In $[]$: $,$ def find$\_$best$\_$k$($X$\_$train, y$\_$train, X$\_$test, y$\_$test, k$\_$max$)$:

Finds the best value of $K$ for KNN based on the given training and testing$/$validation data.

Parameters:

X$\_$train: Training data features.

y$\_$train: Training data labels.

X$\_$test: Testing$/$validation data features.

y$\_$test: Testing$/$validation data labels.

k$\_$max: The maximum value of $K$ to consider.

Returns:

best$\_$k: The optimal value of $K$ that results in the lowest error rate.

best$\_$error$\_$rate: The lowest error rate corresponding to the best K$.$

$"""$

return best$\_$k$,$ best$\_$error$\_$rate

# Usage example:

# best$\_$k$,$ best$\_$error$\_$rate $=$ find$\_$best$\_$k$($X$\_$train, y$\_$train, X$\_$test, y$\_$test, $10)$

# print $(f$ "Best best$\_$k$\}$ with error rate: best$\_$error$\_$rate$\}")$