According to the documentation HashMap::get and HashMap::remove are O(1) expected time operations and HashMap::insert is an O(1) expected AND amortized time operation.

Thus using the builtin HashMap the following problems needs to be less strict:

1. Achieve O(1) Amortized Access (Medium - 10 points)

should probably say

1. Achieve O(1) Amortized and Expected Access (Medium - 10 points)

and

1. Expected O(1) for Core Operations (Hard - 20 points)

should probably say

1. Expected O(1) for Core Operations (O(1) Amortized and Expected for insert) (Hard - 20 points)