-$nearest neighbor classifier using Euclidean distance metric on a binary classification task. We assign the class of the test point to be the class of the majority of the $k$ nearest neighbors.

$($a$)$ In the figure, sketch the $1-$nearest neighbor decision boundary for this dataset.

$($b$)$ What value of $k$ minimizes leave$-$one$-$out cross$-$validation error for this dataset? What is the resulting error? $($Just consider odd values of $k.)$