In my opinion it seems fairly obvious that a $k$ nearest neighbours (KNN) Classifier would be fairly expensive in terms of memory, as the model is the training set itself. However, any notes I've read have only mentioned that the KNN-Classifier is computationally expensive, and have not mentioned any memory requirements as a disadvantage. I assume this to be true, but I wouldn't want to mention it in any exams or anything without proper confirmation. Are the memory requirements implicit and not worth mentioning, or am I overlooking something?
KNN is a memory intensive algorithm and it is already classified as instance-based or memory-based algorithm. The reason behind this is KNN is a lazy classifier which memorizes all the training set O(n) without learning time (running time is constant O(1)).
Inversely, When it comes to querying new points to find the nearest K, the query time will be expensive O(n) in terms of the running time.